Make ESEM Model.

Make lavaan syntax for exploratory structural equation model (ESEM).

Usage

make_esem_model(loadings, anchors)

Arguments

loadings

Dataframe with three columns from exploratory factor analysis (EFA):

• latent = name of the latent factor(s)

• item = name of the item(s)/indicator(s)

• loading = parameter estimate of the factor loading item factor loading on the latent factor

anchors

Dataframe whose names are the latent factors and whose values are the names of the anchor item for each latent factor.

Value

lavaan model syntax.

Details

Makes syntax for exploratory structural equation model (ESEM) to be fit in lavaan.

See also

https://msilvestrin.me/post/esem/

Other structural equation modeling: equiv_chi(), puc(), satorraBentlerScaledChiSquareDifferenceTestStatistic(), semPlotInteraction()

Examples

# Prepare Data
data("HolzingerSwineford1939", package = "lavaan")

# Specify EFA Syntax
efa_syntax <- '
  # EFA Factor Loadings
  efa("efa1")*f1 +
  efa("efa1")*f2 +
  efa("efa1")*f3 =~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9
'

# Fit EFA Model
mplusRotationArgs <- list(rstarts = 30,
  row.weights = "none",
  algorithm = "gpa",
  orthogonal = FALSE,
  jac.init.rot = TRUE,
  std.ov = TRUE, # row standard = correlation
  geomin.epsilon = 0.0001)

efa_fit <- lavaan::sem(
  efa_syntax,
  data = HolzingerSwineford1939,
  information = "observed",
  missing = "ML",
  estimator = "MLR",
  rotation = "geomin",
  # mimic Mplus
  meanstructure = TRUE,
  rotation.args = mplusRotationArgs)

# Extract Factor Loadings
esem_loadings <- lavaan::parameterEstimates(
  efa_fit,
  standardized = TRUE
) |>
  dplyr::filter(efa == "efa1") |>
  dplyr::select(lhs, rhs, est) |>
  dplyr::rename(item = rhs, latent = lhs, loading = est)

# Specify Anchor Item for Each Latent Factor
anchors <- c(f1 = "x3", f2 = "x5", f3 = "x7")

# Generate ESEM Syntax
esemModel_syntax <- make_esem_model(esem_loadings, anchors)

# Fit ESEM Model
lavaan::sem(
  esemModel_syntax,
  data = HolzingerSwineford1939,
  missing = "ML",
  estimator = "MLR")
#> lavaan 0.6-19 ended normally after 145 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        42
#> 
#>   Number of observations                           301
#>   Number of missing patterns                         1
#> 
#> Model Test User Model:
#>                                               Standard      Scaled
#>   Test Statistic                                22.897      23.828
#>   Degrees of freedom                                12          12
#>   P-value (Chi-square)                           0.029       0.021
#>   Scaling correction factor                                  0.961
#>     Yuan-Bentler correction (Mplus variant)