Two competing models for ordinal longitudinal data with time-varying latent effects: an application to evaluate hospital efficiency

We propose a model for longitudinal data with a suitable parameterization based on global logits to account for the ordinal response variable which incorporates observed covariates and time-varying latent unit specific effects. As an example we consider a derived ordinal variable by using the total revenues and discharges of the hospitals. For example, the hospital can vary on the response variable because of the unobserved covariates such as general manager ability (unobserved heterogeneity). The distribution of the latter may be discrete-valued or continuous-valued. In the first case it is based on a first order homogeneous Markov chain with a fixed number of states. In the second case it is a mixture of auto-regressive AR(1) processes with specific mean values and correlation coefficients and common variances. Maximum likelihood estimation of the model parameters is performed by using the Expectation-Maximization algorithm and the Newton-Raphson algorithm. Standard errors are obtained by using the observed information matrix. The results of the application to data referred to some hospitals in Lombardy are illustrated