Latent class models for multiple ordered categorical health data: testing violation of the local independence assumption

Latent class models are now widely applied in health economics to analyse heterogeneity in multiple outcomes generated by subgroups of individuals who vary in unobservable characteristics, such as genetic information or latent traits. These models rely on the underlying assumption that associations between observed outcomes are due to their relationship to underlying subgroups, captured in these models by conditioning on a set of latent classes. This implies that outcomes are locally independent within a class. Local independence assumption, however, is sometimes violated in practical applications when there is uncaptured unobserved heterogeneity resulting in residual associations between classes. While several approaches have been proposed in the case of binary and continuous outcomes, little attention has been directed to the case of multiple ordered categorical outcome variables often used in health economics. In this paper, we develop an approach to test for the violation of the local independence assumption in the case of multiple ordered categorical outcomes. The approach provides a detailed decomposition of identified residual association by allowing it to vary across latent classes and between levels of the ordered categorical outcomes within a class. We show how this level of decomposition is important in the case of ordered categorical outcomes. We illustrate our approach in the context of health insurance and healthcare utilization in the US Medigap market.