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

We consider the estimation of the number of severely disabled people by using data\r\nfrom the Italian survey on ‘Health conditions and appeal to Medicare’. In this survey, disability\r\nis indirectly measured by using a set of categorical items, which consider a set of functions\r\nconcerning the ability of a person to accomplish everyday tasks. Latent class models can be\r\nemployed to classify the population according to different levels of a latent variable connected\r\nwith disability.The survey is designed to provide reliable estimates at the level of administrative\r\nregions (‘Nomenclaturedesunit ´esterritoriales statistiques ’, level 2), whereas local authorities\r\nare interested in quantifying the number of people who belong to each latent class at a subregional\r\nlevel. Therefore, small area estimation techniques should be used. The challenge is that\r\nthe variable of interest is not observed. Adopting a full Bayesian approach, we base small area\r\nestimation on a latent class model in which the probability of belonging to each latent class\r\nchanges with covariates and the influence of age is learnt from the data by using penalized\r\nsplines. Demmler–Reinsch bases are shown to improve speed and mixing of Markov chain\r\nMonte Carlo chains used to simulate posteriors.