Confirmatory factor analysis (model testing in structural equation modeling):
Variables (usually at least 5) are observable indicators of one or more underlying factors that are identified in a theory or model. Structural equation models investigate the plausibility of theoretical models that might explain (summarize) the interrelations among a set of variables.
Hypothesis: The specified theoretical measurement model or the confirmatory factor analysis model better represents (fits) the observed data than do other measurement or confirmatory factor analysis models.
Example: In the field of nutrition, variables indicating the amount of consumption of fruits and vegetables will be intercorrelated, as will variables indicating the amount of consumption of beef, pork, and chicken. A theoretical model that specifies that there are two factors [(1) fruits/vegetables, and (2) meats)] may adequately summarize the interrelationships among the variables.