Statistics and Its Interface

Volume 8 (2015)

Number 2

Special Issue on Modern Bayesian Statistics (Part II)

Guest Editor: Ming-Hui Chen (University of Connecticut)

Binary state space mixed models with flexible link functions: a case study on deep brain stimulation on attention reaction time

Pages: 187 – 194

DOI: http://dx.doi.org/10.4310/SII.2015.v8.n2.a6

Authors

Carlos A. Abanto-Valle (Department of Statistics, Federal University of Rio de Janeiro, Brazil)

Dipak K. Dey (Department of Statistics, University of Connecticut, Storrs, Conn., U.S.A.)

Xun Jiang (Medical Sciences & Biostatistics, Amgen, Thousand Oaks, California, U.S.A.)

Abstract

State space models (SSM) for binary time series data using a flexible skewed link functions are introduced in this paper. Commonly used logit, cloglog and loglog links are prone to link misspecification because of their fixed skewness. Here we introduce two flexible links as alternatives, they are the generalized extreme value (GEV) and the symmetric power logit (SPLOGIT) links. Markov chain Monte Carlo (MCMC) methods for Bayesian analysis of SSM with these links are implemented using the JAGS package, a freely available software. Model comparison relies on the deviance information criterion (DIC). The flexibility of the proposed model is illustrated to measure effects of deep brain stimulation (DBS) on attention of a macaque monkey performing a reaction-time task. Empirical results showed that the flexible links fit better over the usual logit and cloglog links.

Keywords

binary time series, GEV link, logit link, Markov chain, Monte Carlo, probit link, state space models

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