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\title{Studying Development of Psychopathology Across the Lifespan}


\shorttitle{Psychopathology Development Across Lifespan}


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\authorsnames{Isaac T. Petersen,Zachary Demko,Megan Schumer}





\affiliation{
{Department of Psychological and Brain Sciences, University of Iowa}}




\leftheader{Petersen, Demko and Schumer}

\date{2026-08-26}


\abstract{The field has not adequately studied individuals' development
of psychopathology across the lifespan, instead taking a piecewise
approach to development, limiting our understanding of lifespan
development and the origins of psychopathology. We describe why this is
the case---beyond logistical challenges. First, diagnostic and taxonomic
systems do not define psychopathology constructs from a developmental
perspective. A developmental perspective is crucial because
psychopathology constructs often have earlier origins than their full
clinical presentation, and forms of psychopathology frequently show
changes in behavioral manifestation across development (heterotypic
continuity). Second, current assessments do not adequately capture these
changes in behavioral manifestation. Third, traditional scoring systems
do not allow charting individuals' change over time in the face of
changing behavioral manifestation. Fourth, assessments are not
well-suited for capturing individual differences, despite the
dimensional nature of psychopathology. We propose solutions to these
challenges by introducing a developmental scaling framework for
psychopathology. Using externalizing psychopathology as an example, we
draw on our content analysis of externalizing measures, as well as
lessons from the study of other constructs across lengthy developmental
periods. Addressing these challenges will allow charting individuals'
trajectories of psychopathology across the lifespan and identifying risk
and protective factors that influence developmental courses. }

\keywords{psychopathology, lifespan development, longitudinal
trajectories, heterotypic continuity, externalizing behavior problems}

\authornote{\par{\addORCIDlink{Isaac T.
Petersen}{0000-0003-3072-6673}}\par{\addORCIDlink{Zachary
Demko}{0000-0002-5717-6205}}\par{\addORCIDlink{Megan
Schumer}{0009-0009-5488-6541}} 
\par{ }
\par{ The data and code for the present study are published online:
\url{https://github.com/DevPsyLab/studying-psychopathology-development-lifespan}
(\url{https://osf.io/t3zf9}).  We have no conflicts of interest to
disclose. I.P. was funded by Grant HD098235 from the Eunice Kennedy
Shriver National Institute of Child Health and Human Development. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the authors and do not necessarily reflect the
views of the National Institutes of Health. We thank Jordan L. Harris
and Alexis Hosch for their help identifying measures of externalizing
problems and transcribing and coding their content.  Author roles were
classified using the Contributor Role Taxonomy (CRediT;
https://credit.niso.org) as follows:  Isaac T.
Petersen:   conceptualization, data
curation, analysis, funding, investigation, methodology, project
administration, resources, software, supervision, validation, visualization, writing, editing; Zachary
Demko:   conceptualization, data
curation, analysis, investigation, methodology, software, editing; Megan
Schumer:   editing}
\par{Correspondence concerning this article should be addressed to Isaac
T. Petersen, University of Iowa, G60 Psychological and Brain Sciences
Building, Iowa City, IA 52242. Email:
\href{mailto:isaac-t-petersen@uiowa.edu}{\nolinkurl{isaac-t-petersen@uiowa.edu}}}
}

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\begin{document}

\maketitle




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\textbf{\emph{NOTE: this manuscript is in progress of being drafted---it
is incomplete.}}

When entrenched, psychopathology is costly and difficult to treat
(\citeproc{ref-Insel2008}{Insel, 2008};
\citeproc{ref-Wakschlag2019}{Wakschlag et al., 2019}). Understanding its
developmental origins is therefore crucial for preventing later, more
severe psychopathology. Developmental science seeks to build a bridge
that spans the lifespan---from infancy to older adulthood---and not just
transitory periods in people's lives. However, the field has not
adequately studied individuals' development of psychopathology across
the lifespan; instead, the field has taken a piecewise approach to
development that focuses on narrower age ranges. The focus on narrow age
ranges restricts our ability to understand development across important
transitions, such as puberty, school entry, and entry into parenthood,
which in turn limits our understanding of lifespan development and the
origins of psychopathology. In this paper, we describe reasons why this
is the case---beyond logistical challenges of time and money. And we
propose solutions to these challenges by introducing a developmental
scaling framework for psychopathology. Using externalizing
psychopathology as an example, we draw on our content analysis of more
than 270 externalizing measures, as well as lessons from the study of
other constructs such as academic and cognitive skills across lengthy
developmental periods.

\section{The Goal}\label{the-goal}

A key goal of developmental science is to understand how people develop
across the lifespan. A variety of methods, including cross-sectional and
longitudinal designs, could be leveraged for this purpose. In a
cross-sectional design, people are assessed at one timepoint. In a
longitudinal design, the same individuals are followed across time.

Cross-sectional designs provide the ability to relatively cheaply and
quickly assess a wide age range, providing a snapshot at a particular
point in time. Cross-sectional designs may inform our understanding of
general normative patterns of change---such as the typical pattern of
cognitive growth and decline across the lifespan. Thus, cross-sectional
designs provide an important starting point.

However, cross-sectional designs have key limitations. First,
cross-sectional designs do not allow examining individuals' change over
time. Thus, the trajectory of individual differences remains elusive,
and observed age-related differences may reflect processes apart from
developmental change, such as cohort effects. Second, cross-sectional
designs may obscure diverse patterns of change. Individuals show
considerable heterogeneity in level and change across time in many
constructs. As an example, despite the normative pattern of steep
cognitive decline in episodic memory with aging, there are a subset of
individuals who do not show this same pattern. For instance, superagers
are individuals who are older adults (age 80+) who have episodic memory
at or above the normative level of middle-aged adults (50--65 years old)
and who may be resilient to the typical aging process
(\citeproc{ref-Godoy2021}{Godoy et al., 2021}). Theoretical depictions
of the heterogeneity of cognitive decline are depicted in
Figure~\ref{fig-lifespancognitivetrajectories}.

\begin{figure}[H]

{\caption{{Different Cognitive Trajectories of
Aging}{\label{fig-lifespancognitivetrajectories}}}}

\pandocbounded{\includegraphics[keepaspectratio,alt={Different Cognitive Trajectories of Aging}]{index_files/figure-latex/notebooks-analyses-fig-lifespancognitivetrajectories-output-1.png}}

\noindent \emph{Note.} \textbf{Panel~A}: Hypothetical models for
different cognitive trajectories of aging. MCI = mild cognitive
impairment. (Figure in Panel A reprinted from Borelli et al.
(\citeproc{ref-Borelli2018}{2018}), Figure 1, p.~222. Borelli, W. V.,
Carmona, K. C., Studart-Neto, A., Nitrini, R., Caramelli, P., \& Costa,
J. C. d.~(2018). Operationalized definition of older adults with high
cognitive performance. \emph{Dementia \& Neuropsychologia},
\emph{12}(3), 221--227.
\url{https://doi.org/10.1590/1980-57642018dn12-030001}). \textbf{Panel
B}: Theoretical illustration of inter-individual variability in
cognitive aging trajectories. Each gray line represents one individual
hypothetical cognitive health trajectory. The orange line marks the
threshold for functional independence; once an individual's cognitive
health drops below this level, autonomous daily living is compromised.
(Figure in Panel B reprinted from Abrous et al.
(\citeproc{ref-Abrous2026}{2026}), Figure 1, p.~2. Abrous, D. N., Blin,
N., Boraxbekk, C.-J., Catheline, G., Fitzsimons, C. P., Hilscher, M.,
Lemoine, M., Lopes, L. V., Maass, A., Nilsson, M., Nyberg, L.,
Rasmussen, L. J., Remondes, M., Sauvage, M., Schreiber, S., \& Wolbers,
T. (2026). Hallmarks of healthy cognitive aging: Inter-individual
differences in aging trajectories. \emph{Ageing Research Reviews},
\emph{119}, 103102. \url{https://doi.org/10.1016/j.arr.2026.103102}).

\end{figure}

\textsubscript{Source:
\href{https://DevPsyLab.github.io/studying-psychopathology-development-lifespan/notebooks/analyses-preview.html\#cell-fig-lifespancognitivetrajectories}{Analyses}}

Heterogeneity also applies to psychopathology trajectories including
externalizing and criminal behavior. The age-crime curve depicts the
well-known strong association between age and engagement in crime, with
crime rates peaking markedly (in many Western countries) in adolescence
around ages 15--19. An example of the age-crime curve is depicted in
Figure~\ref{fig-externalizing-by-age}.

However, Moffitt's (\citeproc{ref-Moffitt1993}{1993}) developmental
taxonomy of externalizing (``antisocial'') behavior posits that there
are heterogeneous subgroups such that one subgroup exhibits low levels
of externalizing behavior across the lifespan, an ``adolescence
limited'' subgroup exhibits high levels of externalizing behavior during
adolescence but low levels during childhood and adulthood, and a
``life-course persistent'' subgroup that exhibits high levels of
externalizing behavior across the lifespan; in addition, more recent
work has identified a ``childhood limited'' subgroup that exhibits high
levels of externalizing behavior during childhood but low levels after
childhood (\citeproc{ref-Fairchild2013}{Fairchild et al., 2013};
\citeproc{ref-Odgers2008}{Odgers et al., 2008}). The developmental
taxonomy is depicted in Figure~\ref{fig-externalizing-by-age}.

Moffitt's general hypothesis is that life-course persistent
externalizing behavior results from early disruptions in brain
development either in utero (resulting from, for example, maternal
substance use, poor prenatal nutrition, genetics, or exposure to
toxins), during delivery (e.g., delivery complications), or after birth
(e.g., child abuse or neglect, or exposure to toxins) that lead to
impaired cognitive abilities and difficult temperament, in perhaps
conjunction with coercive parent--child interactions or other adverse,
criminogenic environments. Adolescence-limited externalizing behavior,
by contrast, is thought to reflect a more normative---even
adaptive---pattern of social behavior that is driven by exposure to
deviant peers and a maturity gap. Childhood-limited externalizing
behavior, though not hypothesized by the original taxonomy, may in some
cases reflect recovery and in other cases reflect a shift from
externalizing problems into problems in other domains
(\citeproc{ref-Odgers2008}{Odgers et al., 2008}). It has been
hypothesized that both childhood-limited and life-course persistent
externalizing behavior may be characterized by high levels of
individual-level risk (e.g., genetic and neuropsychological risk),
whereas especially life-course persistent externalizing behavior may be
characterized by greater environmental risk (e.g., adversity and trauma;
\citeproc{ref-Fairchild2013}{Fairchild et al., 2013}). A cross-sectional
study that does not capture the subgroups' different developmental
histories would not be well-positioned to adjudicate whether a
particular individual is part of the adolescence-limited versus
life-course persistent developmental course
(\citeproc{ref-Moffitt1993}{Moffitt, 1993}).

The age-crime curve that is based on official police records has key
problems (\citeproc{ref-Moffitt1993}{Moffitt, 1993}). First, it misses
the developmental course of externalizing behavior that leads up to the
commission of crime. Second, it is based on only those (criminalized)
behaviors that are known to official arrest records and does not capture
other behaviors the person engaged in that are known to the individual
or collateral report by caregivers, teachers, siblings, or peers.
Longitudinal work examining informant report of children's behavior
allows estimating the prototypical trajectory of externalizing problems
at ages younger than those encompassed by the age-crime curve, thus
providing important developmental context to the origins of
externalizing behavior. For instance, in a longitudinal study examining
the development of externalizing behavior from childhood to adulthood
that incorporated ratings of the child's externalizing behavior from
mothers, fathers, teachers, peers, and self-report (at relevant ages),
Petersen et al. (\citeproc{ref-Petersen2015}{2015}) found that
externalizing problems normatively tended to decrease from early
childhood to preadolescence, increased during adolescence (peaking
around age 17), and decreased from late adolescence to adulthood.

Since Moffitt (\citeproc{ref-Moffitt1993}{1993}) proposed the
developmental taxonomy of externalizing behavior, work has examined
individual differences in externalizing trajectories to determine
whether they are best represented by categories---i.e., taxa such as
adolescence-limited, life-course persistent, etc.---or dimensionally.
Findings have consistently shown that variation in externalizing
trajectories is better represented dimensionally than with categories
(\citeproc{ref-Fairchild2013}{Fairchild et al., 2013};
\citeproc{ref-Walters2011}{Walters, 2011},
\citeproc{ref-Walters2012}{2012}, \citeproc{ref-Walters2015}{2015};
\citeproc{ref-Walters2013}{Walters \& Ruscio, 2013}), suggesting that
differences between people in their developmental course of
externalizing behavior appear to reflect differences in degree rather
than kind (i.e., quantitative differences rather than qualitative
differences). For example, the trajectories in Petersen et al.
(\citeproc{ref-Petersen2015}{2015}) were characterized by marked
individual differences; some individuals stayed low, some increased,
some decreased, some increased then decreased, and seemingly everything
in between. The heterogeneous trajectories of externalizing problems are
depicted in Figure~\ref{fig-externalizing-by-age}.

In sum, if we rely solely on normative age-related patterns of cognitive
functioning or psychopathology from cross-sectional research, we would
miss the immense differences in people's developmental courses. And
these individual differences are crucial to identify the risk and
protective mechanisms that explain these differing developmental
courses.

\begin{figure}[H]

{\caption{{Externalizing Behavior Across
Development}{\label{fig-externalizing-by-age}}}}

\pandocbounded{\includegraphics[keepaspectratio,alt={Externalizing behavior across development}]{index_files/figure-latex/notebooks-analyses-fig-externalizing-by-age-output-1.png}}

\noindent \emph{Note.} \textbf{Panel~A}: The age-crime participation
curve from age 9 through 64 in cohort members registered for antisocial
and/or criminal behavior in a birth cohort recruited in Stockholm,
Sweden (\emph{N} = 4,825), based on official crime records. The steep
peak in crime rate in the adolescent years is similar to the age-crime
curve in the United States; however, the steepness of the age-crime
curve differs within country across birth cohorts
(\citeproc{ref-Steffensmeier2025}{Steffensmeier et al., 2025}). (Figure
adapted from Sivertsson et al. (\citeproc{ref-Sivertsson2024}{2024}),
Figure 1, p.~7. Sivertsson, F., Carlsson, C., Almquist, Y. B., \&
Brännström, L. (2024). Offending trajectories from childhood to
retirement age: Findings from the Stockholm birth cohort study.
\emph{Journal of Criminal Justice}, \emph{91}, 102155.
\url{https://doi.org/10.1016/j.jcrimjus.2024.102155}). \textbf{Panel B}:
A stylized depiction of Moffitt's (\citeproc{ref-Moffitt1993}{1993})
developmental taxonomy of externalizing behavior, adapted to include a
childhood limited subgroup. \textbf{Panel C}: Individuals' (\emph{N} =
585) longitudinal trajectories of externalizing problems from childhood
to adulthood based on annual assessments of mother-, father-, teacher-,
peer-, and self-report (at relevant ages). Average trajectory in red.
(Figure adapted from Petersen et al.
(\citeproc{ref-Petersen2015}{2015}), Figure 2, Petersen, I. T., Bates,
J. E., Dodge, K. A., Lansford, J. E., \& Pettit, G. S. (2015).
Describing and predicting developmental profiles of externalizing
problems from childhood to adulthood. \emph{Development and
Psychopathology}, \emph{27}(3), 791--818.
\url{https://doi.org/10.1017/S0954579414000789}).

\end{figure}

\textsubscript{Source:
\href{https://DevPsyLab.github.io/studying-psychopathology-development-lifespan/notebooks/analyses-preview.html\#cell-fig-externalizing-by-age}{Analyses}}

Third, in a cross-sectional study, any apparent age-related differences
in a construct could reflect cohort differences instead of developmental
changes. For example, average differences in stress between 5-year-olds
and 10-year-olds could reflect the differing experiences that the
10-year-olds shared, such as going to school during the Coronavirus
pandemic. Fourth, findings from cross-sectional studies can differ from
findings that are based on examining the same people over time---a
violation of the convergence assumption. In cross-sectional studies, the
convergence assumption is the assumption that cross-sectional age
differences and longitudinal age changes converge onto a common
trajectory. An example where the convergence assumption has been shown
to be violated is in studies of cognitive decline. Cross-sectional
studies overestimate age-related cognitive declines compared to
following the same people over time in a longitudinal study, which may
reflect cohort effects such as the Flynn effect (where population
intelligence scores at a given age tend to increase across generations;
\citeproc{ref-Ackerman2013}{Ackerman, 2013}).

Because longitudinal designs follow the same person(s) over time, such a
design allows examining individuals' change across time. However, as we
describe \hyperref[sec-potential-confounds-of-change]{later},
longitudinal designs also have potential confounds of change. Moreover,
compared to cross-sectional designs, longitudinal designs take more time
and tend to be more costly and require more personnel. Thus,
longitudinal studies that span the lifespan are not common. However,
even cross-sectional work spanning the lifespan is not often conducted.

\section{The Problem/Obstacle}\label{the-problemobstacle}

The focal problem examined in this paper is that, despite calls to do so
(\citeproc{ref-DeLosReyes2026}{De Los Reyes, 2026}), the field has not
adequately studied individuals' development of psychopathology across
the lifespan, instead taking a piecewise approach to development. The
piecewise approach to development limits our understanding of lifespan
development and the origins of psychopathology.

A modest number of longitudinal studies have followed people over
lengthy developmental periods. We overview some of the seminal
longitudinal studies that cover a lengthy span of development. A
depiction of the ages spanned by various longitudinal studies is in
Figure~\ref{fig-longitudinalstudies}.

\begin{figure}[H]

{\caption{{(Approximate) Ages Spanned by Various Lengthy Longitudinal
Studies}{\label{fig-longitudinalstudies}}}}

\pandocbounded{\includegraphics[keepaspectratio,alt={(Approximate) Ages Spanned by Various Lengthy Longitudinal Studies}]{index_files/figure-latex/notebooks-analyses-fig-longitudinalstudies-output-1.png}}

\noindent \emph{Note.} The~list of longitudinal studies is as of this
writing and is not exhaustive. Studies that are no longer active are
shown in gray. Solid lines reflect fully longitudinal spans (i.e., the
same individuals were followed over time). Dotted lines reflect ages
assessed cross-sectionally---even if some participants may have been
followed longitudinally. For instance, if a study recruited
5--10-year-old children and followed each child for 20 years, the study
would have dotted lines from ages 5--10 and from ages 25--30. Studies
shown entirely with dotted lines assessed their full age range
cross-sectionally but still included longitudinal follow-up of some
participants. A star at age 0 represents that participants were enrolled
before birth and the study included prenatal assessments. Ages spanned
reflect ages when assessments were collected directly from participants;
ages spanned do not include links to registry data (e.g., birth records,
offending records). Age was truncated at 100; thus, age 100 indicates
that participants were followed into their 90s (or until death).

\end{figure}

\textsubscript{Source:
\href{https://DevPsyLab.github.io/studying-psychopathology-development-lifespan/notebooks/analyses-preview.html\#cell-fig-longitudinalstudies}{Analyses}}

\subsection{Seminal Longitudinal
Studies}\label{seminal-longitudinal-studies}

\subsubsection{Fels Longitudinal Study}\label{fels-longitudinal-study}

The Fels Longitudinal Study (\citeproc{ref-Roche1992}{Roche, 1992}) was
a cohort-sequential study lasting from 1929 to 2018 that recruited
10--20 pregnant mothers each year from the Yellow Springs, Ohio area,
and followed their newborns over time, eventually accruing 2,567 child
participants and following them into older adulthood (e.g., age 82;
\citeproc{ref-Chumlea2012}{Chumlea et al., 2012}). The study collected
data on participants' body composition, including height and weight,
which had key impacts and formed the basis of pediatric growth charts.
In addition, the study collected information on the participants'
behavior---and other constructs---in childhood (based on observation)
and adulthood (based on interview). These rich data allowed researchers
to examine the extent of personality continuity and change from
childhood to adulthood, and the extent to which mothers may influence
the personality development of the child (\citeproc{ref-Moss1964}{Moss
\& Kagan, 1964}). On the basis of predictive associations from childhood
to adulthood in the Fels Longitudinal Study, Kagan and Moss
(\citeproc{ref-Kagan1962}{1962}) noted that girls who had frequent
tantrums at 6 to 10 years of age tended to become women who were more
motivated in school, less dependent on others, and more masculine in
their interests than women who had fewer tantrums as children. They
interpreted the different behaviors at different ages as stemming from
the same psychological process: a tendency to avoid adopting ``female
sex-role standards'' (p.~200). Kagan described such findings, when
psychological processes remain the same but the form of behavior
changes, as examples of heterotypic continuity
(\citeproc{ref-Kagan1969}{Kagan, 1969}, \citeproc{ref-Kagan1971}{1971},
\citeproc{ref-Kagan1980}{1980}).

\subsubsection{Dunedin Multidisciplinary Health and Development
Study}\label{dunedin-multidisciplinary-health-and-development-study}

The Dunedin Multidisciplinary Health and Development Study is an ongoing
birth cohort study that started in 1975 and recruited 1,037 3-year-old
children in Dunedin, New Zealand (who were born in 1972--1973;
\citeproc{ref-Poulton2015}{Poulton et al., 2015}). It has followed
participants to age 52 and includes data on a wide range of health and
behavior constructs. The study has yielded important insights including
that children's self-control is more important than socioeconomic status
or IQ in predicting their health, wealth, and crime in adulthood
(\citeproc{ref-Moffitt2011}{Moffitt et al., 2011}), a general
psychopathology factor (p factor) may account for the strong covariance
among psychological disorders (\citeproc{ref-Caspi2014}{Caspi et al.,
2014}), that mental disorders have earlier developmental origins
(\citeproc{ref-Poulton2015}{Poulton et al., 2015}), a person's mental
disorder tends to shift from one disorder to other disorders over the
life course (\citeproc{ref-Caspi2020}{Caspi et al., 2020}), and
cross-sectional (i.e., retrospective) studies grossly underestimate
lifetime prevalence of psychological disorders (compared to prospective
longitudinal studies; \citeproc{ref-Schaefer2017}{Schaefer et al.,
2017}).

\subsubsection{Harvard Study of Adult
Development}\label{harvard-study-of-adult-development}

The Harvard Study of Adult Development consists of the Grant Study
(\citeproc{ref-Vaillant2012}{Vaillant, 2012}) and the Glueck Study
(\citeproc{ref-Glueck1950}{Glueck \& Glueck, 1950}). The Grant Study
started in 1938 and recruited 268 White men from the Harvard classes of
1939--1944 at ages 18--19, and has followed them into their mid-90s. The
Glueck Study started in 1940 and recruited 456 11--16-year-old boys who
were living in poor, high-crime inner-city neighborhoods in Boston,
Massachusetts, and has followed them into their 80s. One of the key
findings from the Harvard Study of Adult Development, summarized in a
Harvard Gazette article (\citeproc{ref-Mineo2017}{Mineo, 2017}), is the
importance of close relationships for healthy aging: ``Close
relationships, more than money or fame, are what keep people happy
throughout their lives, the study revealed. Those ties protect people
from life's discontents, help to delay mental and physical decline, and
are better predictors of long and happy lives than social class, IQ, or
even genes\ldots people's level of satisfaction with their relationships
at age 50 was a better predictor of physical health than their
cholesterol levels were.''

\subsubsection{Child Development
Project}\label{child-development-project}

The Child Development Project (\citeproc{ref-Dodge1990}{Dodge et al.,
1990}) is a study that recruited 4-year-old children the year before
kindergarten in 1987 and 1988 in Nashville, Tennessee, Knoxville,
Tennessee, and Bloomington, Indiana. Participants included 585 children,
and they have been followed to age 34. One of the key findings from the
Child Development Project is that a hostile attribution bias, an aspect
of social information processing that involves the tendency to interpret
ambiguous social cues as hostile, predicts later aggression and that
part of the association is mediated by peer rejection
(\citeproc{ref-Lansford2010}{Lansford et al., 2010}).

\subsection{Longitudinal Studies of
Psychopathology}\label{longitudinal-studies-of-psychopathology}

Longitudinal studies such as these have had immense impacts. These
studies have yielded many inferences that would not have been possible
without longitudinal designs. Some long-term longitudinal studies have
even followed children of those children who were initially recruited,
and are thus uniquely positioned to study questions of intergenerational
transmission (e.g., \citeproc{ref-Kim2009}{Kim et al., 2009}). However,
relatively few longitudinal studies attempt to assess people's
\emph{change} (in level) in a given psychopathology construct over a
lengthy period. Here, we focus on studies that have examined
trajectories of externalizing behavior.\footnote{We do not consider
  autoregressive/cross-lagged models because such models do not examine
  change in level of externalizing behavior.}

A depiction of the ages spanned by various longitudinal studies is in
Figure~\ref{fig-longitudinal-externalizing-studies}. In the Child
Development Project, Petersen et al. (\citeproc{ref-Petersen2015}{2015})
examined trajectories of externalizing behavior from ages 5--27 with 20
measurement occasions. In the Dunedin Multidisciplinary Health and
Development Study, Odgers et al. (\citeproc{ref-Odgers2008}{2008})
examined trajectories of antisocial conduct problems from ages 7--26
with 8 measurement occasions. In the Mannheim Study of Children at Risk,
Sacu et al. (\citeproc{ref-SacuInPress}{in press}) examined trajectories
of externalizing behavior from ages 8--33 with 8 measurement occasions.
A study using six longitudinal datasets examined trajectories of
disruptive behaviors and delinquency, with the longest trajectory
spanning ages 6--15 with 7 measurement occasions
(\citeproc{ref-Broidy2003}{Broidy et al., 2003}). In addition, a study
examined trajectories of externalizing problems from ages 4--17 with 3
measurement occasions in predicting externalizing problems at age 27
(\citeproc{ref-Korhonen2018}{Korhonen et al., 2018}). Other studies have
examined trajectories of externalizing problems from ages 5--17 with 5
measurement occasions (\citeproc{ref-Bista2025}{Bista et al., 2025}),
from ages 6--18 with 11 measurement occasions
(\citeproc{ref-Shi2020}{Shi et al., 2020}), from ages 1.5--14.5 with 6
measurement occasions (\citeproc{ref-Kjeldsen2016}{Kjeldsen et al.,
2016}), from ages 4--16 with 7 measurement occasions (Avon Longitudinal
Study of Parents and Children {[}ALSPAC{]};
\citeproc{ref-Speyer2022}{Speyer et al., 2022}), from ages 12--23 with 3
measurement occasions (\citeproc{ref-Stringer2020}{Stringer et al.,
2020}), from ages 2--15 with 11 measurement occasions (NICHD Study of
Early Child Care and Youth Development {[}SECCYD{]};
\citeproc{ref-Harris2025}{Harris et al., 2025}), and from ages 3--17
with 10 measurement occasions (\citeproc{ref-Gornik2023}{Gornik et al.,
2023}). Bongers et al. (\citeproc{ref-Bongers2004}{2004}) examined
trajectories of various externalizing problems from ages 4--18 spanning
13 different birth cohorts with up to 5 measurement occasions per
cohort, such that any individual was followed for up to 8 years
(\citeproc{ref-Bongers2004}{Bongers et al., 2004}).

Studies have also examined trajectories of delinquency from ages 7--19
with 13 measurement occasions (Pittsburgh Youth Study;
\citeproc{ref-Keijsers2012}{Keijsers et al., 2012}). Demonstrating an
analytic method (moderated nonlinear factor analysis) to link scores
across measures onto the same scale, Chen and Bauer examined
trajectories of delinquency from ages 12--26 with 3 measurement
occasions in the National Longitudinal Study of Adolescent to Adult
Health (Add Health; \citeproc{ref-ChenPM}{in press b}), and examined
trajectories of externalizing behavior from ages 5--12 with 3
measurement occasions in the National Longitudinal Survey of Youth 1979
Child and Young Adult (NLSCYA; \citeproc{ref-ChenMBR}{in press a}). In
addition, studies have examined trajectories of emotional and behavioral
dysregulation (encompassing externalizing problems and emotional
symptoms) from ages 3--17 with 6 measurement occasions (UK Millennium
Cohort Study; \citeproc{ref-Zhai2026}{Zhai et al., 2026}). Studies have
also leveraged registry data to examine trajectories of offending from
ages 8--61 (\citeproc{ref-LeBlanc2021}{Le Blanc, 2021}), from ages
10--61 (Cambridge Study in Delinquent Development;
\citeproc{ref-Farrington2023}{Farrington et al., 2023}), and from ages
9--64 (Stockholm Metropolitan Study;
\citeproc{ref-Sivertsson2024}{Sivertsson et al., 2024}).

\begin{figure}[H]

{\caption{{(Approximate) Ages Spanned by Externalizing Trajectories in
Various Lengthy Longitudinal Studies Examining Individuals' Trajectories
of Externalizing
Behavior}{\label{fig-longitudinal-externalizing-studies}}}}

\pandocbounded{\includegraphics[keepaspectratio,alt={(Approximate) Ages Spanned by Externalizing Trajectories in Various Lengthy Longitudinal Studies Examining Individuals\textquotesingle{} Trajectories of Externalizing Behavior}]{index_files/figure-latex/notebooks-analyses-fig-longitudinal-externalizing-studies-output-1.png}}

\noindent \emph{Note.} The~list of longitudinal studies is not
exhaustive. Studies that are based on registry data are shown in gray.
Studies that used developmental scaling to harmonize scores across ages
(i.e., to link scores across ages onto the same scale) are in green.
Measurement occasions are depicted with solid circles. Note that, in
some studies, measurement occasions only apply to a subset of
participants in that study---in some cases, no participant was assessed
at all measurement occasions. Solid lines reflect fully longitudinal
spans (i.e., the same individuals were followed over time). Dotted lines
reflect ages assessed cross-sectionally---even if some participants may
have been followed longitudinally. For instance, if a study recruited
5--10-year-old children and followed each child for 20 years, the study
would have dotted lines from ages 5--10 and from ages 25--30. Studies
shown entirely with dotted lines assessed their full age range
cross-sectionally but still included longitudinal follow-up of
participants. `MTSFGCLS' = Montreal Two Samples Four Generations
Cross-sectional and Longitudinal Studies.

\end{figure}

\textsubscript{Source:
\href{https://DevPsyLab.github.io/studying-psychopathology-development-lifespan/notebooks/analyses-preview.html\#cell-fig-longitudinal-externalizing-studies}{Analyses}}

However, as we will describe, these lengthy longitudinal studies of
psychopathology (e.g., \citeproc{ref-Odgers2008}{Odgers et al.,
2008})---including some of our own (e.g.,
\citeproc{ref-Petersen2015}{Petersen et al., 2015})---have important
limitations in (a) how they assessed psychopathology constructs across
development and (b) how they estimated people's scores on those
constructs over time, which prevent strong inferences regarding
individuals' change over time.

\section{Reasons for the Problem}\label{reasons-for-the-problem}

Beyond logistical challenges of time and money, there are several key
reasons why the field has failed to study people's development of
psychopathology longitudinally across the lifespan. First, diagnostic
and taxonomic systems do not define psychopathology constructs from a
developmental perspective. A developmental perspective is crucial
because psychopathology constructs often have earlier origins than their
full clinical presentation, and forms of psychopathology frequently show
changes in behavioral manifestation across development (heterotypic
continuity). Second, current assessments do not adequately capture these
changes in behavioral manifestation. Third, traditional scoring systems
do not allow charting individuals' change over time in the face of
changing behavioral manifestation. Fourth, current assessments are not
well-suited for capturing the full range of individual differences,
despite the dimensional nature of psychopathology. Fifth, because of
these limitations, current assessments are not well-suited for capturing
individuals' change over time.

Below, we describe these reasons in detail. To ground the discussion, we
provide examples relating to externalizing psychopathology; however,
these issues are not specific to externalizing behavior.

\subsection{Problems of Constructs}\label{problems-of-constructs}

The first reason the field has failed to adequately study individuals'
development of psychopathology across the lifespan represents a theory
problem---namely, problems with constructs, and the codifying of those
constructs in diagnostic and taxonomic systems. Our theories do not
fully specify how constructs manifest behaviorally across the lifespan.
For instance, theories do not specify the features (e.g., cognitive,
affective, or biological processes) or behaviors that characterize a
given construct in each developmental period. In addition, theories do
not specify how those features or behaviors change across development
with respect to how strongly they reflect the construct---as indicated
by changes in factor loadings (in factor analysis) or discrimination (in
item response theory)---or how they change in their level on the
construct---as indicated by changes in intercepts (factor analysis) or
difficulty/severity (item response theory).

These gaps are important for several reasons. First, psychopathology
does not come from nowhere; psychopathology constructs often have
earlier origins than their full clinical presentation. For instance,
children who go on to develop later externalizing problems and conduct
problems tend to show earlier temperamental differences such as poorer
self-regulation, poorer emotion regulation, low fearfulness, and a more
difficult temperament (\citeproc{ref-Bates2014}{Bates et al., 2014};
\citeproc{ref-Frick2004}{Frick \& Morris, 2004}). In many cases,
psychopathology may arise from the interaction of genetic and
environmental factors, and their effects on biology, cognition, emotion,
and behavior. Such effects may accumulate and transpire over years.
Second, forms of psychopathology frequently show changes in behavioral
manifestation across development---a phenomenon called heterotypic
continuity (\citeproc{ref-Caspi2006}{Caspi \& Shiner, 2006};
\citeproc{ref-Cicchetti2002}{Cicchetti \& Rogosch, 2002};
\citeproc{ref-Petersen2020}{Petersen et al., 2020};
\citeproc{ref-Petersen2024}{Petersen, 2024}).

Considerable theoretical work attempts to characterize constructs across
development. For instance, Patterson
(\citeproc{ref-Patterson1993}{1993}) characterized externalizing
(``antisocial'') behavior as a chimera. A chimera is a mythical creature
with the body of a goat that, with development, grows the head of a lion
and then the tail of a snake. Patterson
(\citeproc{ref-Patterson1993}{1993}) and Moffitt
(\citeproc{ref-Moffitt1993}{1993}) argued that externalizing behavior
changes in manifestation across development such that underlying
antisociality is maintained while more mature features are added across
development. In particular, Patterson
(\citeproc{ref-Patterson1993}{1993}) noted that some externalizing
behaviors wane with age, such as temper tantrums, whereas other
externalizing behaviors emerge with age, including the ability to
inflict serious damage or harm with violence, burglary, and shoplifting,
in addition to problems such as academic failure, peer rejection,
substance problems, and arrest. Moffitt
(\citeproc{ref-Moffitt1993}{1993, p. 679}) noted that externalizing
behaviors may manifest as ``biting and hitting at age 4, shoplifting and
truancy at age 10, selling drugs and stealing cars at age 16, robbery
and rape at age 22, and fraud and child abuse at age 30'', and that the
prognosis for individuals who engage in externalizing behavior
throughout the life-course includes ``drug and alcohol addiction;
unsatisfactory employment; unpaid debts; homelessness; drunk driving;
violent assault; multiple and unstable relationships; spouse battery;
abandoned, neglected, or abused children; and psychiatric illness''.

In general, externalizing behaviors are often expressed as overt acts in
early childhood, such as physical aggression and temper tantrums;
whereas externalizing behaviors are more often expressed later in
development as covert and indirect or relational forms of aggression,
rule breaking, and substance use (\citeproc{ref-Miller2009}{Miller et
al., 2009}; \citeproc{ref-Petersen2026a}{Petersen, Demko, Lee, et al.,
2026}). These age-differing behaviors show strong stability of
individual differences, indicating a consistent underlying construct
(\citeproc{ref-Moffitt1993}{Moffitt, 1993};
\citeproc{ref-Patterson1993}{Patterson, 1993}). As depicted in
Figure~\ref{fig-absoluteFrequencyByAge}, different externalizing
behaviors are most common at different developmental periods---even into
adulthood, consistent with the notion that externalizing behavior
demonstrates heterotypic continuity. Consistent with the Developmental
Issues Framework (\citeproc{ref-Sroufe2016}{Sroufe, 2016}), the changing
expression of externalizing behavior likely reflects a combination of
time-varying genetic and environmental factors, such as school entry
transition, in combination with varying developmental tasks, different
opportunities, and greater experience-dependent capacity
(\citeproc{ref-Petersen2020}{Petersen et al., 2020}). These factors
likely interact to produce individual differences in heterotypic
continuity of relevance to developmental psychopathology, for instance,
earlier emergence of alcohol consumption (\citeproc{ref-Aiken2018}{Aiken
et al., 2018}).

\begin{figure}[!htbp]

{\caption{{Frequency (Per Month) of Engaging in Various Externalizing
Behaviors by Age (\emph{N} =
1,237)}{\label{fig-absoluteFrequencyByAge}}}}

\includegraphics[width=1\linewidth,height=\textheight,keepaspectratio,alt={Frequency (per Month) of Engaging in Various Externalizing Behaviors by Age (*N* = 1,237).}]{Figures/Petersen2026_figure1.png}

\noindent \emph{Note.} Items~are from the Externalizing Spectrum
Inventory (ESI), but unlike the True/False ESI, participants rated items
on an absolute frequency scale (times per day/week/month/year). The gray
band is the 95\% confidence interval. The figure demonstrates that
different externalizing behaviors are most common at different
developmental periods, consistent with heterotypic continuity. As
examples, hurting others' feelings on purpose (left panel) was most
common in early adulthood; snapping or raising one's voice (middle
panel) was most common in middle adulthood; getting in power struggles
with others (right panel) was most common in older adulthood. (Figure
reprinted from Petersen, Demko, Doebler, et al.
(\citeproc{ref-Petersen2026b}{2026}), Figure 1, p.~301. Petersen, I. T.,
Demko, Z., Doebler, P., Sabel, L., Oleson, J. J., \& Krueger, R. F.
(2026). How often is ``often''? Improving assessment of the
externalizing spectrum using absolute frequency. \emph{Psychological
Assessment}, \emph{38}(4), 295--306.
\url{https://doi.org/10.1037/pas0001441}).

\end{figure}

In addition to externalizing problems, both internalizing
(\citeproc{ref-Petersen2018}{Petersen et al., 2018};
\citeproc{ref-Tyrell2019}{Tyrell et al., 2019};
\citeproc{ref-Weems2008}{Weems, 2008}; \citeproc{ref-Weiss2003}{Weiss \&
Garber, 2003}) and thought-disordered (\citeproc{ref-Rutter2006}{Rutter
et al., 2006}) problems are thought to change in manifestation across
development.

However, more work is needed to developmentally parameterize
constructs---to define constructs developmentally in terms of their
features. Recent empirical work suggests that it is uncommon for
symptoms to change from one symptom to another for a given person at the
subsequent measurement occasion (\citeproc{ref-Applegate2026}{Applegate
\& Lahey, 2026}). Nevertheless, the authors found that adding new
symptoms and subtracting symptoms---other ways that a construct can
change in manifestation---were both relatively common. Moreover, just
because a symptom persists does not mean that the behavioral
manifestation of that symptom stays the same for that individual. For
instance, even if a symptom (e.g., ``fighting'') persists for an
individual, their manifestation of that symptom could differ in form,
function, or mechanism (\citeproc{ref-Petersen2024}{Petersen, 2024}).
Indeed, fighting is considered to differ in meaning from childhood to
adulthood (\citeproc{ref-Patterson1993}{Patterson, 1993};
\citeproc{ref-Tyrell2019}{Tyrell et al., 2019}). Thus, as noted by
Applegate and Lahey (\citeproc{ref-Applegate2026}{2026, p. 10}),
``future causal theories will need to rest on a more detailed and
nuanced description of persistence and change at the level of specific
psychological problems.''

Moreover, where such theories do indicate changes in behavioral
manifestation across development, diagnostic and taxonomic systems do
not incorporate these developmental changes.

\subsubsection{Lack of a Developmental
Perspective}\label{lack-of-a-developmental-perspective}

Diagnostic and taxonomic systems do not define psychopathology
constructs from a developmental perspective. The diagnostic systems,
including the Diagnostic and Statistical Manual of Mental Disorders
(DSM-5-TR; \citeproc{ref-APA2022}{American Psychiatric Association,
2022}) and the International Classification of Diseases (ICD-11;
\citeproc{ref-WHO2022}{World Health Organization, 2022}), specify
various externalizing-related disorders, including
attention-deficit/hyperactivity disorder (ADHD), oppositional defiant
disorder (ODD), conduct disorder (CD), and antisocial personality
disorder (ASPD). Among externalizing-related disorders---with few
exceptions\footnote{In the DSM-5-TR (\citeproc{ref-APA2022}{American
  Psychiatric Association, 2022}), the minimum frequency for considering
  a symptom of ODD to be present is ``most days'' (for a period of six
  months) for children younger than 5 years, whereas it is ``at least
  once per week'' (for at least six months) for children 5 years or
  older. For the diagnosis of ADHD, six or more symptoms are required
  for children and younger adolescents (up to age 16), whereas five or
  more symptoms are required for older adolescents and adults (aged 17
  or over). However, the symptoms for defining ODD and ADHD do not
  differ across development.}---the diagnostic criteria do not differ
across development, even though diagnostic manuals acknowledge that
developmental factors impact symptom presentation\footnote{In the
  DSM-5-TR (\citeproc{ref-APA2022}{American Psychiatric Association,
  2022}), some disorders have a ``Development and Course'' subsection
  that describes when disorders tend to emerge and their rates across
  ages, in addition to describing the types of symptoms that may be more
  or less common at various points in development. However, the symptoms
  that define the disorders do not differ across development. For
  instance, in the section on major depressive disorder, it is noted
  that ``hypersomnia and hyperphagia are more likely in younger
  individuals, and melancholic symptoms, particularly psychomotor
  disturbances, are more common in older individuals. Depressions with
  earlier ages at onset are more familial and more likely to involve
  personality disturbances.'' (p.~189). In the section on ADHD, it is
  noted that, ``In preschool, the main manifestation is hyperactivity.
  Inattention becomes more prominent during elementary school. During
  adolescence, signs of hyperactivity (e.g., running and climbing) are
  less common and may be confined to fidgetiness or an inner feeling of
  jitteriness, restlessness, or impatience. In adulthood, along with
  inattention and restlessness, impulsivity may remain problematic even
  when hyperactivity has diminished.'' (p.~71). In the section on CD, it
  is noted that ``Symptoms of the disorder vary with age as the
  individual develops increased physical strength, cognitive abilities,
  and sexual maturity. Symptom behaviors that emerge first tend to be
  less serious (e.g., lying, shoplifting), whereas conduct problems that
  emerge last tend to be more severe (e.g., rape, theft while
  confronting a victim)\ldots{} When individuals with conduct disorder
  reach adulthood, symptoms of aggression, property destruction,
  deceitfulness, and rule violation, including violence against
  co-workers, partners, and children, may be exhibited in the workplace
  and the home'' (p.~534). Moreover, some disorders in the DSM-5-TR note
  that, to be considered a symptom, the frequency, intensity, or
  persistence of the behavior must be inconsistent with the level
  expected for their developmental level. For instance, in the diagnosis
  of ADHD, it is noted that ``the symptoms have persisted for at least 6
  months to a degree that is inconsistent with developmental level''
  (p.~68). In the diagnosis of ODD, it is noted that ``other factors
  {[}besides a minimum frequency{]} should also be considered, such as
  whether the frequency and intensity of the behaviors are outside a
  range that is normative for the individual's developmental level,
  gender, and culture.'' (p.~522). In addition, some disorders require
  that some symptoms onset before or after a particular age. For
  instance, in the diagnosis of ADHD, several symptoms must be present
  prior to age 12. In the diagnosis of CD, the symptoms ``often stays
  out at night despite parental prohibitions'' and ``is often truant
  from school'' must begin before age 13 (p.~531). In the diagnosis of
  ASPD, symptoms must be persistent since age 15 but have onset prior to
  age 15.}. In addition to diagnostic systems, emerging taxonomies and
frameworks of psychopathology---including the hierarchical taxonomy of
psychopathology (HiTOP) and research domain criteria (RDoC)---do not
incorporate a developmental perspective
(\citeproc{ref-Tackett2022}{Tackett \& Hallquist, 2022}).

\subsection{Problems of Existing Assessments and Traditional Scoring
Systems}\label{problems-of-existing-assessments-and-traditional-scoring-systems}

Other key reasons the field has failed to adequately study individuals'
development of psychopathology across the lifespan represent
methodological problems---namely, problems with existing assessments and
how those assessments are used, based on traditional scoring systems.
There is a mismatch between theory and method. In particular, there is a
mismatch between theory of constructs---including how a construct
manifests behaviorally---and the methods used to assess the construct
and to evaluate people's level and change in that construct.

\subsubsection{Do Not Adequately Capture Constructs' Change in
Behavioral Manifestation Across
Development}\label{do-not-adequately-capture-constructs-change-in-behavioral-manifestation-across-development}

Given the substantial changes in behavioral manifestation of
psychopathology across development, it is important for measures to
capture the constructs' changing behavioral manifestation, to stay
developmentally relevant and construct valid. As noted by Moffitt
(\citeproc{ref-Moffitt1993}{1993, p. 694}), ``Measures of antisocial
behavior should be sensitive to developmental heterogeneity to tap
individual differences while allowing for the emergence of new forms of
antisocial behavior (e.g., automobile theft) or for the forsaking of old
forms (e.g., tantrums).''

However, measures show insufficient differences in which items are
assessed at which ages to account for heterotypic continuity. For
example, among the most widely used measures of externalizing problems
in research and practice is the Child Behavior Checklist (CBCL).
However, the same version of the Child Behavior Checklist (CBCL) spans
ages 6--18. Considerable development occurs during that span including
key developmental transitions---from childhood to adolescence to
emerging adulthood---and the CBCL does not capture such changes.

There are two primary ways that researchers have examined people's
change in psychopathology across development
(Figure~\ref{fig-approachesToLongitudinalAssessment}). The ``common
items'' approach removes items that are age specific.\footnote{For
  simplicity and brevity, we refer to birth age as a proxy for
  developmental time.} For example, in a study of externalizing behavior
from early childhood to adolescence, a study might remove substance use
items that are not be developmentally relevant at all ages. The second
approach, the ``upward/downward extension'' approach, takes items that
are valid at a given age and uses those same items across all ages, even
outside the ages for which the assessment was designed and when the item
may not be valid or useful---i.e., all items are assessed at all ages.
For instance, the upward extension approach might take the item
``disobedient to authority figures'' and apply it to older individuals
for whom such a behavior may no longer validly reflect externalizing
behavior---and may instead reflect prosocial functions including
protesting against societally unjust actions. Both the ``common items''
(e.g., \citeproc{ref-Odgers2008}{Odgers et al., 2008};
\citeproc{ref-Sterba2007}{Sterba et al., 2007}) and ``upward/downward
extension'' (e.g., \citeproc{ref-BriggsGowan2016}{Briggs-Gowan et al.,
2016}; \citeproc{ref-Broeren2013}{Broeren et al., 2013}) approaches are
widely used, likely because they result in the same items assessed
across ages, but both have key problems.

As an example of the common items approach, Odgers et al.
(\citeproc{ref-Odgers2008}{2008, p. 676}) examined children's
development of DSM-IV symptoms of conduct disorder from ages 7 to 26
years, but they dropped age-specific symptoms (e.g., running away,
staying out late) ``because {[}these symptoms{]} did not cover the
study's age span''. As an example of the upward extension approach,
Broeren et al. (\citeproc{ref-Broeren2013}{2013, p. 84}) examined
children's development of anxiety from ages 4 to 11 years; they noted,
``Although the questionnaire was originally developed to measure anxiety
in preschoolers, the current study also employed the scale with older
children to promote uniformity in measures''. As examples of the
downward extension approach, Gornik et al.
(\citeproc{ref-Gornik2023}{2023}) used the CBCL 4--18 with
3-year-olds---i.e., ages younger than the assessment was designed. Zhai
et al. (\citeproc{ref-Zhai2026}{2026}) used items (e.g., ``steals from
home, school or elsewhere'') from the Strengths and Difficulties
Questionnaire for 4--10/11--17-year-olds with 3 year-olds---i.e., ages
younger than the assessment was designed, despite availability of a
version for 2--4-year-olds.

\begin{figure}[!htbp]

{\caption{{Approaches to Longitudinal
Assessment}{\label{fig-approachesToLongitudinalAssessment}}}}

\includegraphics[width=1\linewidth,height=\textheight,keepaspectratio,alt={Approaches to Longitudinal Assessment.}]{Figures/approachesToLongitudinalAssessment.jpg}

\noindent \emph{Note.} Item~set A refers to items that are
construct-valid at only timepoint 1 (T1); item set B is construct-valid
at both T1 and T2; item set C is construct-valid at only T2. A dash
indicates that the item set was not assessed at a given timepoint. A
white box indicates invalid assessment in terms of either a content gap
(i.e., important missing items) or intrusion (i.e., invalid items at a
given timepoint). In a study of externalizing behavior from early
childhood to adulthood, ``biting others'' may be in item set A;
``noncompliant'' in B; ``drug use'' in C. The three approaches are: (1)
common items: B at T1 and T2, (2) upward/downward extension: ABC at T1
and T2, or (3) construct-valid items: AB at T1; BC at T2. The ``common
items'' and ``upward/downward extension'' approaches are by far the most
widely used in the literature, even though they likely lead to
inaccurate scores and thus inaccurate trajectories. (Figure reprinted
from Petersen, Demko, Lee, et al. (\citeproc{ref-Petersen2026a}{2026}),
Figure 1, p.~113. Petersen, I. T., Demko, Z., Lee, W.-C., \& Oleson, J.
J. (2026). Studying development of psychopathology using changing
measures to account for heterotypic continuity. \emph{JAACAP Open},
\emph{4}(1), 111--123.
\url{https://doi.org/10.1016/j.jaacop.2025.10.008}).

\end{figure}

The common items approach yields low content validity because it does
not assess all construct facets, especially age-specific manifestations.
The upward/downward extension approach violates construct validity
because it assesses developmentally inappropriate items.

Due to these problems, both simulation
(\citeproc{ref-Petersen2021a}{Petersen et al., 2021}) and empirical work
(\citeproc{ref-Chen2015}{F. R. Chen \& Jaffee, 2015};
\citeproc{ref-Petersen2018}{Petersen et al., 2018};
\citeproc{ref-Petersen2026a}{Petersen, Demko, Lee, et al., 2026}) have
shown that the ``common items'' and ``upward/downward extension''
approaches---thus failing to account for heterotypic continuity---lead
to inaccurate developmental inferences. The extent of inaccuracy may
vary from small to substantial depending on the approach used, the
criterion examined, and the extent to which the construct changes in
manifestation (whose changes are ignored). Nevertheless, the effects of
failing to account for heterotypic continuity have been large enough to
infer that (a) a sample does not show changes in level when it actually
does (\citeproc{ref-Petersen2018}{Petersen et al., 2018}), (b) a sample
shows increases when it actually decreases
(\citeproc{ref-Petersen2021a}{Petersen et al., 2021}), (c) many
individuals are misclassified as persisting versus desisting in terms of
their externalizing trajectory (\citeproc{ref-Petersen2026a}{Petersen,
Demko, Lee, et al., 2026}), and (d) a subgroup's externalizing behavior
emerges in adulthood when it actually onsets much earlier (i.e.,
adolescence; \citeproc{ref-Chen2015}{F. R. Chen \& Jaffee, 2015}). In
sum, despite the ``common items'' and ``upward/downward extension''
approaches being the most widely used for assessing individuals'
development, they likely lead to inaccurate scores and thus inaccurate
trajectories and ages of onset for individuals and groups.

The problem cannot be solved merely by age-norming. Generating norms
from items that are invalid at a given age or from scales that have
important content gaps at a given age leads to construct-invalid scores
and resulting norms. Likewise, using DSM disorders or diagnoses also
does not solve the problem because DSM disorders are fictive categories
(\citeproc{ref-Petersen2024}{Petersen, 2024}) and, as described above,
DSM disorder criteria do not adequately account for different symptom
presentations at different ages. Moreover, diagnostic criteria naturally
change with subsequent revisions of the DSM, leading people to lose
interest with prior categorizations and to incomparability of diagnoses
across DSM versions.

In addition, forcing use of the same measure across time naturally
limits the ages a study can span, which prevents charting wider age
spans. For example, if a researcher used the CBCL and only wanted to
study trajectories where the same measure was assessed across ages, they
would not be able to examine development from ages 5--6, when there is a
change in the CBCL version (i.e., one for ages 1.5--5 and another for
ages 6--18).

In addition to the behavioral expression of a construct changing across
developmental time, the behavioral expression of a construct can also
change across historical time. Changes in the behavioral manifestation
across historical time can lead existing items and measures to become
obsolete and new items to become relevant. For instance, many measures
and longitudinal studies do not assess important contemporary
manifestations of externalizing behavior, including aggression on social
media and cyberbullying (\citeproc{ref-Nickerson2026}{Nickerson \&
Fredrick, 2026}). Changes in the behavioral manifestation across
historical time provide additional reasons to change the measure by
removing no-longer-valid items and by adding newer valid items.

In sum, many problems arise from using the same measure across ages when
the construct changes in behavioral manifestation across development and
historical time.

\subsubsection{Do Not Allow Charting Individuals' Change Over Time When
the Construct Changes in Behavioral
Manifestation}\label{do-not-allow-charting-individuals-change-over-time-when-the-construct-changes-in-behavioral-manifestation}

Current assessments fail to implement the construct-valid item approach
across development---existing measures do not assess the most
construct-relevant items at particular ages and thus show insufficient
differences in which items are assessed at which ages. Even in cases
where the items of a measure differ across ages (e.g., CBCL: ages 1.5--5
vs.~ages 6--18), the scoring systems do not link scores across ages to
be on the same scale while preserving change in level. For instance,
when using age-differing measures of externalizing behavior to account
for changes in behavioral manifestation across development, Kjeldsen et
al. (\citeproc{ref-Kjeldsen2016}{2016, p. 999}) noted in their study,
``Due to change in measures and rescaled variables, only relative change
across classes can be interpreted and not absolute (developmental)
change.'' Thus, the measures do not yield scores that are comparable
across time and that enable change in an individual's level to be
observed across a lengthy developmental span. In some cases, mean scores
and proportion of maximum scores have been used to account for the
age-differing measures having different numbers of items
(\citeproc{ref-Owens2003}{Owens \& Shaw, 2003};
\citeproc{ref-Petersen2015}{Petersen et al., 2015};
\citeproc{ref-SacuInPress}{Sacu et al., in press}). However, such
approaches assume that the age-differing measures have the same overall
functioning in terms of difficulty and discrimination (described later),
which is unlikely.

Age norms and standardized scores (e.g., \emph{T}- or \emph{z}-scores)
have also been used to study development of externalizing problems
(\citeproc{ref-Bista2025}{Bista et al., 2025};
\citeproc{ref-Korhonen2018}{Korhonen et al., 2018}). However, age norms
and standardized scores do not allow observing individuals' absolute
change because scores have a fixed mean and variance, and they do not
equal developmental understanding. Absolute change is necessary to
identify true growth for an individual, and is thus important for
treatment monitoring and longitudinal growth curves. Thus, age-norming
is problematic in longitudinal studies
(\citeproc{ref-Moeller2015}{Moeller, 2015}).

It is important for scores across ages to be on the same
apples-to-apples scale so the scores can be compared across ages, which
would be valuable even in a cross-sectional study that spans a wide age
range, as might be found in an epidemiological study. There is a
misperception that no practical approach exists that can handle
different measures across ages or time. Consider the following statement
by LeBlanc (\citeproc{ref-LeBlanc2021}{2021, p. 15}), ``The theoretical
position is that a form of antisocial behavior, for example, fraud, has
to be measured by distinct behaviors with adolescents and adults, in
summary adapted to their age. Nevertheless, different scale composition
is an integral part of the common concept of fraud. To our knowledge
there is no recognized analytical procedure to assess such a construct
and the life cycle validity of heteromorphous measures.''

However, considerable research in educational psychology links scores
across age-differing measures to be on the same scale. For instance,
standardized tests are frequently administered in schools to determine
the extent of growth across grades. Because of substantial changes in
ability level across grades, the same math and reading items cannot be
administered at all grades. Otherwise, respondents would receive items
that are too easy (thus evoking boredom) or too difficult (thus evoking
frustration), relative to their ability. To address this, the test
developers write the tests so that some items are in common across
adjacent grades---used for linking the scores across grades onto the
same scale---along with items that are unique to a particular grade.
Then, the researchers apply widely used methods to link the scores from
the different measures onto the same scale so they can observe
individuals' growth across grades. The same general methods are also
used to place people's scores on the same scale for standardized tests
like the ACT, SAT, GRE, MCAT, LSAT, etc., despite respondents receiving
different item content.

For examples of studies applying various linking methods to academic and
cognitive skills, see McArdle et al. (\citeproc{ref-McArdle2009}{2009}),
McArdle and Grimm (\citeproc{ref-McArdle2011}{2011}), Murayama et al.
(\citeproc{ref-Murayama2013}{2013}), Oleson et al.
(\citeproc{ref-Oleson2016}{2016}), Petscher et al.
(\citeproc{ref-Petscher2018}{2018}), Ward et al.
(\citeproc{ref-Ward2022}{2022}), and Weeks
(\citeproc{ref-Weeks2018}{2018}). However, the use of linking methods is
rare in studies of social and behavioral development broadly and
psychopathology specifically. For studies that have applied such methods
in studying social and behavioral development, see studies on
self-concept (\citeproc{ref-Hancock2008}{Hancock \& Buehl, 2008}),
neuroticism (\citeproc{ref-Lai2023}{Lai, 2023}), self-regulation
(\citeproc{ref-Hosch2022}{Hosch et al., 2022}),
underactivity/overactivity (and their subdimensions;
\citeproc{ref-McDermott2013}{McDermott et al., 2013}),
thought-disordered problems (\citeproc{ref-Petersen2026a}{Petersen,
Demko, Lee, et al., 2026}), internalizing problems
(\citeproc{ref-Harris2025}{Harris et al., 2025};
\citeproc{ref-Petersen2018}{Petersen et al., 2018};
\citeproc{ref-Petersen2026a}{Petersen, Demko, Lee, et al., 2026};
\citeproc{ref-Tyrell2019}{Tyrell et al., 2019}), and externalizing
problems (\citeproc{ref-ChenMBR}{S. M. Chen \& Bauer, in press a},
\citeproc{ref-ChenPM}{in press b}; \citeproc{ref-Harris2025}{Harris et
al., 2025}; \citeproc{ref-Petersen2026a}{Petersen, Demko, Lee, et al.,
2026}; \citeproc{ref-Petersen2021b}{Petersen \& LeBeau, 2021},
\citeproc{ref-Petersen2022}{2022}).

A failure to apply linking methods has consistently been shown to yield
less accurate trajectories---at the person and group level
(\citeproc{ref-ChenMBR}{S. M. Chen \& Bauer, in press a};
\citeproc{ref-Petersen2018}{Petersen et al., 2018};
\citeproc{ref-Petersen2021a}{Petersen et al., 2021};
\citeproc{ref-Petersen2026a}{Petersen, Demko, Lee, et al., 2026}). Thus,
it is imperative that studies link scores across age-differing measures
of psychopathology. However, psychopathology assessments do not include
scoring tools for linking scores across age- (or rater-) differing
versions. The lack of scoring tools that link scores from age-differing
psychopathology assessments leads researchers to restrict the age range
of study. For instance, in their study, Bista et al.
(\citeproc{ref-Bista2025}{2025, p. 179}) noted ``A different version of
the questionnaire (CBCL/2--3), designed for 2--3-year-olds, was used for
the year 2 follow-up {[}compared to the CBCL/4--18 assessed from ages
5--17{]}. Therefore, we excluded age 2 from our trajectory analysis.''

\subsubsection{Not Well-Suited for Capturing the Full Range of
Individual
Differences}\label{not-well-suited-for-capturing-the-full-range-of-individual-differences}

Many measures use coarse, subjective response scales such as Likert-type
response scales (e.g., ``rarely,'' ``sometimes,'' ``often,'' ``very
often'') leading to cultural bias (\citeproc{ref-Paalman2013}{Paalman et
al., 2013}; \citeproc{ref-Schaeffer1991}{Schaeffer, 1991};
\citeproc{ref-Schwarz1999}{Schwarz, 1999}) and insensitivity to change.
Items with few discrete response categories tend to show less
sensitivity to the full range of individual differences
(\citeproc{ref-Elliott1980}{Elliott \& Ageton, 1980}) and less
sensitivity to change (i.e., responsiveness;
\citeproc{ref-Grant1999}{Grant et al., 1999}) compared to items with
more response options that have greater variability in scores. In
general, items with more response options yield more information (i.e.,
greater reduction of uncertainty in estimates of a person's construct
level; though there are diminishing returns when using more than six
response options; \citeproc{ref-Culpepper2013}{Culpepper, 2013};
\citeproc{ref-Simms2019}{Simms et al., 2019}). Indeed, as depicted in
Figure~\ref{fig-absoluteFrequencyInformation}, items assessing absolute
frequency have been shown to yield more information than dichotomized
versions of the same items and than the Achenbach Adult Self-Report,
which uses Likert-type response options. In addition, if a respondent
implicitly uses the target's same-aged peers as the normative reference
group for determining the relative frequency of a behavior, this could
have the implicit effect of resulting in age-normed scores, which works
against the goal of detecting change. Moreover, Likert-type scales tend
to focus on frequency of misbehavior and ignore intensity and severity.
It can be helpful to explicitly assess---and distinguish---frequency
versus problematic impact of behavior. Instead of assessing relative
frequency, researchers advise assessing absolute frequency of behavior
(\citeproc{ref-Burns2001}{Burns et al., 2001};
\citeproc{ref-Schwarz1999}{Schwarz, 1999})---in addition to other
aspects of behavior including onset, timing, duration, intensity,
function, and resulting impairment.

\begin{figure}[!htbp]

{\caption{{Test Information Functions of Absolute Frequency Versus
Dichotomized Versus Adult Self-Report Items: Test Information as a
Function of Theta (θ)}{\label{fig-absoluteFrequencyInformation}}}}

\includegraphics[width=1\linewidth,height=\textheight,keepaspectratio,alt={Test Information Functions of Absolute Frequency Versus Dichotomized Versus Adult Self-Report Items: Test Information as a Function of Theta (θ).}]{Figures/Petersen2026_figure4.png}

\noindent \emph{Note.} ``Absolute~Frequency'' refers to count items;
``Dichotomized'' refers to dichotomized versions of the count items;
``Adult Self-Report'' refers to items from the Achenbach Adult
Self-Report. Theta represents the person's level on the latent
externalizing problems factor. The figure demonstrates that items
assessing absolute frequency yield more information (i.e., measurement
precision) than dichotomized versions of the same items and the
Likert-type response options of the Adult Self-Report. (Figure reprinted
from Petersen, Demko, Doebler, et al.
(\citeproc{ref-Petersen2026b}{2026}), Figure 4, p.~303. Petersen, I. T.,
Demko, Z., Doebler, P., Sabel, L., Oleson, J. J., \& Krueger, R. F.
(2026). How often is ``often''? Improving assessment of the
externalizing spectrum using absolute frequency. \emph{Psychological
Assessment}, \emph{38}(4), 295--306.
\url{https://doi.org/10.1037/pas0001441}).

\end{figure}

In addition, the measures focus on extreme or clinical-range behaviors;
scores are thus positively skewed with floor effects and have
unacceptably low reliability (including the CBCL;
\citeproc{ref-Kaat2019}{Kaat et al., 2019};
\citeproc{ref-Pavlovich2026}{Pavlovich et al., 2026};
\citeproc{ref-Tiego2023}{{Tiego et al.}, 2023}), making the CBCL and
existing measures unsuitable for dimensional research
(\citeproc{ref-Pavlovich2026}{Pavlovich et al., 2026};
\citeproc{ref-Tiego2023}{{Tiego et al.}, 2023}). Considerable evidence
indicates that externalizing problems (and psychopathology, more
generally; \citeproc{ref-Haslam2012}{Haslam et al., 2012};
\citeproc{ref-Haslam2020}{Haslam et al., 2020};
\citeproc{ref-Kotov2017}{Kotov et al., 2017};
\citeproc{ref-Krueger2016}{Krueger \& DeYoung, 2016};
\citeproc{ref-Krueger2011}{Krueger \& Markon, 2011};
\citeproc{ref-Krueger2002}{Krueger \& Piasecki, 2002};
\citeproc{ref-Markon2011}{Markon et al., 2011};
\citeproc{ref-Wright2013}{Wright et al., 2013}) and their trajectories
(\citeproc{ref-Burt2012}{Burt, 2012};
\citeproc{ref-Fairchild2013}{Fairchild et al., 2013};
\citeproc{ref-Walters2011}{Walters, 2011},
\citeproc{ref-Walters2012}{2012}, \citeproc{ref-Walters2015}{2015};
\citeproc{ref-Walters2013}{Walters \& Ruscio, 2013}) and risk factors
(\citeproc{ref-Walters2014}{Walters, 2014}) are best conceptualized
dimensionally (or multi-dimensionally;
\citeproc{ref-Bolhuis2017}{Bolhuis et al., 2017};
\citeproc{ref-Wakschlag2014}{Wakschlag et al., 2014}), not categorically
(\citeproc{ref-Barry2013}{Barry et al., 2013};
\citeproc{ref-Coghill2012}{Coghill \& Sonuga-Barke, 2012};
\citeproc{ref-Forbes2016}{Forbes et al., 2016};
\citeproc{ref-Kliem2018}{Kliem et al., 2018};
\citeproc{ref-Kliem2022}{Kliem et al., 2022};
\citeproc{ref-Krueger2004}{{Krueger et al.}, 2004};
\citeproc{ref-Krueger2005}{Krueger et al., 2005};
\citeproc{ref-Krueger2007}{Krueger et al., 2007};
\citeproc{ref-Krueger2021}{Krueger et al., 2021};
\citeproc{ref-Markon2005}{Markon \& Krueger, 2005};
\citeproc{ref-Sellbom2016}{Sellbom, 2016};
\citeproc{ref-Walton2011}{Walton et al., 2011}). Thus, the existing
measures are impoverished for studying the full range of individual
differences on the externalizing spectrum, which prevents subthreshold
children who are at risk for impairment from being identified. Better
identification of subthreshold externalizing is critical, in both
research and practice, for identifying at-risk individuals in the
early-stage trajectory of psychopathology. As noted by Pavlovich et al.
(\citeproc{ref-Pavlovich2026}{2026, p. 1}), ``These
findings\ldots highlight the need for measures explicitly developed and
validated for dimensional psychopathology in population-scale
research.''.

To provide better phenotypic resolution, and to better identify
biological processes underlying psychopathology, {Tiego et al.}
(\citeproc{ref-Tiego2023}{2023}) argue for including content covering
the full range, including items assessing the adaptive end of the
continuum. Doing so would help move the field away from a focus of
symptoms (and absence of symptoms) and toward consideration of the full
range of functioning, including thriving. As they note, low scores on
clinical measures are typically intended to assess absence of
pathological functioning rather than the opposite end of the latent
continuum---i.e., the presence of adaptive functioning. For instance, it
can be valuable to consider ``positive opposites''---i.e., positive
behaviors that compete with and are (simultaneously) incompatible with
the particular antisocial behavior. For instance, in a study of
externalizing behavior, it would be valuable to consider prosocial
behavior (e.g., kindness, helping others, sharing, dependability,
compliance, accountability). Indeed, in a machine learning study of
children's conduct problems in the ABCD study, prosocial behavior was
the strongest predictor (\citeproc{ref-Berluti2026}{Berluti et al.,
2026}). Moreover, measures of externalizing behavior tend to focus on
just global scores or just one or a few subdimensions. For better
phenotypic resolution, instruments should assess a wide range of
phenotypes to better capture the full range of externalizing behaviors,
which will be important to distinguish various forms of behavior---e.g.,
physical versus verbal versus destructive versus relational
aggression---and their functions---e.g., proactive versus reactive.

Based on our content analysis of over 270 measures of externalizing
behavior, we identified a wide range of facets that would be important
for measures of externalizing behavior to capture (see
Table~\ref{tbl-externalizingfacets}). We also identified potential
positive opposites of each facet.

{

\begin{longtable}[]{@{}
  >{\raggedright\arraybackslash}p{(\linewidth - 4\tabcolsep) * \real{0.3731}}
  >{\raggedright\arraybackslash}p{(\linewidth - 4\tabcolsep) * \real{0.2332}}
  >{\raggedright\arraybackslash}p{(\linewidth - 4\tabcolsep) * \real{0.3834}}@{}}

\caption{\label{tbl-externalizingfacets}Externalizing Facets Identified
in Content Analysis of Externalizing Measures.}

\tabularnewline

\toprule\noalign{}
\begin{minipage}[b]{\linewidth}\raggedright
Facet
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
Definition
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
Potential Positive Opposite
\end{minipage} \\
\midrule\noalign{}
\endhead
\bottomrule\noalign{}
\endlastfoot
Apathy/Indolence/Disengagement & Unconcerned about achievement, low
motivation, low concern about how one's abilities or actions are
evaluated, specific to contexts in which others have expectations for
performance (e.g., school and work), specifically low effort rather than
performance & Diligence/Achievement motivation \\
Attention seeking/Exhibitionism & Exaggerated or dramatic expressions,
interrupting others, inappropriate or provocative behaviors, provoking
reactions & Humility/Appropriate self-expression \\
Behavioral addiction & Impulsive/compulsive engagement in rewarding
non-substance behaviors (e.g., gambling, video games, risky sex,
pornography, food, the internet, mobile devices, shopping) &
Self-regulated engagement \\
Blame externalization & Attribute cause of problems or failures to
external factors, falsely claiming victimhood, blaming others & Personal
responsibility/Accountability \\
Boredom proneness & Expressing boredom often, difficulty maintaining
interest, lack of engagement & Curiosity/Sustained engagement \\
Callous aggression & Inflicting harm without feeling remorse or concern,
usually proactive/intentional & Compassionate protection/Benevolence \\
Callousness/Disregard for others/Selfishness/Egocentricity & Emotional
detachment, indifference to well-being of others &
Empathy/Compassion/Concern for others/Helping others/Sharing \\
Deceitfulness/Fraud/Lying/Cheating/Dishonesty/Sneakiness/Exploitation &
Keeping the truth hidden, especially to get an advantage (e.g., lying,
withholding information, manipulation, making false promises) &
Honesty/Integrity/Fairness \\
Deviant peer affiliation & Affiliating with peers who engage in deviant
or delinquent behaviors & Prosocial peer affiliations \\
Destructive aggression/Destruction of property & Destruction of
property, self, or others, objects & Constructiveness/Care for
property \\
Distractibility/Inattention/Attention
dysregulation/Forgetfulness/Daydreaming & Difficulty maintaining focus,
attention, or concentration, frequent attention shifts & Attentional
control/Sustained attention \\
Domineering/Bossiness & Asserting control, power, and authority in an
overbearing or oppressive manner & Collaborativeness \\
Excitement seeking/Risk taking/Sensation seeking & Tendency to
impulsively pursue new and different sensations, especially ones that
are intense, exhilarating, thrilling, unsafe, etc. (e.g., risk taking,
preference for novelty, intensity) & Prudent exploration/Measured
novelty seeking \\
Grandiosity/Overconfidence & Exaggerated sense of self-importance, sense
of superiority or specialness & Realistic self-confidence \\
Hostility/Rudeness & Hostile behavior, unfriendliness, resentment,
antagonism, ranging from mild irritation to intense rage, interpret
others' behavior as hostile & Warmth/Friendliness/Kindness \\
Hyperactivity & High levels of physical activity, restlessness,
difficulty engaging in quiet activities & Behavioral regulation \\
Impulsivity/Disinhibition/Impatient urgency & Tendency to act without
thinking, disinhibited engagement & Planful control \\
Irresponsibility/Unreliability/Disorganization & Failing to meet
obligations, avoiding addressing difficulties, inconsistency, lack of
organization and planning &
Responsibility/Conscientiousness/Dependability/Reliability/Organization \\
Manipulativeness/Psychological aggression & Tendency to influence or
control others to achieve one's own goals or desires, e.g., playing the
victim, flattery, gaslighting, guilt-tripping, psychological aggression
& Sincerity/Authenticity \\
Mistrust/Suspiciousness/Paranoia & Lack of confidence in the
reliability, intentions of others, difficulty forming close
relationships with others, difficulty forgiving & Interpersonal trust
(appropriately calibrated) \\
Oppositionality/Stubbornness & Persistent and defiant attitude, tendency
to challenge authority, refusal to comply, argumentativeness (could
include while complying), etc. & Cooperativeness \\
Physical aggression & Use of physical force or violence to harm others
or their property & Respect for others' bodies/Helping others \\
Punishment insensitivity & Does not change behavior after punishment,
high tolerance for negative outcomes & Responsive to consequences \\
Rebelliousness/Rule-breaking/Noncompliance & Doing things differently
than one is asked to do (e.g., breaking house rules) & Compliance/Civic
responsibility \\
Relational aggression & Aggression intended to harm others through
deliberate manipulation of their social standing and relationships
(e.g., exclusion, speaking negatively of another, etc.) & Inclusion \\
Sexual aggression & Engaging in sexual activity with someone who does
not or cannot consent to that behavior, or threatening to do so (e.g.,
harassment) & Respect for consent \\
Impulsive sexual behavior/Risky sexual behavior & Engaging in risky
sexual activity (e.g., sex without contraceptives) & Responsible sexual
decision-making \\
(Harmful) Substance Use/Problems & Harmful use of any drugs (e.g.,
alcohol, tobacco, illegal drugs) & Healthy choices around substance
use \\
Theft/Stealing & Unauthorized taking of someone else's property without
their knowledge or consent & Respect for people's possessions \\
Verbal Aggression & Communication with an intention to harm an
individual through words, tone, or manner & Respectful communication \\

\end{longtable}

}

\vspace{-12pt}
\noindent \emph{Note.} Transdiagnostic~facets of psychopathology, which
encompass externalizing problems, include irritability/reactive anger,
unemotionality, sleep problems, social problems, learning problems, and
low functional independence.

\textsubscript{Source:
\href{https://DevPsyLab.github.io/studying-psychopathology-development-lifespan/notebooks/analyses-preview.html\#cell-tbl-externalizingfacets}{Analyses}}

Because existing measures do not capture the full range of individual
differences, this naturally further limits the measures' sensitivity to
detect change (i.e., responsiveness), which is crucial for clinical
utility and for longitudinal research. Moreover, it is important for
measures not to show restriction of range owing to ceiling or floor
effects.

\subsubsection{Not Well-Suited for Capturing Individuals' Change Over
Time}\label{not-well-suited-for-capturing-individuals-change-over-time}

In sum, although they have been helpful, existing measures are poorly
suited to classify individuals' development of psychopathology across a
lengthy span, which is necessary for tracking individuals' change and
identifying mechanisms in the development of psychopathology. As we
described above, existing assessments of externalizing behavior---and of
other forms of psychopathology---have key limitations. To address this
concern, the field will need to develop better assessments. In addition,
there are problems with how assessments are used to examine
development---studies have primarily used problematic approaches
including the common items approach or the upward/downward extension
approach across ages, leading to inaccurate scores and resulting
trajectories and developmental inferences. Moreover, studies have
largely failed to place scores on a comparable scale across development.
Researchers studying psychopathology development are doing their best to
grapple with developmental equivalence in the ways they know how, such
as by dropping items, using items outside the age range of validation,
restricting the age range of analysis (or data collection) to the ages
when the same measure was (or would be) used, using diagnostic
categories, averaging scores, and age-norming. However, it is important
for the field to advance its awareness of stronger approaches for
placing scores on a comparable scale across development. To address
these concerns, we propose a potential solution to account for
heterotypic continuity and to allow charting individuals' change across
the lifespan: a developmental scaling framework.

\section{Solution: A Developmental Scaling
Framework}\label{solution-a-developmental-scaling-framework}

A developmental scaling framework informs both assessment---including
item selection---and linking of scores.

\subsection{Item Selection}\label{item-selection}

When a construct changes in behavioral manifestation across development,
which we would argue is the norm rather than the exception when
considering constructs across the lifespan, it is essential to account
for such changes in item selection. Thus, it is important to use the
construct-valid items at a given age, even if that leads to using
different measures across ages. A conceptual depiction of an example
construct-valid item design spanning infancy to adulthood is in
Figure~\ref{fig-constructValidItemDesign}. In the construct-valid item
design, some items represent the core of the phenotype and are assessed
across all ages, whereas other items are age-specific. Despite some
age-specific items, some age-common items are assessed at adjacent ages,
which help serve as anchor items for linking the scores across the
adjacent ages. The use of overlapping yet distinct items is widely used
in educational testing to help link individuals' scores across grades,
and is called vertical scaling because the item sets appear to form a
line moving upward (see Figure~\ref{fig-constructValidItemDesign}). For
example, for a standardized test of math ability, kindergartners may
receive items assessing counting, 1st graders may receive items
assessing counting and addition, 2nd graders may receive items assessing
addition and subtraction, and so on.

\begin{figure}[!htbp]

{\caption{{Conceptual Depiction of a Construct-Valid Item Design from
Infancy to Adulthood}{\label{fig-constructValidItemDesign}}}}

\includegraphics[width=1\linewidth,height=\textheight,keepaspectratio,alt={Conceptual depiction of a construct-valid item design from infancy to adulthood.}]{Figures/constructValidItemDesign.png}

\noindent \emph{Note.} The~age(s) at which an item set is assessed are
represented by the letter \texttt{x} and a colored box. Some items
(``Core'', in green) represent the core of the phenotype and are
assessed across all ages. Some items (in varying shades of brown) are
age-specific and are assessed at only one or a few ages. However, some
of the items assessed at a given age are shared with those assessed at
adjacent ages, to facilitate linking the scores across ages. For
instance, item set \texttt{f} can be used to help link scores from age 6
to those at age 5, and item set \texttt{g} can be used to help link
scores from age 6 to those at age 7. Hypothetically, items could be
assessed for as many or as few years as desired---as long as the items
are construct valid for those ages and there enough age-common items
between adjacent ages for linking scores across ages.

\end{figure}

\subsection{Linking of Scores}\label{linking-of-scores}

After the age-differing measures have been assessed, the scores from the
age-differing measures can be linked to be on the same scale. To perform
developmental scaling, a variety of approaches can be used, including
partial measurement invariance, the alignment method, moderated
nonlinear factor analysis (MNLFA), and item response theory (IRT). These
are all approaches to harmonization---i.e., linking scores from
different measures onto the same scale so they can be meaningfully
compared. Harmonization is also used for integrative data analysis, to
pool data from different measures in various studies
(\citeproc{ref-Curran2008}{Curran et al., 2008};
\citeproc{ref-McDaniel2023}{McDaniel et al., 2023}). The aforementioned
approaches to harmonization attempt to estimate latent variables---using
either confirmatory factor analysis (CFA) or IRT---on a common scale
across ages. They do so by trying to align the item parameters for at
least a subset of items. To be able to chart individuals' change over
time, it is helpful to ensure that the scores are on the same number
line across time---that is, they have the same scale and location across
ages. Scale refers to the size of a unit on the number line. If scores
have the same scale across ages, a one-unit difference represents the
same amount of the construct at each age. Location refers to the origin
or zero point on the number line. If scores have the same location
across ages, a score of zero corresponds to the same position on the
construct across ages. Collectively, if scores have the same scale and
location across ages, the measure is constantly calibrated across ages,
and the same score corresponds to the same level on the construct across
ages. CFA and IRT each have item parameters corresponding to scale and
location.

In CFA, scale is informed by an item's factor loading, and location is
informed by an item's intercept. A factor loading reflects the strength
of association between the item and the latent factor, with larger
loadings indicating stronger associations. For instance, an item
assessing the extent to which a child hits others would have a stronger
factor loading on an externalizing factor than an item assessing the
extent to which a child likes ice cream. The intercept is the expected
score on the item when the latent factor equals zero. When the latent
factor is centered to have a mean of zero, the intercept represents the
expected score on the item for someone at the mean level of the
construct. Items with lower intercepts tend to be endorsed by
individuals with higher levels of the latent factor and therefore often
reflect more severe behaviors. For example, an item assessing the extent
to which a child sets fires would be expected to have a lower intercept
than an item assessing the extent to which a child argues.

In IRT, scale is informed by an item's discrimination, and location is
informed by an item's difficulty. An item's discrimination reflects how
strongly the item differentiates individuals at various levels of the
construct, with higher discrimination indicating a stronger association
with the latent factor. In a two-parameter IRT model, an item's
difficulty reflects the level on the latent factor where there is a 50\%
probability of endorsing the item. Items with higher difficulty require
a higher level of the latent factor to have a 50\% probability of
endorsing the item and therefore represent more severe behaviors.

\subsubsection{Partial Invariance}\label{partial-invariance}

The partial invariance method can be used to link scores across
different measures (\citeproc{ref-Tyrell2019}{Tyrell et al., 2019}) and
can be paired with second-order growth functions to examine individuals'
change over time (\citeproc{ref-Hancock2008}{Hancock \& Buehl, 2008}).
The partial invariance approach attempts to establish partial strong
longitudinal factorial invariance\footnote{Strong invariance is also
  called ``scalar invariance''.}---i.e., invariant intercepts and factor
loadings across ages for a subset of items to set the latent factor
across ages on a comparable scale, with some items' intercepts and/or
factor loadings allowed to differ across ages. The researcher first
identifies which items show invariant factor loadings and/or intercepts
and which items show noninvariant factor loadings or intercepts. The
researcher then constrains the factor loadings across time for any items
with invariant factor loadings, to serve as anchor items and establish
an equivalent scale of the measures across time, and allows the factor
loadings to differ across time for the items with noninvariant factor
loadings. In addition, the researcher constrains the intercepts across
time for any items with invariant intercepts, to serve as anchor items
and establish an equivalent location of the measures across time, and
allows the intercepts to differ across time for the items with
noninvariant intercepts. The anchor items thus equate the latent factor
over time, preventing drift in the scale calibration and rendering
scores comparable across time (\citeproc{ref-ChenPM}{S. M. Chen \&
Bauer, in press b}). Then, the researcher estimates second-order growth
functions (e.g., intercept and slope) of the first-order latent factor
across time. The method can allow different indicators across ages,
either by dropping or adding indicators or by using item parcels
composed of differing items across ages
(\citeproc{ref-Tyrell2019}{Tyrell et al., 2019}).

However, the partial invariance approach requires identifying---and
accurately specifying---invariant items and any noninvariant items,
which can be both inefficient and error-prone (\citeproc{ref-ChenPM}{S.
M. Chen \& Bauer, in press b}; \citeproc{ref-Lai2023}{Lai, 2023}).
Moreover, the partial invariance approach tends not to work as well when
a large proportion of items are noninvariant
(\citeproc{ref-Lai2023}{Lai, 2023}), there are many timepoints, there is
considerable variability in the numbers of responses provided to items
such as might occur due to missing data or when not all items are
assessed at all timepoints, or the researcher wants to consider
factorial invariance or differential item functioning (DIF) as a
function of multiple variables or continuous variables
(\citeproc{ref-ChenPM}{S. M. Chen \& Bauer, in press b}).

\subsubsection{Alignment Optimization}\label{alignment-optimization}

The alignment optimization method (\citeproc{ref-Muthen2014}{Muthén \&
Asparouhov, 2014}) has been used to link scores across time
(\citeproc{ref-Lai2023}{Lai, 2023}). The alignment optimization method
within confirmatory factor analysis attempts to identify a model with
approximate longitudinal factorial invariance---that is, to retain any
instances of large noninvariance across ages and to keep other
parameters approximately invariant across ages---to adjust for
violations of invariance. The approach uses a component loss function to
align the item parameters across ages so that the scores on the latent
factors are on the same scale. Unlike the partial invariance method, the
alignment method does not require a priori identification of any
noninvariant items (\citeproc{ref-Lai2023}{Lai, 2023}).

\subsubsection{Moderated Nonlinear Factor
Analysis}\label{moderated-nonlinear-factor-analysis}

MNLFA (\citeproc{ref-Bauer2017}{Bauer, 2017}) has also been used to link
scores across different measures (\citeproc{ref-Curran2014}{Curran et
al., 2014}), including across ages (\citeproc{ref-ChenPM}{S. M. Chen \&
Bauer, in press b}, \citeproc{ref-ChenMBR}{in press a};
\citeproc{ref-Student2025}{Student, 2025}). Unlike the partial
invariance approach, MNLFA represents the measurement model in
continuous time (rather than discrete time). MNLFA allows simultaneous
estimation of growth functions while estimating and accounting for DIF
effects. It allows estimating DIF as a function of time and as a
function of multiple variables, including categorical and continuous
variables. Bayesian approaches can be used to apply MNLFA. A key benefit
of Bayesian approaches is the use of regularizing priors that allow
estimating the model without having to identify noninvariant/DIF items
and anchor items in advance (\citeproc{ref-ChenPM}{S. M. Chen \& Bauer,
in press b}, \citeproc{ref-ChenMBR}{in press a}). Using regularization,
unimportant DIF effects are shrunken toward zero---while retaining
larger DIF effects---thus identifying potential anchor items without
having to specify them in advance (\citeproc{ref-ChenPM}{S. M. Chen \&
Bauer, in press b}). In addition, Bayesian approaches are often better
suited to handling small sample sizes and data with sparse responses
(\citeproc{ref-ChenPM}{S. M. Chen \& Bauer, in press b}). Using a
simulation, Chen and Bauer (\citeproc{ref-ChenMBR}{in press a}) found
that MNLFA estimated change more accurately than traditional first- or
second-order growth curve models.

\subsubsection{Item Response Theory}\label{item-response-theory}

IRT can also be used to link scores across different measures
(\citeproc{ref-Kolen2014}{Kolen \& Brennan, 2014}). The IRT approach to
developmental scaling is depicted in Figure~\ref{fig-linking}. The IRT
approach to developmental scaling identifies scaling parameters that
minimize the differences in the probability of a person endorsing the
age-common items across two measures, at a given construct level. That
is, IRT links measures' scales based on the difficulty and
discrimination of the age-common items. In developmental scaling, scores
on the construct-valid items at the reference age set the scale; the
age-common items adjusts subsequent scores to that scale, and all
construct-valid items (i.e., both age-common and age-unique items) at a
given timepoint are used to estimate each person's score on that scale.
Thus, the age-common items are used to determine the general form of
change on an identical scale, but all developmentally relevant,
construct-valid items are used to estimate each person's construct level
on this scale. Traditionally IRT represents the measurement model in
discrete time. Like MNFLA, however, IRT (particularly in the mixed model
formulation) can represent the measurement model in continuous time and
allows testing DIF over time and as a function of multiple variables and
continuous variables. Moreover, like MNLFA, it allows simultaneous
estimation of growth functions while estimating and accounting for DIF
effects. In addition, like MNFLA, IRT allows Bayesian estimation and
regularizing priors to identify anchor items without having to specify
them in advance.

\begin{figure}[!htbp]

{\caption{{Example of Linking Scores From Measures Across Ages Using the
Item Response Theory Approach to Developmental
Scaling}{\label{fig-linking}}}}

\includegraphics[width=1\linewidth,height=\textheight,keepaspectratio,alt={Example of linking scores from measures across ages using the item response theory approach to developmental scaling.}]{Figures/Petersen2021_figure1.png}

\noindent \emph{Note.} The~figure illustrates the effect of linking the
latent externalizing problems scores, θ, across ages, using
developmental scaling. The left panel illustrates the test
characteristic curves representing the model-implied proportion out of
total possible scores across the latent externalizing problems score at
age 4 and 5, before the linking process. The right panel illustrates the
test characteristic curves after the linking process. The shading
between the age 4 and age 5 test characteristic curves represents
differences between the two test characteristic curves in terms of
discrimination and/or severity, where larger differences reflect scores
that are less comparable. Linking minimizes differences between the
discrimination and severity of the age-common items. Discrimination is
depicted by the steepness of the slope at the inflection point of the
test characteristic curve. Severity is represented by the value on the
x-axis at the inflection point of the test characteristic curve. The
left panel indicates that the externalizing problem items showed higher
severity (i.e., its inflection point is further right) and somewhat
stronger discrimination (i.e., its slope is steeper) at age 5 than at
age 4. The right panel shows considerably smaller differences between
the two test characteristic curves, which provides empirical evidence
that the linking successfully placed the latent externalizing problem
scores across age on a more comparable scale (i.e., more similar
discrimination and severity of the age-common items). (Figure reprinted
from Petersen and LeBeau (\citeproc{ref-Petersen2021b}{2021}), Figure 1,
p.~74. Petersen, I. T., \& LeBeau, B. (2021). Language ability in the
development of externalizing behavior problems in childhood.
\emph{Journal of Educational Psychology}, \emph{113}(1), 68--85.
\url{https://doi.org/10.1037/edu0000461}).

\end{figure}

Nevertheless, for many of these approaches, at least one anchor item is
necessary to link the scale of the latent factor across timepoints
(\citeproc{ref-ChenPM}{S. M. Chen \& Bauer, in press b}). Moreover, when
treating time continuously, the functional form of any DIF as a function
of time must be correctly specified (\citeproc{ref-ChenPM}{S. M. Chen \&
Bauer, in press b}).

\section{Other Key Challenges to
Address}\label{other-key-challenges-to-address}

In addition to linking scores across time to be on the same scale, to
study the development of psychopathology across the lifespan, there are
additional key challenges to address, including considering and/or
addressing potential confounds of change, factorial invariance,
integration across multiple sources, and obsolescence of items.

\subsection{Potential Confounds of
Change}\label{sec-potential-confounds-of-change}

It is important for longitudinal research to consider and, to the extent
possible, account for potential confounds of change, such as practice
effects, period and cohort effects, measurement error, selective
attrition, and changes in the meaning of the scores
(\citeproc{ref-Hertzog2003}{Hertzog \& Nesselroade, 2003}). By confound
of change, we mean that such effects can make it appear that people have
changed in their level on the construct when, in reality, they have not
changed (or vice versa).

\subsubsection{Practice/Retest Effects}\label{practiceretest-effects}

Practice effects (also called retest effects) occur to the extent that a
person's score changes due to repeated assessment rather than due to
changes in their construct level. For instance, if researchers intend to
study people's intelligence across development and they use the same
measure and stimuli at each measurement occasion, it is possible that
people may perform better over time because they are learning the task
and thus improving their score---even if their intelligence has not
changed. In a longitudinal study of externalizing problems using
repeated surveys, retest effects might be most likely to be detected in
the form of decreases for a person across ages, which may reflect
fatigue in reporting (\citeproc{ref-Averdijk2014}{Averdijk, 2014}).
Lower ratings for an individual across time may be especially likely if
the surveys include branching logic such that the respondent learns that
additional items appear whenever they endorse an item (and that those
additional items would not have appeared had they not endorsed the
item). Ways to reduce retest effects include changing the measure and/or
stimuli (\citeproc{ref-Tyrell2019}{Tyrell et al., 2019}) and increasing
the retest interval. Thus, an added benefit of accounting for
heterotypic continuity (by changing the measure across development to
align with changes in the construct manifestation) is the reduction of
retest effects. A way to account for retest effects is through the use
of accelerated longitudinal (i.e., cross-sequential) designs that can
separately estimate the effects of age versus timepoint because, unlike
in a single-cohort longitudinal design, age and timepoint are decoupled
(\citeproc{ref-Ferrer2004}{Ferrer et al., 2004}).

\subsubsection{Period and Cohort
Effects}\label{period-and-cohort-effects}

Researchers are commonly interested in how people develop as a function
of age. Age refers to a person's chronological age at the time of
measurement. Age is a proxy for development---a stand-in for the myriad
ways in which one's biology and social roles---and one's corresponding
employment, income, and family structure---change as people age
(\citeproc{ref-Rohrer2025}{Rohrer, 2025}). However, apparent age-related
differences in a cross-sectional or longitudinal study could reflect
period or cohort effects instead of development. Thus, it is important
to consider and, to the extent possible, account for period and cohort
effects.

Period refers to the historical time at which measurement occurs. If
people are assessed during a given time period (e.g., during a war,
recession, pandemic, or stressor), their scores could be influenced by
the historical time period. The extent to which scores are attributable
to the time period (e.g., the economic situation or prevailing standard
of living) in which they are assessed is called a period effect.

Cohort refers to a group of people who experience similar events or
historical contexts at similar ages. Cohort commonly refers to birth
cohort, which represents the group of people who were born around the
same time. If a group of people were born around the same time (e.g., in
1940), their scores may differ from those of people born in other eras
because they experienced different historical, social, educational,
economic, or technological contexts during development. The extent to
which scores are attributable to an individual's birth cohort is called
a cohort effect---that is, ``the (enduring, constant) effects of having
been a certain age at a certain point in historic time.''
(\citeproc{ref-Rohrer2025}{Rohrer, 2025, p. 2}). Period and
cohort---like age---are proxy variables for other, causal processes.

Part of the challenge of estimating the unique contributions of age,
period, and cohort is that they are deterministically related. If you
know two of these (e.g., age and period), you can determine the third
(e.g., cohort). That is, \(\text{age} = \text{period} - \text{cohort}\).

Various types of cross-sectional and longitudinal designs are depicted
in Figure~\ref{fig-longitudinalDesigns}. In a cross-sectional study, any
age-related differences are confounded with cohort differences. Thus,
age-related differences in a cross-sectional study may not reflect
development. In a single-cohort longitudinal design, any observed
changes with age could be due to period effects (rather than
developmental change associated with aging) or could be specific to that
cohort. To combat these limitations, studies may employ longitudinal
sequential designs that incorporate multiple cohorts, such as
time-sequential, cross-sequential, or cohort-sequential designs. For
instance, a cross-sequential study (also called accelerated longitudinal
study) starts as a cross-sectional study with participants from multiple
cohorts, and then follows the participants longitudinally. In a
cohort-sequential design, multiple cohorts enter the study at the same
age (e.g., age 22) and are then followed longitudinally (typically
across the same duration and ages), like starting a longitudinal study
at the same age over and over again. A time-sequential design is an
extension of a time-lag design. A time-lag design assesses multiple
cohorts at the same age (e.g., age 12). A time-sequential design adds
age groups to a time-lag design, repeatedly assessing the same age range
(e.g., ages 12--18), with some participants followed longitudinally.

\begin{figure}[!htbp]

{\caption{{Research Designs by Time of Measurement and
Cohort}{\label{fig-longitudinalDesigns}}}}

\includegraphics[width=1\linewidth,height=\textheight,keepaspectratio,alt={Research Designs by Time Of Measurement and Cohort}]{Figures/longitudinalDesigns.png}

\noindent \emph{Note.} Values~in the cells are ages of the participants.
Dashed line indicates different participants were assessed at each time
of measurement. (Figure reprinted from Petersen
(\citeproc{ref-PetersenPrinciplesPsychAssessment}{2026}), Petersen, I.
T. (2026). \emph{Principles of psychological assessment: With applied
examples in R}. University of Iowa Libraries.
\url{https://doi.org/10.25820/work.007199}). Although the depictions of
cohort-sequential and cross-sequential designs differ from the
depictions by Schaie (\citeproc{ref-Schaie2005}{2005}) (i.e., they are
reversed), they are consistent with contemporary definitions of these
designs (\citeproc{ref-Little2024}{Little, 2024};
\citeproc{ref-Masche2004}{Masche \& Dulmen, 2004};
\citeproc{ref-Whitbourne2019}{Whitbourne, 2019}).

\end{figure}

Longitudinal sequential designs provide greater leverage for
distinguishing age, period, and cohort influences by collecting
information from multiple cohorts at multiple periods and ages.
Nevertheless, they do not eliminate the confounding between age, period,
and cohort (\citeproc{ref-Rohrer2025}{Rohrer, 2025}). No research design
can fully disentangle age, period, and cohort effects. Confidence that
observed age-related differences reflect developmental change increases
when there is converging evidence across multiple research designs.
However, in a given study, there may be ways to account for period or
cohort effects. For instance, in an accelerated longitudinal study, it
would be valuable to evaluate the extent to which the differing cohorts
are comparable---i.e., that they show similar scores at the same ages.
Moreover, there is an entire set of analytic approaches, known as
age-period-cohort analysis (\citeproc{ref-Yang2013}{Yang \& Land,
2013}), whose goal is to disentangle the effects of age, period, and
cohort. Rohrer (\citeproc{ref-Rohrer2025}{2025}) provides additional
suggestions for considering age, period, and cohort effects.

\subsubsection{Measurement Error}\label{measurement-error}

Measurement error is another potential confound of change that can make
it look like change has occurred when, in reality, change has not
occurred. Consider the difference between scores at two measurement
occasions, a so called ``difference score,'' which is a common way of
examining change. Difference scores are notoriously unreliable.
Difference scores tend to be lower in reliability than each of the
indices that comprise it, especially when the two indexes are correlated
because differences depend on the reliability of both indices in the
subtraction (\citeproc{ref-Revelle2019}{Revelle \& Condon, 2019}). To be
reliable, difference scores require high reliability of the individual
indices compared to the correlation between them. That is, the more two
things are the same thing, the more likely that subtracting one from the
other leaves measurement error rather than construct variance. Ways of
accounting for (random) measurement error include (a) combining multiple
measures in estimation of a latent variable and (b) using growth curve
models with at least three timepoints to estimate model-implied
trajectories and reduce the influence of occasion-specific random error.

In general, the inference of change is strengthened to the extent that:
(a) the magnitude of the difference between the scores at the timepoints
is large (i.e., a large effect size), (b) the measurement error
(unreliability) at each timepoint is small, (c) the measure has the same
meaning and is on a comparable scale at each timepoint, and (d) evidence
suggests that the differences across time are not likely to be due to
potential confounds of change such as practice effects, cohort effects,
period effects, or selective attrition.

\subsubsection{Selective Missingness and
Attrition}\label{selective-missingness-and-attrition}

Another potential confound of change is selective (or systematic)
missingness or attrition. If people who drop out of a longitudinal study
differ in systematic ways from those who are retained, inferences about
growth patterns and about associations with growth parameters can be
biased. Consider an intervention study with two groups: a treatment
group that received medication and a control group that received a
placebo. The control group showed a 30\% reduction in externalizing
problems, on average. In the treatment group, some individuals showed a
reduction in externalizing problems whereas others dropped out of the
study due to side effects or worsening behavior. If we analyzed only
those who were followed until the end of the study, it might appear that
the treatment was effective merely because we were excluding individuals
for whom the treatment was harmful. Thus, it is important to report the
extent of missingness, whether missingness is systematically related to
demographic and study variables, and to leverage modern approaches for
handling missing data so that one does not exclude participants in the
analysis merely because they have missing data
(\citeproc{ref-Nicholson2017}{Nicholson et al., 2017}). Multiple
imputation and full information maximum likelihood are useful if data
are missing at random or completely at random
(\citeproc{ref-Nicholson2017}{Nicholson et al., 2017}). Enders
(\citeproc{ref-Enders2022}{2022}, \citeproc{ref-Enders2025}{2025})
provides contemporary guidelines for handling missing data, including
when data are missing not at random using selection models and pattern
mixture models---including in longitudinal studies
(\citeproc{ref-Enders2022}{Enders, 2022}). Nicholson et al.
(\citeproc{ref-Nicholson2017}{2017}) provides recommendations for
reporting about attrition and missingness in longitudinal studies.

\subsubsection{Change in Meaning of the
Scores}\label{change-in-meaning-of-the-scores}

Another potential confound of change is if the same score has different
meaning (with respect to the construct) at different points in
development. That is, the scores are not on the same number line across
time---they do not have the same scale or location across ages. If
scores do not have the same scale or location across ages, any
inferences about change (or lack thereof) could be incorrect. Consider,
for example, if a behavior such as physical aggression becomes more
severe (i.e., higher difficulty) with age. In this example, the same
score---i.e., endorsement of physical aggression---would reflect a
higher level of externalizing behavior in adulthood compared to early
childhood. Or, consider if a behavior such as disobedience becomes less
construct-valid (i.e., lower discrimination) with age. In this example,
the same score difference---i.e., between endorsement (1) versus
non-endorsement (0) of disobedience to authority---would reflect a
greater difference in the level of externalizing behavior in early
childhood compared to adulthood. Thus, it is important to consider and
account for changes in the meaning of scores across development. If a
measure changes in the construct it assesses, this is called construct
shift. Next, we describe longitudinal factorial invariance as a way to
evaluate---and account for---the possibility that scores have changed in
meaning across ages.

\subsection{Factorial Invariance Across
Time}\label{factorial-invariance-across-time}

Traditionally, it had been considered necessary to establish factorial
invariance\footnote{Factorial invariance is also called measurement
  invariance. In this context, we prefer the term ``factorial
  invariance'' because, as described, the actual measures used may
  differ across time.} of the measure(s) across time---that is, the
measure(s) assess the construct in the same way across time---to study
individuals' change in those constructs
(\citeproc{ref-Widaman2010}{Widaman et al., 2010}). As described
earlier, a goal of longitudinal factorial invariance is to increase
confidence that the latent factor at multiple timepoints is on the same
scale so that meaningful changes in people's level can be observed. It
had been considered necessary to establish at least strong factorial
invariance---i.e., invariance of intercepts and factor loadings in
factor analysis, or invariance of difficulty and discrimination in item
response theory. Otherwise, a researcher may wrongly conclude that
levels in the construct change over time when the apparent changes in
the observed scores (and the latent variables) are driven by
noninvariant loadings and/or intercepts for one or more items
(\citeproc{ref-Lai2023}{Lai, 2023}). However, it is now understood that
violations of longitudinal factorial invariance do not mean that
questions of change cannot be answered (\citeproc{ref-Lai2023}{Lai,
2023}). Strong factorial invariance frequently does not hold, so in such
situations, it may be necessary to find ways to accommodate or adjust
for noninvariance (\citeproc{ref-Lai2023}{Lai, 2023}).

At least partial strong factorial invariance (i.e., invariance of
intercepts and factor loadings for a subset of items---the anchor items)
is often considered a requirement for modeling individuals' change, such
that the more items that show invariance, the greater the confidence
that the latent factor is on a comparable scale at each age for
examining individuals' change. However, even that requirement may be too
strong. Researchers have argued that, in many cases, establishing
factorial invariance may be unnecessary to compare latent means
(\citeproc{ref-DeLosReyes2025}{De Los Reyes et al., 2025};
\citeproc{ref-Funder2024}{Funder \& Gardiner, 2024};
\citeproc{ref-QuantitudeS3E18}{Hancock \& Curran, 2022};
\citeproc{ref-Knight2010}{Knight \& Zerr, 2010};
\citeproc{ref-Petersen2020}{Petersen et al., 2020};
\citeproc{ref-Robitzsch2023}{Robitzsch \& Lüdtke, 2023};
\citeproc{ref-Welzel2023a}{Welzel, Brunkert, et al., 2023};
\citeproc{ref-Welzel2023b}{Welzel, Kruse, et al., 2023}). Indeed, failed
longitudinal invariance can be an artifact of differing means across
groups/time rather than bias or differences in the functioning of the
measure (\citeproc{ref-Welzel2023a}{Welzel, Brunkert, et al., 2023};
\citeproc{ref-Welzel2023b}{Welzel, Kruse, et al., 2023}). As noted by
Hancock (\citeproc{ref-QuantitudeS3E18}{2022}), to model differences in
latent means (e.g., change over time), you do not need invariance; ``you
need to have a model that is correct\ldots That means that\ldots you are
modeling {[}items'{]} invariance properly.''

When a construct demonstrates heterotypic continuity, longitudinal
factorial invariance would not necessarily be expected because the
construct's factor structure, by definition, changes with development
(\citeproc{ref-Petersen2020}{Petersen et al., 2020}). That is,
noninvariances across development can be expected by theory
(\citeproc{ref-Sterner2026}{Sterner et al., 2026}). As a result,
theoretical considerations are crucial and establishing even partial
longitudinal factorial invariance may not be required when the construct
shows heterotypic continuity (\citeproc{ref-Knight2010}{Knight \& Zerr,
2010}; \citeproc{ref-Petersen2020}{Petersen et al., 2020}). As noted by
Millsap (\citeproc{ref-Millsap2011}{2011, p. 1}), ``Measurement
invariance is built on the notion that a measuring device should
function in the same way across varied conditions, \emph{so long as
those varied conditions are irrelevant to the attribute being
measured}'' (emphasis added). However, age/development would not be
considered irrelevant to psychopathology. As described earlier,
externalizing (antisocial) behavior is considered to demonstrate
heterotypic continuity; therefore, longitudinal factorial
\emph{noninvariance} for measures assessing the development of
externalizing behavior may be expected.

As noted by De Los Reyes et al. (\citeproc{ref-DeLosReyes2025}{2025, p.
301}), ``developmental variations in antisocial behavior are unlikely to
reflect confounds or biases in measurement.'' De Los Reyes and
colleagues characterize such tests of invariance across development---in
which the conditions (age) are relevant to the construct of
interest---as a questionable research practice, noting, ``To be
justified in testing measurement invariance {[}across ages{]}, one would
have to assume that when systematic differences manifest between
ratings\ldots for younger versus older youth, they cannot possibly
reflect anything valid. For a scholar to make such an assumption, they
must again ignore decades of theory and research in developmental
psychopathology.'' (p.~308). Moreover, removing noninvariant items is
not recommended if the item retains construct validity
(\citeproc{ref-DeLosReyes2025}{De Los Reyes et al., 2025};
\citeproc{ref-Knight2010}{Knight \& Zerr, 2010}). When the construct
changes in manifestation, models with failed longitudinal factorial
invariance can yield valid inferences. For instance, simulation work
demonstrated that IRT linking approaches accurately captured changes in
level on the latent factor even in the present of DIF and changing
dimensionality (\citeproc{ref-Edwards2012}{Edwards \& Wirth, 2012}).

There are multiple ways of handling noninvariance as described above,
including alignment optimization, MNLFA, and IRT-based linking. In
addition, another approach is to allow approximate factorial invariance.
Approximate measurement invariance allows invariance parameters to have
a small amount of noninvariance rather than fixing invariance parameters
to zero (\citeproc{ref-VanDeSchoot2013}{Van De Schoot et al., 2013}).
Approximate measurement invariance is more accurate than full or partial
measurement invariance for estimating true latent mean differences when
there are many small differences in the intercepts and factor loadings
(\citeproc{ref-Cieciuch2014}{Cieciuch et al., 2014};
\citeproc{ref-VanDeSchoot2013}{Van De Schoot et al., 2013}). Approximate
measurement invariance has also been applied in the longitudinal context
(e.g., \citeproc{ref-Seddig2018}{Seddig \& Leitgöb, 2018};
\citeproc{ref-Winter2020}{Winter \& Depaoli, 2020}). Robitzsch and
Lüdtke (\citeproc{ref-Robitzsch2023}{2023, p. 859}) argue that
establishing factorial invariance is neither necessary nor sufficient
for comparing latent means, and they note that ``there is no support for
preferring the partial invariance approach over competing approaches,
such as invariance alignment, robust linking, or Bayesian approximate
invariance.''

\subsection{Integration Across Multiple
Sources}\label{integration-across-multiple-sources}

The most accurate informant(s) for a person can change with development,
so it may be necessary to include different informants across time.
There is widespread agreement that including multiple sources of
data---e.g.. multiple informants or multiple measurement methods---is
preferable. However, there is less agreement about how to use multiple
sources of data (\citeproc{ref-Bauer2013}{Bauer et al., 2013}),
particularly because informants often show low correspondence with one
another when rating the same person. Some of these discrepancies may be
confounded by the person behaving differently in different contexts or
with different people. The inclusion of multiple measurement methods can
help account for measurement error given the considerable variance that
is attributable to method bias (\citeproc{ref-Podsakoff2012}{Podsakoff
et al., 2012}). The inclusion of multiple informants can be relevant for
informing about the pervasiveness of a person's behavior across contexts
(e.g., home, school).

When including multiple or different informants across development, it
is important to consider how to leverage the multi-informant ratings.
Some researchers advocate for integrating scores using principal
component approaches (while disentangling variance attributable to
trait, perspective, and context; \citeproc{ref-Kraemer2003}{Kraemer et
al., 2003}) or latent variable approaches (e.g.,
\citeproc{ref-Bauer2013}{Bauer et al., 2013}), and others advocate for
keeping different informants' ratings separate without integrating them
(but including them in the same model; \citeproc{ref-Aitken2023}{Aitken
et al., 2023}). As an example of a latent variable modeling approach,
Bauer et al. (\citeproc{ref-Bauer2013}{2013}) demonstrate a trifactor
model that attempts to disentangle construct variance from the method
effects tied to the specific item and the informant. De Los Reyes et al.
(\citeproc{ref-DeLosReyes2013}{2013}) provide the Operations Triad Model
as a framework for using and interpreting reports from multiple
informants (for more information, see \citeproc{ref-Makol2025}{Makol et
al., 2025}). In sum, finding ways to leverage the information from
multiple informants will be crucial for studying the development of
psychopathology across the lifespan (\citeproc{ref-DeLosReyes2026}{De
Los Reyes, 2026}).

\subsection{Obsolescence of Items and
Measures}\label{obsolescence-of-items-and-measures}

Another challenge is that questionnaire items---whether the particular
wording or the behavior itself---can become obsolete and irrelevant with
secular changes. For instance, due to technological changes, items
focused on television use---without considering other forms of screen
use---may miss important contemporary screen-related use. Additionally,
ways people use substances change over historical time. For instance,
vaping is a more contemporary way that many adolescents use nicotine.
The ways in which aggressive behavior manifests also change across
historical time. Items focused on physical aggression would miss
important contemporary manifestations of aggression, including
cyberaggression, cyberbullying, online harassment, and aggression on
social media (e.g., exclusion). In sum, it is important to keep items
relevant for current use, and that naturally means changing item content
and/or wording across historical time, a further reason linking of
scores (given differing item content) is crucial.

\section{Conclusion}\label{conclusion}

Due to a variety of challenges---both conceptual and
methodological---that we discuss, the field has not adequately studied
individuals' development of psychopathology across the lifespan, instead
taking a piecewise approach to development that limits our understanding
of lifespan development and the origins of psychopathology. To address
these challenges, we discuss the importance of defining psychopathology
constructs from a developmental perspective, developing new assessments
that (a) capture changes in behavioral manifestation of psychopathology,
(b) apply scoring systems that allow charting individuals' change over
time in the face of changing behavioral manifestation, and (c) capture
the full range of individual differences. We introduce a developmental
scaling framework to help address these challenges. Addressing these
challenges will allow charting individuals' trajectories of
psychopathology across the lifespan and identifying risk and protective
factors that influence their developmental courses. Doing so is critical
for understanding how psychopathology develops, when to intervene, and
how to most effectively prevent psychopathology. Although this paper
focuses on development of psychopathology, the principles discussed
likely apply to many other developmental domains.

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