A hierarchical latent class model for predicting disability small area counts from survey data

TL;DR

This paper develops a Bayesian hierarchical latent class model to estimate the distribution of severely disabled individuals at small regional levels using survey data, incorporating covariates and age effects with improved computational methods.

Contribution

It introduces a novel hierarchical latent class model with penalized splines for small area disability estimation from survey data, addressing the challenge of unobserved variables.

Findings

Effective small area estimates of disability levels were obtained.

The model improved computational efficiency with Deimmler-Reisch bases.

Results demonstrated accurate classification of disability levels at sub-regional levels.

Abstract

This article considers the estimation of the number of severely disabled people using data from the Italian survey on Health Conditions and Appeal to Medicare. Disability is indirectly measured using a set of categorical items, which survey a set of functions concerning the ability of a person to accomplish everyday tasks. Latent Class Models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey, however, is designed to provide reliable estimates at the level of Administrative Regions (NUTS2 level), while local authorities are interested in quantifying the amount of population that belongs to each latent class at a sub-regional level. Therefore, small area estimation techniques should be used. The challenge of the present application is that the variable of interest is not directly observed. Adopting a full Bayesian approach, we base small area estimation on a Latent Class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data using penalized splines. Deimmler-Reisch bases are shown to improve speed and mixing of MCMC chains used to simulate posteriors.