Regularized multigroup exploratory approximate factor analysis for easy analysis of complex data

Exploring multigroup data for similarities and differences in the measurement model is a substantial part of the research conducted in the behavioral and social sciences. Examples include studying the measurement invariance of psychological scales over age or ethnic groups and comparing symptom correlations between different psychological disorders. Multigroup exploratory factor analysis is often the method of choice. However, currently available methods are restrictive in their use. First, these methods cannot handle complex data with small sample sizes relative to the number of variables, while high-dimension, low-sample-size data are increasingly used as a result of digitalization (e.g., word counts obtained by text mining of online messages or omics data). Second, the use of existing software is often arduous. Here, we propose a regularized exploratory approximate factor analysis method that addresses these issues by building on a strong computational framework: The resulting method yields solutions that are constrained to show simple structure and similarity of the loadings over groups when supported by the data. The minimal input required is restricted to the data and number of factors. In a simulation study, we show that the method considerably outperforms existing methods, also in the low-dimensional setting; publicly available genomics data on different psychopathologies are used to illustrate that the method works in the ultrahigh-dimensional setting. Implementation of the method in the R software language for statistical computing is publicly available on GitHub, including the code used to conduct the simulation study and to perform the analyses of the three empirical data sets.