Roberto Colombi

Multinomial Poisson Models subject to inequality constraints

Lang’s Multinomial-Poisson Homogeneous (MPH) models and Homogeneous Linear Predictor (HLP) Multinomial-Poisson models include as special cases many models for contingency table analysis that have been introduced in the effort to overcome well-known limitations of the log-linear models. Here the definitions of MPH and HLP models are extended to include inequality constraints. It is shown that inequality constrained MPH and HLP models are very flexible and rich family of models for contingency table analysis. The inequality constrained hierarchical multinomial marginal models which are an important sub-class of MPH models are also examined.

Determinants of transient and persistent hospital efficiency: The case of Italy

In this paper, we extend the 4-random-component closed skew-normal stochastic frontier model by including exogenous determinants of hospital persistent (long-run) and transient (short-run) inefficiency, separated from unobserved heterogeneity. We apply this new model to a dataset composed by 133 Italian hospitals during the period 2008-2013. We show that average total inefficiency is about 23%, higher than previous estimates; hence, a model where the different types of inefficiency and hospital unobserved characteristics are not confounded allows us to get less biased estimates of hospital inefficiency. Moreover, we find that transient efficiency is more important than persistent efficiency, as it accounts for 60% of the total one. Last, we find that ownership (for-profit hospitals are more transiently inefficient and less persistently inefficient than not-for-profit ones, whereas public hospitals are less transiently inefficient than not-for-profit ones), specialization (specialized hospitals are more transiently inefficient than general ones; i.e., there is evidence of scope economies in short-run efficiency), and size (large-sized hospitals are better than medium and small ones in terms of transient inefficiency) are determinants of both types of inefficiency, although we do not find any statistically significant effect of multihospital systems and teaching hospitals.

A class of smooth models satisfying marginal and context specific conditional independencies

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional independence models which are known to be non-smooth belong to this class. We introduce a new marginal log-linear parameterization and show that smoothness may be restored by restricting one or more independence statements to hold conditionally to a restricted subset of the configurations of the conditioning variables. Our results are based on a specific reconstruction algorithm from log-linear parameters to probabilities and fixed point theory. Several examples are examined and a general rule for determining the implied conditional independence restrictions is outlined.

Graphical models for multivariate Markov chains

The aim of this paper is to provide a graphical representation of the dynamic relations among the marginal processes of a first order multivariate Markov chain. We show how to read Granger-noncausal and contemporaneous independence relations off a particular type of mixed graph, when directed and bi-directed edges are missing. Insights are also provided into the Markov properties with respect to a graph that are retained under marginalization of a multivariate chain. Multivariate logistic models for transition probabilities are associated with the mixed graphs encoding the relevant independencies. Finally, an application on real data illustrates the methodology.

Modelling two way contingency tables with recursive logits and odds ratios

In this work a new type of logits and odds ratios, which includes as special cases the continuation and the reverse-continuation logits and odds ratios, are defined. We prove that these logits and odds ratios define a parameterization of the joint probabilities of a two way contingency table. The problem of testing equality and inequality constraints on these logits and odds ratios is examined with particular regard to two new hypotheses of monotone dependence.

A multivariate logit model with marginal canonical association

In this work, a generalization of the Goodman Association Model to the case of q, q > 2, categorical variables which is based on the idea of marginal modelling discussed by Gloneck–McCullagh is introduced; the difference between the proposed generalization and two models, previously introduced by Becker and Colombi, is discussed. The Becker generalization is not a marginal model because it does not imply Logit Models for the marginal probabilities, and because it is based on the conditional approach of modelling the association. The Colombi model is only partially a marginal model because it uses simple logit models for the univariate marginal probabilities but is based on the conditional approach of modelling the association. It is also shown that the maximum likelihood estimation of the parameters of the new model is feasible and, to compute the maximum likelihood estimates, an algorithm is proposed, which is a numerically convenient compromise between the constrained optimization approach of Lang and t...

A class of log-linear models with constrained marginal distributions

In the log-linear model for bivariate probability functions the conditional and joint probabilities have a simple form. This property make the log-linear parametrization useful when modeling these probabilities is the focus of the investigation. On the contrary, in the log-linear representation of bivariate probability functions, the marginal probabilities have a complex form. So the log-linear models are not useful when the marginal probabilities are of particular interest. In this paper the previous statements are discussed and a model obtained from the log-linear one by imposing suitable constraints on the marginal probabilities is introduced.

Latent class models for ecological inference on voters transitions

This paper introduces some new models of ecological inference within the context of estimation of voter transitions across elections. In particular, we assume that voters of a given party in a given occasion may be split into two latent types: faithful voters, who will certainly vote again for the same party and movers, who will reconsider their choice. Our models allow for unobserved heterogeneity across polling stations both in the weights of the two latent classes within each party and also when modelling the choice of unfaithful voters. Different ways of modelling the unobserved heterogeneity are considered by exploiting properties of the Dirichlet-multinomial distribution and the Brown Payne model of voting transitions can be seen as a special case within the class of models presented here. We discuss pseudo-maximum likelihood estimation and present an application to recent elections in Italy.

Marginal Nested Interactions for Contingency Tables

We introduce a new definition of generalized marginal interactions, called marginal nested interactions, which includes baseline, local, continuation and reverse continuation logits and odds ratios as special cases. The significant aspect of this definition is the inclusion of new types of logits and odds ratios that can handle non-ordinal, ordinal and partially ordered categorical variables in a flexible and appropriate way. It is proved also that the marginal nested interactions define a saturated model of a multi-way contingency table.

Multiple hidden Markov models for categorical time series

We introduce multiple hidden Markov models (MHMMs) where a multivariate categorical time series depends on a latent multivariate Markov chain. MHMMs provide an elegant framework for specifying various independence relationships between multiple discrete time processes. These independencies are interpreted as Markov properties of a mixed graph and a chain graph associated respectively to the latent and observation components of the MHMM. These Markov properties are also translated into zero restrictions on the parameters of marginal models for the transition probabilities and the distributions of observable variables given the latent states.