  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.
