S Minotti

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.

Model-based clustering via linear cluster-weighted models

A novel family of twelve mixture models with random covariates, nested in the linear t cluster-weighted model (CWM), is introduced for model-based clustering. The linear t CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical-random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented.

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.

Local Multilevel Modeling for Comparisons of Institutional Performance

We propose a general methodology for evaluating the quality of public sector activities such as education, health and social services. The traditional instrument used in comparisons of institutional performance is Multilevel Modeling (Goldstein, H., Multilevel statistical models, Arnold, London, 1995). However, rankings based on confidence intervals of the organization-level random effects often prevent to discriminate between institutions, because uncertainty intervals may be large and overlapped. This means that, in some situations, a single global model is not sufficient to explain all the variability, and methods able to capture local behaviour are necessary. The proposal, which is entitled Local Multilevel Modeling, consists of a two-step approach which combines Cluster-Weighted Modeling (Gershenfeld, N., The nature of mathematical modeling, Cambridge University Press, Cambridge, 1999) with traditional Multilevel Modeling. An example regarding the evaluation of the “relative effectiveness” of healthcare institutions in Lombardy region is discussed.

Erratum to: 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.

An EM Algorithm for the Student-t Cluster-Weighted Modeling

Cluster-Weighted Modeling is a flexible statistical framework for modeling local relationships in heterogeneous populations on the basis of weighted combinations of local models. Besides the traditional approach based on Gaussian assumptions, here we consider Cluster Weighted Modeling based on Student-t distributions. In this paper we present an EM algorithm for parameter estimation in Cluster-Weighted models according to the maximum likelihood approach.

Some Notes on the Applicability of Cluster-Weighted Modeling in Effectiveness Studies

In the nineties, numerous authors proposed the use of Multilevel Models in effectiveness studies. However, this approach has been strongly criticized. Cluster-Weighted Modeling (CWM) is a flexible statistical framework, which is based on weighted combinations of local models. While Multilevel Models provide rankings of the institutions, in the CWM approach many models of effectiveness are estimated, each of them being valid for a certain subpopulation of users.

A New Version of the Structural Dynamic Model with Unique Latent Scores

The indeterminacy of the Structural Models, i.e. the arbitrariness of latent scores, due to the factorial nature of the measurement models, is, in the dynamic context, more problematic. We propose an alternative formulation of the Structural Dynamic Model, based on the Replicated Common Factor Model (Haagen e Oberhofer, 1999), where latent scores are no more indeterminate.