Building a better model: an introduction to structural equation modelling.

Confirmatory factor analysis (CFA) and structural equation modelling (SEM) are powerful extensions of path analysis, which was described in a previous article in this series. CFA differs from the more traditional exploratory factor analysis in that the relations among the variables are specified a priori, which permits more powerful tests of construct validity for scales. It can also be used to compare different versions of a scale (for example, English and French) and to determine whether the scale performs equivalently in different groups (for example, men and women). SEM expands on path analysis by allowing paths to be drawn between latent variables (which, in other techniques, are called factors or hypothetical constructs), that is, variables that are not seen directly but, rather, through their effect on observable variables, such as questionnaires and behavioural measures. Each latent variable and its associated measured variables form small CFAs, with the added advantage that the correlations among the variables can be corrected for the unreliability of the measures.