Giuliano Galimberti

Model-based methods to identify multiple cluster structures in a data set

There is an interest in the problem of identifying different partitions of a given set of units obtained according to different subsets of the observed variables (multiple cluster structures). A model-based procedure has been previously developed for detecting multiple cluster structures from independent subsets of variables. The method relies on model-based clustering methods and on a comparison among mixture models using the Bayesian Information Criterion. A generalization of this method which allows the use of any model-selection criterion is considered. A new approach combining the generalized model-based procedure with variable-clustering methods is proposed. The usefulness of the new method is shown using simulated and real examples. Monte Carlo methods are employed to evaluate the performance of various approaches. Data matrices with two cluster structures are analyzed taking into account the separation of clusters, the heterogeneity within clusters and the dependence of cluster structures.

Penalized factor mixture analysis for variable selection in clustered data

A model-based clustering approach which contextually performs dimension reduction and variable selection is presented. Dimension reduction is achieved by assuming that the data have been generated by a linear factor model with latent variables modeled as Gaussian mixtures. Variable selection is performed by shrinking the factor loadings though a penalized likelihood method with an L1 penalty. A maximum likelihood estimation procedure via the EM algorithm is developed and a modified BIC criterion to select the penalization parameter is illustrated. The effectiveness of the proposed model is explored in a Monte Carlo simulation study and in a real example.

Evaluating patient satisfaction through latent class factor analysis.

This paper introduces Health and Place readers interested in studying the latent concept of satisfaction to the methodology of latent variable analysis. In particular, some suitable methods for analyzing individual opinions expressed on ordinal scales are illustrated. The basic theory behind these methods is explained and a step by step description of how they should be used in practice is given. The discussion of the subject starts with the simplest methods, in which opinions are grouped into two categories: typically positive and negative. Furthermore, more complex methods are presented to deal with opinions expressed on ordinal scales (e.g., very satisfied, somewhat satisfied, and not satisfied). All methods are described by showing various results obtained through the analysis of a dataset containing patients opinions about their satisfaction with hospital care, collected through a survey conducted after their discharge from an Italian hospital. The database was created using a questionnaire covering different aspects of satisfaction and a five-point Likert scale. This represents an example of multi-level data: patients are clustered according to the hospital ward in which they were hospitalized. Thus, some specific latent variable methods able to deal with this particular structure of the data are also described.

Latent Classes of Objects and Variable Selection

In this paper we present a model based clustering approach which contextually performs dimension reduction and variable selection. In particular we assume that the data have been generated by a linear factor model with latent variables modeled as gaussian mixtures (thus obtaining dimension reduction) and we shrink the factor loadings, resorting to a penalized likelihood method, with an L1 penalty (thus realizing automatic variable selection). We derive an EM algorithm to obtain the penalized model estimates and a modified BIC criterion to select the penalization parameter. We evaluate the performance of the proposed method on simulated data.

Identifying Multiple Cluster Structures Through Latent Class Models

Many studies addressing the problem of selecting or weighting variables for cluster analysis assume that all the variables define a unique classification of units. However it is also possible that different classifications of units can be obtained from different subsets of variables. In this paper this problem is considered from a model-based perspective. Limitations and drawbacks of standard latent class cluster analysis are highlighted and a new procedure able to overcome these difficulties is proposed. The results obtained from the application of this procedure on simulated and real data sets are presented and discussed.

Finite mixture models for clustering multilevel data with multiple cluster structures

Finite mixture models are useful tools for clustering two-way datasets within a sound statistical framework which can assess some important questions, such as how many clusters are there in the data. Models that can also be used for clustering multilevel data have been proposed, with the intent to produce clusterings of units at every level on the basis of all the available variables, considering the hierarchical structure of the dataset. This paper introduces a new class of mixture models for datasets with two levels that makes it possible to discover a clustering of level 2 units and different clusterings of level 1 units corresponding to different subsets of the variables (multiple cluster structures). This new class is obtained by adapting a mixture model proposed to identify multiple cluster structures in a data matrix to the multilevel situation. The usefulness of the new method is shown using simulated data and a real example.

The FAGenomicH project: towards a whole candidate gene approach to identify markers associated with fatness and production traits in pigs and investigate the pig as a model for human obesity

Abstract Fatness in pigs is a complex trait for which a large number of genes are expected to be involved. Genetics of human obesity could take advantages from genetic information coming from the pig and vice versa. To these aims, a comprehensive candidate gene approach could be helpful. We catalogued all genes affecting fatness on both species, and identified in silico and by resequencing porcine SNPs on a large number of candidate genes. In addition, we applied a selective genotyping approach to identify markers associated with fat deposition in pigs. This approach was tested genotyping the IGF2 intron3-g.3072G>A mutation and novel markers in the PCSK1 and TBC1D1 genes. Polymorphisms in these genes resulted associated with back fat thickness in Italian Large White pigs.