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

Abstract

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.

A General 3-Step Maximum Likelihood Approach to Estimate the Effects of Multiple Latent Categorical Variables on a Distal Outcome

“…Through the simulation study, we evaluate the relative performance of the two methods when the within-class distribution of a continuous Z exhibits skewness, excess kurtosis, and bimodality, respectively. The results for bimodality are given in the supplementary material as they are similar to results for the single latent variable case (Bakk et al, 2014; but with slightly lower coverage in situations with poor class separation. We also conduct simulations using the modified BCH approach (detailed results in the supplementary material) as previous research confirmed its robustness to violations of distributional assumptions (Asparouhov & Muthén, 2014b;.…”

“…One possible explanation is that at low entropy levels, the differences between classes are over-stated, which leads to an underestimation of the classification error (Bakk et al, 2014;Vermunt, 2010). Standard errors are severely underestimated using the modified BCH approach, although using a sandwich variance estimator provides a slight correction.…”

“…First, the measurement model cannot include covariates as otherwise both the covariates and the outcomes will be predicted by C after Bayes transformation (Asparouhov & Muthén, 2014a). Second, when the within-class distribution of Z has outliers, the estimated mean of Z is severely biased Bakk, Oberski, and Vermunt (2014). They also find that for continuous Z the LTB approach produces heavy bias when heterogeneity across classes is not accounted for.…”

“…A standard error correction method was proposed by Bakk et al (2014) that takes into account this additional source of variation.…”

“…Similar to previous research (Asparouhov & Muthén, 2014a;Bakk et al, 2014;, varying sample sizes are considered and we manipulate the entropy levels through class-specific thresholds in the measurement model. Specifically, entropy values of 0.7 (high) and 0.4 (low) correspond to logit thresholds of 1.25 and 0.75, respectively.…”