Investigating the Applicability of Alignment-A Monte Carlo Simulation Study.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Traditional multiple-group confirmatory factor analysis (CFA) relies on strict scalar invariance assumptions.
• The alignment methodology offers an alternative for evaluating measurement invariance and enabling factor mean comparisons without scalar invariance.
• Previous research has explored alignment's applicability, but further investigation into group sizes and performance with cross-loadings is needed.

Purpose of the Study:

• To determine the minimal group sizes required for the alignment methodology in three-factor models.
• To compare the performance of multiple-group CFA, multiple-group ESEM, and alignment under varying conditions of cross-loadings.
• To provide recommendations for the application of these methods based on simulation results.

Main Methods:

• A simulation study was conducted in two parts.
• Study 1 investigated minimal group sizes for alignment with varying numbers of groups and presence/absence of noninvariant parameters.
• Study 2 compared multiple-group CFA, multiple-group ESEM, and alignment by manipulating proportions and magnitudes of cross-loadings.

Main Results:

• Alignment requires lower group sizes (e.g., 150-250) when no noninvariant parameters exist. With noninvariant parameters, group sizes of 250-350 are recommended depending on the number of groups.
• Multiple-group CFA performs well with minimal cross-loadings. Multiple-group ESEM is robust to small or few medium cross-loadings.
• Alignment is suitable for models with small cross-loadings and few noninvariant parameters. Aligned ESEM (AESEM) is effective when both noninvariant parameters and cross-loadings are present.

Conclusions:

• The alignment methodology demonstrates superior performance across a wider range of conditions compared to multiple-group CFA and multiple-group ESEM.
• Recommendations are provided for selecting between multiple-group CFA, multiple-group ESEM, alignment, and AESEM based on model characteristics and invariance assumptions.
• The choice of method depends on the presence and nature of noninvariant parameters and cross-loadings, with alignment and AESEM offering greater flexibility.