Psychological Variables and Multi-Item Scales

For psychological variables, the typical data- gathering tool is a multi-item scale completed by the respondent. For such data, we gener­ally require evidence of reliability, especially internal consistency reliability as assessed, for example, by Cronbach’s α.

If using PCA or EFA, the investigator attempts to create a set of measures, with all the measures in the set being indicators of one or more scale dimensions. Then the investiga­tor may (a) eliminate items that do not load on a particular factor of interest by some criteria and then add or average the resulting items, or (b) compute component or factor scores for the one or more dimensions that the researcher deems to be interpretable (e.g., Vangelisti & Crumley’s, 1998, study of underlying factors of hurtful messages). For the second method, Serlin and Kaiser (1976) have demonstrated how to easily compute Cronbach’s α from a PCA (see also Hancock & Mueller, 2001, for a maximal reliability coefficient, H, which is used to estimate the information captured by the indicators in a measurement model).

Measurement models consist of indicators (e.g., items from a multi-item scale or scores by coders or judges) and the unobserved fac­tors that are considered to be the causes of the indicators and that are supposed to account for the correlations among them.

There are a number of theoretical and ana­lytical advantages of a CFA or SEM over EFA and PCA, although all these techniques may be used in a single study. Although EFA and PCA reveal the dimensionality of the measures as well as their loadings on the dimensions, they do not actually test the structure imposed by the investigator. Typically, an investigator using EFA or PCA finds that there is likely to be more than one dimension for a scale that was hypothesized to be unidimensional and that a given item may be associated with more than one dimension, but there is no overall hypothesis that tests these findings.

There are two broad options for conduct­ing a CFA: First, one may impose a specific model on the set of items (e.g., they are uni­dimensional) for each multi-item construct included in the study and test the model for each construct. Second, one may include all multi-item measures and simultaneously test them all. A third option, SEM, includes each CFA measurement model within an overall model that also includes the predicted rela­tions among the theoretical (latent) variables. The advantage of SEM and of both options of CFA is in the word test: With the causal relations specified among the measures and their factors (meeting the necessary statistical assumptions, and with enough items per fac­tor and a reasonable sample size), CFA and SEM test a null hypothesis that the population model imposed by the investigator accounts for the estimated covariances (or correlations) among the items. In addition, CFA and SEM have various measures of goodness of fit and are rigorous ways of assessing the structure of sets of measures or sets of measures plus their theoretical relationships (see Fink, 1980; Hayduk, 1987; for an SEM example for con­flict resolution, see O’Connell-Corcoran & Mallinckrodt, 2000).