Local Dependence in Latent Class Analysis of Rare and Sensitive Events

Abstract

For survey methodologists, latent class analysis (LCA) is a powerful tool for assessing the measurement error in survey questions, evaluating survey methods, and estimating the bias in estimates of population prevalence. LCA can be used when gold standard measurements are not available and applied to essentially any set of indicators that meet certain criteria for identifiability. LCA offers quality inference, provided the key threat to model validity-namely, local dependence-can be appropriately addressed either in the study design or in the model-building process. Three potential causes threaten local independence: bivocality, behaviorally correlated error, and latent heterogeneity. In this article, these threats are examined separately to obtain insights regarding (a) questionnaire designs that reduce local dependence, (b) the effects of local dependence on parameter estimation, and (c) modeling strategies to mitigate these effects in statistical inference. The article focuses primarily on the analysis of rare and sensitivity outcomes and proposes a practical approach for diagnosing and mitigating model failures. The proposed approach is empirically tested using real data from a national survey of inmate sexual abuse where measurement errors are a serious concern. Our findings suggest that the proposed modeling strategy was successful in reducing local dependence bias in the estimates, but its success varied by the quality of the indicators available for analysis. With only three indicators, the biasing effects of local dependence can usually be reduced but not always to acceptable levels.

Keywords: National Inmate Survey (NIS); bivocality; correlated error; expeculation; latent heterogeneity; local dependence; model misspecification.

Figure 1.

Relative bias in the false-negative rate of a bivocal indicator by correlation level between the latent variables X and Y.

Figure 2.

Relative bias in estimated prevalence probability due to correlated error as a function of the correlation and false-negative probability.

Figure 3.

False-negative rate in indicator by group as correlation between G and H increases.