EFA.dimensions (version 0.1.8.8)

Factorial_Invariance: Factor Model Invariance

Description

Conducts tests for configural, metric, scalar, and strict invariance of factor models across groups.

Usage

Factorial_Invariance(model, data, group, estimator = 'ML', verbose = TRUE)

Value

A list containing the following components:

fitcoefs_by_group

The model fit coefficients for each group separately

model_Configural

The parameter estimates for the configural invariance model

model_Metric

The parameter estimates for the metric invariance model

model_Scalar

The parameter estimates for the scalar invariance model

model_Strict

The parameter estimates for the strict invariance model

inv_model_fits

The invariance model fit coefficients

inv_model_fit_diffs

Differences in the invariance model fit coefficients

chisq_diffs

Chi-Squared model differences tests

Arguments

model

A CFA model in lavaan package format. Example:

model_RSE <- '
pos_items =~ Q1 + Q2 + Q4 + Q6 + Q7
neg_items =~ Q3_R + Q5_R + Q8_R + Q9_R + Q10_R '

data

A dataframe with the model variables and the group factor.
Example: data = data_RSE_sex

group

The name of the group variable in data.
Example: group = 'gender'

estimator

The name of the lavaan estimator to be used in the analyses.
The options for basic estimators (continuous data) are ML, GLS, WLS, DWLS, ULS, DLS, and PML.
The options for robust estimators are MLM, MLMVS, MLMV, MLF, MLR, WLSM, WLSMVS, WLSMV, ULSM, ULSMVS, and ULSMV.
Example: estimator = 'ML'

verbose

(optional) Should detailed results be displayed in console?
TRUE (default) or FALSE

Author

Brian P. O'Connor

Details

This is a wrapper function that uses functions from the lavaan (Rosseel, 2012) and semTools (Jorgensen et al., 2026) packages.

The analyses can be run for regular CFAs or for ESEM measurement models. See the Examples below.

References

Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling. R package version 0.5-8. Retrieved from https://CRAN.R-project.org/package=semTools

Milfont, T. L., & Fischer, R. (2015). Testing measurement invariance across groups: Applications in cross-cultural research. International Journal of Psychological Research, 3, 111130.

Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 136.

Stark, S., Chernyshenko, O. S., & Drasgow, F. (2006). Detecting differential item functioning with confirmatory factor analysis and item response theory: Toward a unified strategy. Journal of Applied Psychology, 91(6), 12921306.

Stein, J. A., Lee, J. W., & Jones, P. S. (2006). Assessing cross-cultural differences through use of multiple-group invariance analyses. Journal of Personality Assessment, 87(3), 249258.

Tan, T. (2024) Frequentist and Bayesian factorial invariance using R. Practical Assessment, Research, and Evaluation. 29(8), 1-34.

Examples

model_RSE <- '
   pos_items =~ Q1 + Q2 + Q4 + Q6 + Q7
   neg_items =~ Q3_R + Q5_R + Q8_R + Q9_R + Q10_R '

Factorial_Invariance(model = model_RSE, data = data_RSE_sex, 
                     group = 'gender', estimator = 'ML')
# \donttest{
# run Factorial_Invariance for an ESEM model
# first, use the ESEM function to obtain the esem_model_syntax (without the group variable, gender)
esem_output <- ESEM(data = subset(data_RSE_sex, select = -c(gender)), Nfactors = 2)

Factorial_Invariance(model = esem_output$esem_model_syntax, data = data_RSE_sex, 
                     group = 'gender', estimator = 'ML')
# }