Confirmatory Factor Analysis and Structural Equation Models

Abstract

An exploratory factor analysis as described in Chapter 5 is used in the early investigation of a set of multivariate data to determine whether the factor analysis model is useful in providing a parsimonious way of describing and accounting for the relationships between the observed variables. The analysis will determine which observed variables are most highly correlated with the common factors and how many common factors are needed to give an adequate description of the data. In an exploratory factor analysis, no constraints are placed on which manifest variables load on which factors. In this chapter, we will consider confirmatory factor analysis models in which particular manifest variables are allowed to relate to particular factors whilst other manifest variables are constrained to have zero loadings on some of the factors. A confirmatory factor analysis model may arise from theoretical considerations or be based on the results of an exploratory factor analysis where the investigator might wish to postulate a specific model for a new set of similar data, one in which the loadings of some variables on some factors are fixed at zero because they were “small” in the exploratory analysis and perhaps to allow some pairs of factors but not others to be correlated. It is important to emphasise that whilst it is perfectly appropriate to arrive at a factor model to submit to a confirmatory analysis from an exploratory factor analysis, the model must be tested on a fresh set of data. Models must not be generated and tested on the same data.