Elena Stanghellini

Graphical models for skew-normal variates

This paper explores the usefulness of the multivariate skew-normal distribution in the context of graphical models. A slight extension of the family recently discussed by Azzalini & Dalla Valle (1996) and Azzalini & Capitanio (1999) is described, the main motivation being the additional property of closure under conditioning. After considerations of the main probabilistic features, the focus of the paper is on the construction of conditional independence graphs for skew-normal variables. Necessary and sufficient conditions for conditional independence are stated, and the admissible structures of a graph under restriction on univariate marginal distribution are studied. Finally, parameter estimation is considered. It is shown how the factorization of the likelihood function according to a graph can be rearranged in order to obtain a parameter based factorization.

Incidence of bacterial meningitis (2001–2005) in Lazio, Italy: the results of a integrated surveillance system

BackgroundMonitoring the incidence of bacterial meningitis is important to plan and evaluate preventive polices. The studys aim was to estimate the incidence of bacterial meningitis by aetiological agent in the period 2001–2005, in Lazio Italy (5.3 mln inhabitants).MethodsData collected from four sources – hospital surveillance of bacterial meningitis, laboratory information system, the mandatory infectious diseases notifications, and hospital information system – were combined into a single archive.Results944 cases were reported, 89% were classified as community acquired. S. pneumoniae was the most frequent aetiological agent in Lazio, followed by N. meningitis. Incidence of H. influenzae decreased during the period. 17% of the cases had an unknown aetiology and 13% unspecified bacteria. The overall incidence was 3.7/100,000. Children under 1 year were most affected (50.3/100.000), followed by 1–4 year olds (12.5/100,000). The percentage of meningitis due to aetiological agents included in the vaccine targets, not considering age, is 31%. Streptococcus spp. was the primary cause of meningitis in the first three months of life. The capture-recapture model estimated underreporting at 17.2% of the overall incidence.ConclusionVaccine policies should be planned and monitored based on these results. The integrated surveillance system allowed us to observe a drop in H. influenzae b meningitis incidence consequent to the implementation of a mass vaccination of newborns.

A Discrete Variable Chain Graph for Applicants for Credit

A bank offering unsecured personal loans may be interested in several related outcome variables, including defaulting on the repayments, early repayment or failing to take up an offered loan. Current predictive models used by banks typically consider such variables individually. However, the fact that they are related to each other, and to many interrelated potential predictor variables, suggests that graphical models may provide an attractive alternative solution. We developed such a model for a data set of 15 variables measured on a set of 14 000 applications for unsecured personal loans. The resulting global model of behaviour enabled us to identify several previously unsuspected relationships of considerable interest to the bank. For example, we discovered important but obscure relationships between taking out insurance, prior delinquency with a credit card and delinquency with the loan.

Bayesian inference for graphical factor analysis models

We generalize factor analysis models by allowing the concentration matrix of the residuals to have nonzero off-diagonal elements. The resulting model is named graphical factor analysis model. Allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables, which can be used both in the confirmatory and exploratory context. We first present a sufficient condition for global identifiability of this class of models with a generic number of factors, thereby extending the results in Stanghellini (1997) and Vicard (2000). We then consider the issue of model comparison and show that fast local computations are possible for this purpose, if the conditional independence graphs on the residuals are restricted to be decomposable and a Bayesian approach is adopted. To achieve this aim, we propose a new reversible jump MCMC method to approximate the posterior probabilities of the considered models. We then study the evolution of political democracy in 75 developing countries based on eight measures of democracy in two different years.

Introduzione ai metodi statistici per il credit scoring

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Item Response Models to Measure Corporate Social Responsibility

Corporate social responsibility (CSR) is a multidimensional concept that involves several aspects, ranging from environment to social and governance. Companies aiming to comply with CSR standards have to face challenges that vary from one aspect to the other and from one industry to the other. Latent variable models may be usefully employed to provide a unidimensional measure of the grade of compliance of a firm with CSR standards, which is both understandable and theoretically solid. A methodology based on item response theory has been implemented on the multidimensional sustainability rating as expressed by KLD data-set from 1991 to 2007. Results suggest that companies in the oil and gas industry together with firms in industrials, basic materials and telecommunications have a higher difficulty to meet the CSR standards. Criteria based on human rights, environment, community and product quality have a large capacity to select the best performing firms, as they are very discriminant, while governance does not exhibit similar behaviour. A stock selection based on the ranking of the firms according to the proposed CSR measure supports the hypothesis of a positive relationship between CSR and financial performance.

Identification of Principal Causal Effects Using Additional Outcomes in Concentration Graphs

Unless strong assumptions are made, nonparametric identification of principal causal effects can only be partial and bounds (or sets) for the causal effects are established. In the presence of a secondary outcome, recent results exist to sharpen the bounds that exploit conditional independence assumptions. More general results, though not embedded in a causal framework, can be found in concentration graphical models with a latent variable. The aim of this article is to establish a link between the two settings and to show that adapting and extending results pertaining to concentration graphical models can help achieving identification of principal casual effects in studies when more than one additional outcome is available. Model selection criteria are also suggested. An empirical illustrative example is provided, using data from a real social experiment.

Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables

Abstract Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects.

Graphical factor analysis models: specification and model comparison

We introduce a graphical factor analysis model as a graphical Gaussian model with latent variables satisfying a set of conditional independence constraints. After a brief introduction of the factor analysis model, we generalise the class of such models by allowing the concentration matrix of the residuals to have non-zero off-diagonal elements. The study of the associations left unexplained by the latent factors allows a better interpretation of the model. We concentrate on models with one latent variable, for which the identifiability condition is well established. A real data example is then presented to clarify the ideas. Two model selection procedures are presented, one based on the calculations of deviance differences and the other based on the calculation of the posterior probability of the model. Given the analytical intractability of the latter, we propose a Markov Chain Monte Carlo method to approximate both the model probabilities and the inferences on the quantities of interest.

IDENTIFICATION OF PRINCIPAL CAUSAL EFFECTS USING SECONDARY OUTCOMES

Unless strong assumptions are made, identification of principal causal effects in causal studies can only be partial and bounds (or sets) for the causal effects are established. In the presence of a secondary outcome, recent results exist to sharpen the bounds that exploit conditional independence assumptions (Mealli and Pacini, J. Am. Stat. Assoc. 108:1120–1131, 2013). More general results, though not embedded in a causal framework, can be found on concentration graphs with a latent variable (Stanghellini and Vantaggi, Bernoulli 19:1920–1937, 2013). The aim of this paper is to establish a link between the two settings and to show that adapting results contained in the latter paper can help achieving identification of principal casual effects in studies with more than one secondary outcome. An empirical illustrative example is also provided, using data from a real social job training experiment.