Factor analysis is a statistical method that is used to determine the number of underlying dimensions contained in a set of observed variables and to identify the subset of variables that corresponds to each of the underlying dimensions. The underlying dimensions are referred to as continuous latent variables or factors. The observed variables are referred to as factor indicators. There are two types of factor analysis: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA).
EFA is a technique that attempts to determine the minimum number of continuous latent variables or factors that can adequately describe the correlations among a set of observed variables. The model is exploratory in the sense that it does not impose a structure on the relationship between the observed variables and the continuous latent variables but only specifies the number of continuous latent variables. The goal of exploratory factor analysis is to find the smallest number of interpretable factors that can adequately explain the correlations among a set of variables. It is important that the factors be interpretable according to a recognized theory in addition to the model fitting the data well. Exploratory factor analysis results can be influenced by the set of variables included in the analysis. Therefore, it is important that the set of variables be developed carefully with the aim of measuring specific content areas prior to using EFA to study the intended dimensionality. When used with such a set of variables, EFA can be a useful tool not only for understanding the dimensionality of a set of variables but also for isolating variables that do not measure the dimensions well. EFA can be helpful during pilot work in the development of a set of items.
In Mplus, factor indicators for EFA may be continuous, categorical (binary or ordered polytomous), or a combination of continuous and categorical. When factor indicators are all continuous, Mplus has four estimator choices: maximum likelihood (ML), maximum likelihood with robust standard errors and chi-square (MLM, MLMV), and unweighted least squares (ULS). When at least one factor indicator is categorical, Mplus has four estimator choices: weighted least squares (WLS), robust weighted least squares (WLSM, WLSMV), and unweighted least squares (ULS).