Giorgio Vittadini

Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions

Cluster-weighted modeling (CWM) is a mixture approach to modeling the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both theoretical and numerical point of view; in particular, we show that Gaussian CWM includes mixtures of distributions and mixtures of regressions as special cases. Further, we introduce CWM based on Student-t distributions, which provides a more robust fit for groups of observations with longer than normal tails or noise data. Theoretical results are illustrated using some empirical studies, considering both simulated and real data. Some generalizations of such models are also outlined.

Indeterminacy Problems in the Lisrel Model.

The latent variables and errors of the Lisrel model are indeterminate even when the parameters of the model are perfectly identified. The reason for the indeterminacy is that the Lisrel model gives a solution in terms of estimation of latent variables by means of observed variables. The indeterminacy is relevant also in practice; the minimum correlation between equivalent latent variables, is often negative in empirical examples. The degree of indeterminacy of the latent variables depends on the data. The average minimum correlation is a linear combination of the eigenvalues of the correlation matrix of solutions and it is always included in weak bounds which depend on the same eigenvalues.

Assessment of School Performance Through a Multilevel Latent Markov Rasch Model

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to which he or she belongs. The latter effect is modeled by a discrete latent variable associated to each cluster. For the maximum likelihood estimation of the model parameters, an Expectation-Maximization algorithm is outlined. Through the analysis of a data set collected in the Lombardy Region (Italy), it is shown how the proposed model may be used for assessing the development of cognitive achievement. The data set is based on test scores in mathematics observed over 3 years on middle school students attending public and non-state schools. Manuscript received March 20, 2009 Revision received July 2, 2010 Accepted July 10, 2010

Comparing health outcomes among hospitals: the experience of the Lombardy Region

In recent years, governments and other stakeholders have increasingly used administrative data for measuring healthcare outcomes and building rankings of health care providers. However, the accuracy of such data sources has often been questioned. Starting in 2002, the Lombardy (Italy) regional administration began monitoring hospital care effectiveness on administrative databases using seven outcome measures related to mortality and readmissions. The present study describes the use of benchmarking results of risk-standardized mortality from Lombardy regional hospitals. The data usage is part of a general program of continuous improvement directed to health care service and organizational learning, rather than at penalizing or rewarding hospitals. In particular, hierarchical regression analyses - taking into account mortality variation across hospitals - were conducted separately for each of the most relevant clinical disciplines. Overall mortality was used as the outcome variable and the mix of the hospitals’ output was taken into account by means of Diagnosis Related Group data, while also adjusting for both patient and hospital characteristics. Yearly adjusted mortality rates for each hospital were translated into a reporting tool that indicates to healthcare managers at a glance, in a user-friendly and non-threatening format, underachieving and over-performing hospitals. Even considering that benchmarking on risk-adjusted outcomes tend to elicit contrasting public opinions and diverging policymaking, we show that repeated outcome measurements and the development and dissemination of organizational best practices have promoted in Lombardy region implementation of outcome measures in healthcare management and stimulated interest and involvement of healthcare stakeholders.

The Generalized Linear Mixed Cluster-Weighted Model

Cluster-weighted models (CWMs) are a flexible family of mixture models for fitting the joint distribution of a random vector composed of a response variable and a set of covariates. CWMs act as a convex combination of the products of the marginal distribution of the covariates and the conditional distribution of the response given the covariates. In this paper, we introduce a broad family of CWMs in which the component conditional distributions are assumed to belong to the exponential family and the covariates are allowed to be of mixed-type. Under the assumption of Gaussian covariates, sufficient conditions for model identifiability are provided. Moreover, maximum likelihood parameter estimates are derived using the EM algorithm. Parameter recovery, classification assessment, and performance of some information criteria are investigated through a broad simulation design. An application to real data is finally presented, with the proposed model outperforming other well-established mixture-based approaches.

On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme

A new approach for the estimation and the validation of a structural equation model with a formative-reflective scheme is presented. The basis of the paper is a proposal for overcoming a potential deficiency of PLS path modeling. In the PLS approach the reflective scheme assumed for the endogenous latent variables (LVs) is inverted; moreover, the model errors are not explicitly taken into account for the estimation of the endogenous LVs. The proposed approach utilizes all the relevant information in the formative manifest variables (MVs) providing solutions which respect the causal structure of the model. The estimation procedure is based on the optimization of the redundancy criterion. The new approach, entitled redundancy analysis approach to path modeling (RA-PM) is compared with both traditional PLS Path Modeling and LISREL methodology, on the basis of real and simulated data.

Formative Indicators and Effects of a Causal Model for Household Human Capital with Application

Dagum and Slottje (2000) estimated household human capital (HC) as a latent variable (LV) and proposed its monetary estimation by means of an actuarial approach. This paper introduces an improved method for the estimation of household HC as an LV by means of formative and reflective indicators in agreement with the accepted economic definition of HC. The monetary value of HC is used in a recursive causal model to obtain short- and long-term multipliers that measure the direct and total effects of the variables that determine household HC. The new method is applied to estimate US household HC for year 2004.

Structural Equation Models in a Redundancy Analysis Framework With Covariates

A recent method to specify and fit structural equation modeling in the Redundancy Analysis framework based on so-called Extended Redundancy Analysis (ERA) has been proposed in the literature. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in the presence of direct effects linking exogenous and endogenous variables, or concomitant indicators, the composite scores are estimated by ignoring the presence of the specified direct effects. To fit structural equation models, we propose a new specification and estimation method, called Generalized Redundancy Analysis (GRA), allowing us to specify and fit a variety of relationships among composites, endogenous variables, and external covariates. The proposed methodology extends the ERA method, using a more suitable specification and estimation algorithm, by allowing for covariates that affect endogenous indicators indirectly through the composites and/or directly. To illustrate the advantages of GRA over ERA we propose a simulation study of small samples. Moreover, we propose an application aimed at estimating the impact of formal human capital on the initial earnings of graduates of an Italian university, utilizing a structural model consistent with well-established economic theory.

Does community care work? A model to evaluate the effectiveness of mental health services

The aim of this paper is to evaluate the effectiveness of community Mental Health Departments in Lombardy (Italy), and analyse the eventual differences in outcome produced by different packages of care. The survey was conducted in 2000 on 4,712 patients treated in ten Mental Health Departments. Patients were assessed at least twice in a year with HoNOS (Health of the Nation Outcome Scales). Data on treatment packages were drawn from the regional mental health information system, which includes all outpatient and day-care contacts, as well as general hospital and inpatient admissions provided by Mental Health Departments. Multilevel growth models were used for outcomes statistical analysis, expressed in terms of change of the total HoNOS score. On the whole, Mental Health Departments were effective in reducing HoNOS scores. The main predictor of improvement was treatment, while length of care, gender and diagnosis were weaker predictors. After severity adjustment, some packages of care proved more effective than others. Appropriate statistical methods, comprehensive treatment descriptions and routine outcome assessment tools are needed to evaluate the effectiveness of community mental health services in clinical settings.

Analysis of Qualitative Variables in Structural Models with Unique Solutions

A new method based on the Multidimensional Scaling and the Restricted Regression Component Decomposition is proposed in order to obtain solutions for structural models with mixed variables.