Relating Latent Class Assignments to External Variables: Standard Errors for Correct Inference

Latent class analysis is used in the political science literature in both substantive applications and as a tool to estimate measurement error. Many studies in the social and political sciences relate estimated class assignments from a latent class model to external variables. Although common, such a “three-step” procedure effectively ignores classification error in the class assignments; Vermunt (2010, “Latent class modeling with covariates: Two improved three-step approaches,” Political Analysis 18:450–69) showed that this leads to inconsistent parameter estimates and proposed a correction. Although this correction for bias is now implemented in standard software, inconsistency is not the only consequence of classification error. We demonstrate that the correction method introduces an additional source of variance in the estimates, so that standard errors and confidence intervals are overly optimistic when not taking this into account. We derive the asymptotic variance of the third-step estimates of interest, as well as several candidate-corrected sample estimators of the standard errors. These corrected standard error estimators are evaluated using a Monte Carlo study, and we provide practical advice to researchers as to which should be used so that valid inferences can be obtained when relating estimated class membership to external variables.