Longitudinal Data Analysis
1 Approaches for Modeling Longitudinal Data
- Growth curve model (GCM)
- Latent growth curve model (LGCM)
- Latent change score model (LCSM)
- Cross-lagged panel model (CLPM)
- Random intercept cross-lagged panel model (RI-CLPM)
- Autoregressive latent trajectory (ALT) model
- Latent curve model with structured residuals (LCM-SR)
- Latent curve model with structured residuals with long data in multilevel SEM (LCM-SR)
2 Ensuring/Evaluating Whether Longitudinal Scores are on the Same Statistical Scale Across Time
3 Estimating Nonlinear Growth
There are a variety of ways to estimate nonlinear growth in a growth curve model using a mixed-effects or structural equation model:
- polynomial growth model
- fractional polynomial model (more parsimonious than traditional polynomials because can capture nonlinear growth with fewer parameters, thus reducing overfitting)
- piecewise/spline model
- can have fixed or random knots
- location of knots can be estimated for the data
- each individual can have a different numbers of knots and different location for the knots
- latent basis growth model
- can specify the rate of change between T1 and T2 to be one; can allow the rate of change to freely vary between remaining timepoints
- exponential growth model
- exponential asymptotic model: e.g., 3-parameter asymptotic exponential
- logistic growth model
- logarithmic growth model
- e.g., “an exponential pattern of change—in which change appears to ‘level off’ over time—can be approximated through linear (and potentially quadratic) slopes for a natural-log-transformed” version of time in a mixed-effects model or by fixing the latent change factor loadings to these values in SEM (Hoffman, 2025)
- i.e.,
log(time + 1)
- i.e.,
- e.g., “an exponential pattern of change—in which change appears to ‘level off’ over time—can be approximated through linear (and potentially quadratic) slopes for a natural-log-transformed” version of time in a mixed-effects model or by fixing the latent change factor loadings to these values in SEM (Hoffman, 2025)
- generalized additive model
- nonparametric growth model (e.g., kernel smoothing)
- Gompertz growth model
- Richards growth model
- Taylor series approximation model
- latent change score model
