Exploratory Factor Analysis
You should already understand the difference between exploratory and confirmatory factor analysis. MPlus can estimate either one, and even use exploratory factor analysis for one part of a model while it uses confirmatory factor analysis for another part of the same model.
Exploratory factor analysis can be specified either through the analysis: command or by using a parenthetic label in the model: command.
title: EFA, specified as analysis data: file is ex4.1a.dat; variable: names are y1-y12; analysis: type = EFA 1 4;
Specifying type = EFA requires you to specify a minimum number and a maximum number of factors to be extracted, and compares the fit of these different models. The other way to specify an exploratory factor analysis is through the model: command:
title: EFA, specified as model data: file is ex4.1a.dat; variable: names are y1-y12; model: f1-f4 BY y1-y12 (*1);
Here, the parenthetical (*label) is the crucial part of the command that signifies an exploratory factor analysis. The output now describes your model in terms similar to a structural equation model, and also produces a diagram. But note that factors have been extracted and rotated (this is described in the preliminary portion of the output), and this is not the simple SEM estimation that might be suggested by the parameter output and the diagram.
Many different optimizing rotations are available, but there is no simple specification for principal components analysis, and some rotations like varimax cannot be used in combination with other modeling requests, i.e. not as a component within a larger model.
The MPlus documentation does not describe any of this in technical detail, but points to references in the literature.
title: EFA, varimax rotation data: file is ex4.1a.dat; variable: names are y1-y12; analysis: type=efa 1 4; rotation=varimax;