Statistical Methodology

How many underlying characteristics (or factors) does a set of survey questions measure? When subjects answer a set of self-report questions, is it more appropriate to analyze the questions individually, to pool responses to all of the questions to form one global score, or to combine subsets of related questions to define multiple underlying factors? Factor analysis is the statistical method of choice for answering such questions. When researchers have no idea beforehand about what factors may underlie a set of questions, they use exploratory factor analysis to infer the best explanatory model from observed data "after the fact." If, on the other hand, researchers have a hypothesis beforehand about the underlying factors, then they can use confirmatory factor analysis (CFA) to evaluate how well this model explains the observed data and to compare the model's goodness-of-fit with that of other competing models. This article describes the basic rules and building blocks of CFA: what it is, how it works, and how researchers can use it. The authors begin by placing CFA in the context of a common research application-namely, assessing quality of medical outcome using a patient satisfaction survey. They then explain, within this research context, how CFA is used to evaluate the explanatory power of a factor model and to decide which model or models best represent the data. The information that must be specified in the analysis to estimate a CFA model is highlighted, and the statistical assumptions and limitations of this analysis are noted. Analyzing the responses of 1,614 emergency medical patients to a commonly-used "patient satisfaction" questionnaire, the authors demonstrate how to: 1) compare competing factor-models to find the best-fitting model; 2) modify models to improve their goodness-of-fit; 3) test hypotheses about relationships among the underlying factors; 4) examine mean differences in "factor scores"; and 5) refine an existing instrument into a more streamlined form that has fewer questions and better conceptual and statistical precision than the original instrument. Finally, the role of CFA in developing new instruments is discussed.