Measurement and Structural Models

When learning SEM, an important distinction to recognize from the start is that between a measurement model and a structural model.

A measurement model consists only of factor-loading paths from the latent constructs (factors) to their manifest indicators, non-directional correlations between constructs (like an oblique factor analysis), and in rare circumstances, correlations between the some of the indicators' residual (error) terms.

When the implementation of a measurement model involves only a single questionnaire instrument and the researcher is seeking to verify an a priori conceptualization of which constructs (subscales) go with which items, then that particular kind of model is a confirmatory factor analysis (CFA).

The differences between confirmatory (CFA) and exploratory (EFA) types of factor analysis should be apparent:

1. In EFA, the number of factors is empirically determined by consulting numerical values generated by the computer (i.e., Kaiser criterion, scree test, parallel analyses), whereas in CFA, the researcher decides the number of factors, based on conceptual/theoretical grounds or precedent in the literature.

2. In EFA, determination of which items go with which factors is, again, done empirically via the factor loadings generated by the computer (which can sometimes create problems if an item loads strongly on more than one factor). In CFA, the assignment of items (manifest indicators) to constructs is, again, done on conceptual grounds. Dual-loading items are avoided in CFA, as the researcher will have each manifest indicator receive an incoming factor-loading path from only one construct (factor).

Once the researcher settles on his or her measurement model (i.e., what the constructs are, and what the manifest indicators are of each), then he or she can develop the structural model. A structural model is simply the network of directional, "causal" paths between constructs. For example, a "life stress" construct (with, perhaps, manifest indicators for work stress, home stress, and miscellaneous stress) might have a directional arrow to a "physical symptoms" construct (with indicators for head and stomach ache, fatigue, and back and joint pain).

This study of family functioning and adolescent development by Cumsille et al. provides some nice diagrams of measurement and structural models (and will also be good to return to later in the semester when we cover multiple-group modeling).