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Latent SEM for Solomon Four-Group designs (POST means; optional latent ANCOVA)

Source: R/solomon_sem_latent.R
fit_solomon_sem_latent.Rd

This function provides a fully latent analysis path: (A) A 4-group SEM that defines a latent POST factor from multiple indicators and estimates group-specific latent means for P1, P0, U1, and U0. From these we compute ATE, Sens (Pretest x Treat), and simple effects on the latent outcome. (B) Optionally, a 2-group SEM in pretested groups only (P1 vs P0) with a latent PRE factor and latent POST factor, fitting a latent ANCOVA (POST ~ PRE), and reporting the pretested simple effect.

Usage

fit_solomon_sem_latent(
  data,
  post_items,
  treat,
  pretested,
  pre_items = NULL,
  invariance_post = c("scalar", "metric", "configural"),
  ancova = FALSE,
  invariance_pre = c("scalar", "metric", "configural"),
  estimator = "MLR",
  std_lv = TRUE,
  conf_level = 0.95
)

Arguments

data

data.frame containing all variables

post_items

character vector of posttest item names (required)

treat

0/1 (or logical) treatment indicator (length nrow(data))

pretested

0/1 (or logical) pretest indicator (length nrow(data))

pre_items

character vector of pretest item names (for ANCOVA branch)

invariance_post

measurement invariance for POST; must be "scalar"

ancova

logical; if TRUE, also fit latent ANCOVA in pretested groups

invariance_pre

measurement invariance for the pretested branch; must be "scalar"

estimator

lavaan estimator, default "MLR" (robust)

std_lv

logical; if TRUE (default), std.lv=TRUE to put factors on SD=1 scale

conf_level

confidence level for intervals (default 0.95)

Value

An object of class solomon_sem_latent with:

  • fit_post: lavaan object for the 4-group POST model

  • effects_post: data.frame of ATE, Sens, Pre_Eff, Unpre_Eff on latent POST

  • fitmeasures_post: named vector (CFI, RMSEA, SRMR, df)

  • fit_pre (optional): lavaan object for pretested latent ANCOVA

  • effects_pre (optional): data.frame with Pre_Eff on latent POST (pretested)

  • fitmeasures_pre (optional)

Details

Latent mean contrasts require scalar measurement invariance (equal loadings and intercepts) across groups (Meredith, 1993; Vandenberg & Lance, 2000). invariance_post and invariance_pre therefore accept only "scalar"; configural and metric models are rejected with an explanation.

Identification: with scalar invariance, the latent POST mean of the unpretested control group (U0) is fixed at 0 and the other latent means are estimated relative to it. In the pretested ANCOVA model, the pretested control group (P0) is the reference. The Solomon contrasts are differences between latent means, so they do not depend on the reference choice.

Tests and confidence intervals for the contrasts are lavaan's Wald results, which use a large-sample normal reference distribution.

References

Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525-543.

Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36.

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4-70.