Impact of error structure misspecification when testing measurement invariance and latent-factor mean difference...

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Error variance-covariance structures can differ across groups in multiple-group comparisons.
• Inaccurate assumptions about these structures can affect statistical testing outcomes.

Purpose of the Study:

• To investigate the impact of misspecified error structures on measurement invariance testing.
• To examine the effects on latent-factor mean difference estimation between groups.

Main Methods:

• A Monte Carlo simulation study was conducted.
• Employed multiple-group confirmatory factor analysis (MGCFA) and the multiple-indicator multiple-causes (MIMIC) model.
• Assessed rejection rates for metric and strict invariance, estimation accuracy, and statistical inference for factor mean differences under misspecification.

Main Results:

• Misspecification of error structures significantly affected metric invariance testing, often leading to rejection, particularly when error covariance was ignored.
• Scalar invariance testing was not significantly affected by error structure misspecification.
• Both MGCFA and MIMIC demonstrated robust performance in detecting latent-factor mean differences, showing acceptable power and controlled Type I errors.

Conclusions:

• Researchers should carefully consider and test for heterogeneity in error structures when conducting multiple-group analyses.
• While metric invariance testing is sensitive to error structure misspecification, latent mean difference estimation remains reliable with appropriate models.