Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects

In this paper, we aim at ranking a set of nursing homes based on their ability in maintaining their residents’ physical conditions as good as possible. In this respect, we propose a nursing home performance indicator, which is essentially a probability to avoid resident health status worsening. Specifically, latent Markov models with covariates and normally distributed continuous random effects are fitted to produce standardised 180-day ahead transition matrices, upon which the aforementioned index is based. Nursing home effects on these transition matrices are modelled through fixed as well as random effects. The performance index is used to build two distinct rankings, one of which also accounts for the variability induced by the estimation process. In this framework, several rankings can be obtained by combining the model specification (fixed vs. random effects), the kind of ranking and the number of latent states, which is the typical sensitivity parameter of latent Markov models. Our methodological approach is applied to a dataset which was gathered from a health protocol implemented in Umbria (Italy). Results for this data show a rather high degree of robustness, in the sense that the obtained rankings are almost the same.