*My understanding is that when an indicator has no relation to the latent construct of interest, this is represented differently in LCA than in factor analysis. Can you explain how and why this works? ––**Signed, Latently Lost*

Dear Lost,

In factor analysis, factor loadings are regression coefficients, so a factor loading of zero represents “no relation” between the manifest indicator and the latent factor, whereas factor loadings closer to -1 and 1 represent stronger relations. In comparison, in latent class analysis, item-response probabilities play the same conceptual role as factor loadings, but they are conditional probabilities, not regression coefficients. Item-response probabilities closer to 0 and 1 represent stronger relations between the manifest indicator and latent class variable. The closer item-response probabilities are to 1/(marginal probability) for all classes, the weaker the relation between the manifest variable and the latent class variable. “High homogeneity” refers to the degree to which item-response probabilities are close to 0 and 1 in latent class analysis; this concept is similar to the concept of “saturation” in factor analysis.

Ideally, the pattern of item-response probabilities also clearly identifies latent classes with distinguishable interpretations; this concept of “latent class separation” is similar to the concept of “simple structure” in factor analysis. When model selection is difficult due to conflicting information from fit criteria, the concepts of homogeneity and latent class separation can be a helpful way to approach model selection based on relevant theory from your specific field.

Happy analyzing!