Local Associations in Latent Class Analysis: Using Configural Frequency Analysis for Model Evaluation

Abstract

It is proposed to enrich the arsenal of methods for the evaluation of local independence within latent classes by methods from Configural Frequency Analysis (CFA). CFA provides researchers with two additional options. The first involves identifying those patterns of categories of manifest variables that contradict the assumption of local independence within a given class. If such patterns exist, local independence is viewed as violated not (only) at the level of relations among variables, but at the level of individual patterns that occur at rates significantly different than expected under the assumption of variable inde-pendence. The second option involves comparing classes at the level of individual patterns. The results of such a comparison of classes can be that outlying patterns are identified as class-specific. Second, it is possible that classes differ in the occur-rence rates of individual patterns (i.e., specific response patterns may be more likely to occur in certain classes). This can occur even when these patterns do not contradict the assumption of local independence. An empirical example is given using data on alcohol consumption behavior among college students. Extensions and applications of the proposed methods are discussed.