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

• Published in: Journal of the Royal Statistical Society. Series A, Statistics in society Vol. 179; no. 1; pp. 103 - 131
• Main Authors: Fabrizi, Enrico, Montanari, Giorgio E., Giovanna Ranalli, M.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.01.2016; John Wiley & Sons Ltd; Oxford University Press
• Subjects: Appeals; Bayesian analysis; Classification; Computer simulation; Counting; Demmler-Reinsch bases; Disabilities; Disability; Estimating techniques; Health interview survey; Markov analysis; Mathematical models; Medicare; Monte Carlo simulation; Non-parametric regression; Penalized splines; Small area estimation; Statistics; Tasks; Unit level model; Italy
• ISSN: 0964-1998; 1467-985X
• DOI: 10.1111/rssa.12112

We consider the estimation of the number of severely disabled people by using data from the Italian survey on 'Health conditions and appeal to Medicare'. In this survey, disability is indirectly measured by using a set of categorical items, which consider 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 is designed to provide reliable estimates at the level of administrative regions ('Nomenclature des unités territoriales statistiques', level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not 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 by using penalized splines. Demmler-Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors.