Methods to Account for Uncertainty in Latent Class Assignments When Using Latent Classes as Predictors in Regression Models, with Application to Acculturation Strategy Measures

Abstract

Latent class models have become a popular means of summarizing survey questionnaires and other large sets of categorical variables. Often these classes are of primary interest to better understand complex patterns in data. Increasingly, these latent classes are reified into predictors of other outcomes of interests, treating the most likely class as the true class to which an individual belongs even though there is uncertainty in class membership. This uncertainty can be viewed as a form of measurement error in predictors, leading to bias in the estimates of the regression parameters associated with the latent classes. Despite this fact, there is very limited literature treating latent class predictors as measurement error models. Most applications ignore this issue and fit a two-stage model that treats the modal class prediction as truth. Here, we develop two approaches—one likelihood-based, the other Bayesian—to implement a joint model for latent class analysis and outcome prediction. We apply these methods to an analysis of how acculturation behaviors predict depression in South Asian immigrants to the United States. A simulation study gives guidance for when a two-stage model can be safely implemented and when the joint model may be required.

Associations of Four sensitization patterns revealed by Latent Class Analysis with Clinical symptoms: A multi-center study of China

“…To evaluate the potential bias resulting from treating the most likely class revealed by LCA as the true class to estimate the regression parameters in the logistic regression model. 22 The BCH approach was additionally performed to investigate the associations of sensitization patterns with clinical symptoms using the SAS % LCA_Distal_BCH macro. 23 Moreover, multivariate model1 was established to adjust for some potential confounding factors with a p -value less than 0.05 in the univariate analysis, including age, smoking exposure, habitual residence, ethnic group and region.…”

Describing complex disease progression using joint latent class models for multivariate longitudinal markers and clinical endpoints

“…Linking latent classes to external outcomes, as done in MSA with MRI, CSF and plasma markers, constitutes one direction of research of its own due to the difficulty to account for the uncertainty in the estimated latent class structure [34,33,40,32]. In our work, we chose to directly integrate the external outcomes into the joint model program to correctly handle the uncertainty on the latent class membership, as suggested by others in a different latent class framework [32].…”

“…In both cases, a naive approach consists in running the posterior regressions on an estimate of c i (for instance the most likely class ĉi ) instead of the true unknown c i , and neglecting the uncertainty in the estimate of c i . The inference quality of this naive method, usually called "2-stage" [32] or "3-step" method [33], highly depends on the discrimination of the latent classes. While it can provide negligible bias in case of high separated classes (with high posterior probabilities, high entropy), it may become substantially biased in the case of rather poor discrimination [32,34,33].…”

“…The inference quality of this naive method, usually called "2-stage" [32] or "3-step" method [33], highly depends on the discrimination of the latent classes. While it can provide negligible bias in case of high separated classes (with high posterior probabilities, high entropy), it may become substantially biased in the case of rather poor discrimination [32,34,33]. Alternatives consist either in corrections in the multi-step analysis to account for the uncertainty [33], or directly in the joint estimation of all the variables of interest including the external information X i extern and/or Y extern i to internally handle the measurement error in the latent class assignment [32].…”

Hypertension and Diabetes Status by Patterns of Stress in Older Adults From the US Health and Retirement Study: A Latent Class Analysis

“…In addition, LCA is well suited to address calls for comprehensive psychosocial measures of stress given the ability of latent class modeling to explicitly model measurement error when estimating complex relationships. 39 …”