Estimating the association between latent class membership and external variables using bias-adjusted three-step approaches

Latent class analysis is a clustering method that is nowadays widely used in social science research. Researchers applying latent class analysis will typically not only construct a typology based on a set of observed variables but also investigate how the encountered clusters are related to other, external variables. Although it is possible to incorporate such external variables into the latent class model itself, researchers usually prefer using a three-step approach. This is the approach wherein after establishing the latent class model for clustering (step 1), one obtains predictions for the class membership scores (step 2) and subsequently uses these predicted scores to assess the relationship between class membership and other variables (step 3). Bolck, Croon, and Hagenaars (2004) showed that this approach leads to severely downward-biased estimates of the strength of the relationships studied in step 3. These authors and later also Vermunt (2010) developed methods to correct for this bias. In the current study, we extended these correction methods to situations where class membership is not predicted but used as an explanatory variable in the third step, a situation widely encountered in social science applications. A simulation study tested the performance of the proposed correction methods, and their practical use was illustrated with real data examples. The results showed that also when the latent class variable is used as a predictor of external variables, the uncorrected three-step approach leads to severely biased estimates. The proposed correction methods perform well under conditions encountered in practice.
Keywords: latent class analysis, three-step approach, bias adjustment, covariates, distal outcomes, multiple latent variables