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Selection of Factor Extraction Methods in Complicated Research Contexts: Practice Recommendations
It is a common practice among social scientists to use “factor analysis” and “principal components analysis” interchangeably, even though PCA is not a factor extraction method, but a dimension reduction technique. Most of the recent studies with factor analysis rely solely on PCA or fail to specify which factor extraction method was used. Supposedly, it is caused by the lack of structured and comprehensive guidance on the selection of factor extraction methods. The aim of this study is to develop a theoretically and empirically justified algorithm of factor extraction method selection, depending on a combination of research context features, such as (a) sample size, (b) number of indicators specifying each factor, (c) size, (d) range of communalities, (e) presence of model error and (f) distribution of indicators. Seven factor extraction methods were studied: principal component analysis, weighted and generalized least squares method, maximum likelihood method, principal axis analysis, alpha-factor analysis, and image factoring.
Theoretically justified algorithm was created and tested via statistical experiment with Monte Carlo simulation. Following the general outline of previous works’ experimental designs, we specified factor loadings matrices for each research context with nonzero loadings, derived correlation matrices and produced 500 Monte Carlo simulated samples (3000 samples in total) per research context. Every factor extraction method was applied to every sample and the resulting factor loadings matrices and communalities were recorded and summarized. Four criteria of factor analysis extraction adequacy were applied: squared mean errors of factor loadings, squared mean errors and absolute mean errors of communalities, and number of Heywood cases.
As a result we formulated four main recommendations: it is advised to use (1) principal axis analysis or alpha-factor analysis, if a model error is suspected, (2) maximum likelihood method or generalized least squares method, if the sample is large enough and indicators are normally distributed, or vice versa, if the sample is not large enough and distribution of indicators differs from normal, (3) maximum likelihood method, if the sample is large enough, but the indicators are not normally distributed, or if the indicators are normally distributed, but the sample size is not large enough and the communalities are small, (4) generalized least squares method, if the indicators are normally distributed and the communalities are large, but the sample size is not large enough.