Título: Decoupling Shrinkage and Selection in Gaussian Linear Factor Analysis

Palestrante: Hedibert Freitas Lopes (Insper)
Data: 06/10/2021
Horario: 15:30h
Local: Transmissão online

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Resumo: Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a decision-theoretic approach that brings to light the relation between a sparse representation of the loadings and factor dimension. This relation is done through a summary from information contained in the multivariate posterior. To construct such summary, we introduce a three-step approach. In the first step, the model is fitted with a conservative factor dimension. In the second step, a series of point-estimates with a decreasing number of factors is obtained by minimizing an expected predictive loss function. In step three, the degradation in utility in relation to the sparse loadings and factor dimensions is displayed in the posterior summary. The findings are illustrated with a simulation study, and an application to personality data. We used different prior choices and factor dimensions to demonstrate the flexibility of the proposed method. This is joint work with
Henrique Bolfarine (USP), Carlos Carvalho (UT Austin) and Jared Murray (UT Austin).

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