[Forum SIS] Seminario 11 dicembre Prof. Enrico Fabrizi

[Dip. Scienze Statistiche - Mi]

Il Dipartimento di Scienze Statistiche dell'Università Cattolica del Sacro Cuore ha organizzato un seminario, presentato dal Prof. Enrico FABRIZI, dell'Università Cattolica di Piacenza, dal titolo:



Hierarchical Beta regression models for the estimation of poverty and inequality parameters in small areas



Giovedì 11 Dicembre dalle ore 12,00

in Aula NI 010



Università Cattolica del Sacro Cuore - Milano

Via Nirone, 15

Abstract:
Many parameters that describe poverty, social exclusion and inequality can take values in the (0; 1) interval. We assume that estimates of this type of parameters are needed for small subpopulations for which only small or no samples are available. In this paper, we discuss area level models for the estimation of this parameters. The idea of area models is that of complementing often imprecise direct estimators with auxiliary information available at the area level obtained from external sources. Given the nature of the target parameters we consider Beta regression models, as the Beta distribution is very exible over the (0; 1) range and it allows for asymmetric sampling distribution.
In this paper we adopt a Bayesian approach with approximate inference for relevant posterior distributions relying on MCMC algorithms. We focus on few specific problems that we think that may be particularly relevant for small area applied researchers and discuss them with reference to a specific data set.
The problems we consider are: i ) the estimation of the at-risk-of-poverty rate; ii ) the joint estimation of the material deprivation and severe material deprivation rates (i.e. two rates based on increasing thresholds); iii ) the joint estimation of two correlated parameters; specifically, for illustrative purposes we consider at-risk-of-poverty and Gini inequality index for the equivalized disposable income. When estimating the at-risk-of-poverty rate we face the problem of areas with no poors in the sample that leads us to consider zero-mixture Beta regressions, a class of models that will be considered also in the estimation of other parameters; to reach the goals ii and iii we introduce multivariate extensions of the Beta regression model: in the first case we discuss a multivariate logistic-normal model for the expected values of the Beta distributions, while in the second setting, we exploit the correlation between direct estimators using the theory of copula functions
We illustrate the models using an empirical application based on real data from the EU-SILC survey data.



Segreteria Organizzativa:
Sig.ra Barbara Villa
Tel. 02-7234.2647 - Fax 02-7234.3064
e-mail: dip.scienzestatistiche at unicatt.it<mailto:dip.scienzestatistiche at unicatt.it>




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