How Correcting Latent Class Bias Can Underestimate Uncertainty

Insights from the Field

latent class

classification error

standard errors

three-step

Monte Carlo

Relating Latent Class Assignments to External Variables: Standard Errors for Correct Inference was authored by Zsuzsa Bakk, Daniel L. Oberski and Jeroen K. Vermunt. It was published by Cambridge in Pol. An. in 2014.

🔎 What's at stake?

Latent class analysis (LCA) is widely used in political science for substantive applications and to estimate measurement error. A common "three-step" practice relates estimated class assignments from an LCA to external variables while effectively ignoring classification error. Vermunt (2010, Latent class modeling with covariates: Two improved three-step approaches, Political Analysis 18:450–69) demonstrated that this omission produces inconsistent parameter estimates and proposed a bias correction that is now implemented in standard software. Inconsistency, however, is not the only problem.

📉 A hidden source of uncertainty

The bias-correction method that fixes inconsistency also introduces an additional source of variance into third-step estimates. If that extra variance is not accounted for, reported standard errors and confidence intervals are overly optimistic, producing anti-conservative inference.

📐 What was derived and proposed

The asymptotic variance of the third-step estimates of interest was derived to capture the extra variability introduced by the correction.
Several candidate sample estimators that correct standard errors were developed to allow valid inference in practice.

🧪 How the corrections were evaluated

A Monte Carlo study was used to evaluate the performance of the proposed corrected standard error estimators across scenarios representative of typical LCA applications.

✅ Key findings

The Vermunt (2010) correction removes bias (resolves inconsistency) but increases estimator variance.
Ignoring the additional variance leads to underestimated standard errors and overly narrow confidence intervals.
The derived asymptotic variance provides the theoretical basis for accurate inference about relations between estimated class membership and external variables.
Several practical sample-based standard error estimators were assessed; their finite-sample performance is documented to guide applied work.

🛠️ Practical takeaway

Guidance is provided on which corrected standard error estimators researchers should use so that valid inferences can be obtained when relating estimated class membership to external variables.