Event

Alexandra Schmidt, McGill University

Thursday, April 12, 2018 15:00to16:00
Room PK-5115 , UQAM Pavillon Kennedy, CA

A spatial hierarchical model for zero-inflated beta distributed data.

Abstract: We propose a spatial hierarchical model for zero-inflated beta distributed data. This model is motivated by data on the performance of students in the Brazilian Mathematical Olympiads for Public Schools (OBMEP). We assume that the score of student j in school i, located in micro-region s, is a realization from a mixture between a Bernoulli and a beta distribution. The Bernoulli component accounts for zero scores present in the data. And the mean of the beta distribution accounts for the intrinsic hierarchical nature of the data. It is decomposed as the sum of student's fixed and random effects, school's fixed effects, and a random effect that captures the characteristics of the micro-region the school is located at. We explore different prior distributions for this micro-region random effect, ranging from independent to different specifications of the conditional autoregressive distribution. Because we have available the human development index (HDI) of the micro-region the school is located at, and HDI varies spatially, we also investigate if the inclusion of spatially structured random effects change the estimates associated with HDI and other covariates in the model. Inference procedure follows the Bayesian paradigm, and uncertainty about unknowns in the model are naturally accounted for. Different fitted models are compared through two different model comparison criteria. Our study suggests that for the OBMEP data, students that attend federal schools which are located in regions with higher values of HDI tend to perform better in OBMEP. Also, models that assume the spatial random effects to be orthogonal to the school's level covariates provide different estimates of some of the fixed effects. This is joint work with João B. M. Pereira (IM-UFRJ, Brazil), Widemberg S. Nobre (IM-UFRJ,Brazil) and Igor Fernandes (IM-UFRJ, Brazil).

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