Efficient MCMC Methods for Estimating Binomial Logit Models

Meeting: 
ISBA 2012
Meeting Program Chair: 
ISBA 2012
Presenter First Name: 
Agnes
Presenter Last Name: 
Fussl
Presenter's Email: 
agnes.fussl@jku.at
Affiliation: 
Johannes Kepler University Linz
Country: 
Austria
Presentation Type: 
Poster
Abstract: 
Our work considers efficient Bayesian methods for data originating from experiments where binary outcome variables are aggregated in terms of binomial outcome variables. Such data arise e.g. if repeated measurements are taken for each covariate pattern in the design matrix of a planned experiment or when frequencies in the form of two-way or three-way contingency tables are observed. For any of these examples, the data are modeled by a binomial regression model. We present estimation methods based on various MCMC sampling procedures for fitting binary logit models with data augmentation, where the regression coefficients are estimated by rewriting the logit model as random utility model (RUM) or difference RUM (dRUM). Using the reconstructed binary observations to estimate the parameters in the binomial model leads to a high-dimensional latent variable. To reduce the dimension of this individual representation, we introduce an aggregated RUM version of the binomial model like in (Frühwirth-Schnatter, Frühwirth, Held and Rue, 2009, Statistics and Computing, 19: 479 – 492). To improve the sampler further, we suggest a new aggregated dRUM representation of the binomial logistic regression model. The parameters are estimated by using three different MCMC algorithms: a data-augmented MH-sampler, an auxiliary mixture sampler and a novel hybrid auxiliary mixture (HAM) sampler. To show that the modifications lead to a considerable reduction of computing time and a noticeable gain in efficiency, we present a comparison of their performances within a comparative case study on various data sets.
Keywords: 
binomial logit model
Keywords: 
repeated measurements
Keywords: 
data augmentation
Keywords: 
random utility model
Keywords: 
aggregated dRUM
Keywords: 
Markov Chain Monte Carlo
Keywords: 
HAM sampler
Co-authors: 
Sylvia Frühwirth-Schnatter, and Rudolf Frühwirth
Date/Time: 
Tuesday, June 26, 2012 - 18:30