Mixing CFA and EFA to handle data heterogeneity

In psychological and social sciences, rating scales and questionnaires are often administered to samples which may show some levels of heterogeneity. This heterogeneity could bias statistical analyses if not properly treated. Standard factor analysis models assume that all the subjects would follow a common model, ignoring the effects of sample heterogeneity. In this contribution we propose a mixture of Confirmatory Factor Analysis (CFA) and Exploratory Factor Analysis (EFA) to cluster heterogeneity showed by respondents. The goal is to allow EFA to account for clusters of respondents that do not follow the confirmatory model hypothesized by the researcher. A simulation study has been conducted to assess the properties of the proposed mixture CFA model.