Factor Analysis: Confirmatory

Confirmatory Factor Analysis Defined

In social sciences, the hypotheses are often generated from conceptual definitions or theoretical models. The conceptual definitions provide a description of the construct in question, and a factor analysis is performed to test the consistency between what is theorized as a construct and what is actually observed. The confirmatory factor analysis, then, is a technique used to determine how well a theoretical model fits the factor structure in reference to a second-order construct. A researcher may decide that three factors, for example, make up a factor structure, and are unrelated to one another; however, when [Page 506]all three factors operate at the same time, a second-order, or latent, variable emerges. Generally, the degree to which the data fit the theoretical model generates evidence to confirm the inferences about the latent factor, or underlying theory.

A major difference between other types of factor analysis and confirmatory factor analysis depends on the application of hypotheses. A researcher only interested in exploring how sample data reflect consistency among an indefinite amount of factors may perform factor analysis. In that case, specific hypotheses about how factors relate to one another or even how many factors emerge are not necessary. The researcher’s primary focus is on exploring how many and which type of factors emerge; hence, exploratory factor analysis. However, once a researcher believes specific details about factors ahead of time, a priori, and believes that such factors share a specific quantity of variance, the hypotheses become necessary. Such is the case for confirmatory factor analysis. The hypotheses are derived from rationale, and apply constraints to testing techniques, such as theorized covariance among factors and loading among items. The confirmatory factor analysis then becomes useful to confirm specific theoretical assumptions surrounding the factor structure. In other words, confirmatory factor analysis is theory-driven, whereas exploratory is not.

Social sciences tend to prefer an order for performing exploratory and confirmatory factor analyses. Typically, not exclusively, any time research is performed, a rationale or theoretical reasoning precedes testing. From the rationale, the hypotheses are generated. Given results from the factor analysis indicate a good model fit according to the hypotheses, an exploratory factor analysis holds little value to establish further evidence for the argument. However, when confirmatory factor analytic results indicate the model does not fit, an exploratory factor analysis becomes more appropriate. That is because exploratory factor analyses allow for more freedom, or fewer constraints among factor and loading structures, and therefore often provide insight on valuable modifications for future research.

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