Asymptotic efficiency of the pseudo-maximum likelihood estimator in multi-group factor models with pooled data

Area of Science:

• Statistics
• Psychometrics
• Econometrics

Background:

• Multi-group factor models are effective for stratified data but demand large sample sizes to prevent convergence issues.
• Pooling data and fitting a single-group factor model using maximum likelihood is a potential alternative.
• Pseudo-maximum likelihood (PML) estimators offer a method for analyzing pooled data.

Purpose of the Study:

• To investigate the properties of pseudo-maximum likelihood (PML) estimators when applied to pooled data.
• To compare the asymptotic efficiency of PML estimators with multi-group maximum likelihood estimators.
• To examine the impact of data pooling on factor loading variances, particularly in two-group scenarios.

Main Methods:

• Analysis of pseudo-maximum likelihood (PML) estimators for pooled data, assuming normal distribution.
• Comparison of asymptotic efficiency between PML and multi-group maximum likelihood estimators.
• Investigation of a two-group factor model to assess the effects of pooling.
• Monte Carlo simulation to evaluate small-sample properties of PML estimators.

Main Results:

• Under normal theory, pooled data factor loading variances can be underestimated when error variances are larger in the smaller group.
• This underestimation arises from the dependence between pooled factors and pooled error terms.
• The asymptotic efficiency of PML estimators was compared to multi-group maximum likelihood estimators.

Conclusions:

• Pooling data with PML estimators can lead to underestimation of factor loading variances, particularly when group error variances differ.
• The dependence between pooled factors and errors is identified as the cause of underestimation.
• Further Monte Carlo studies are needed to fully understand the small-sample performance of PML estimators in such contexts.