Analysis of Poisson varying-coefficient models with autoregression

ABSTRACT In the regression analysis of time series of event counts, it is of interest to account for serial dependence that is likely to be present among such data as well as a nonlinear interaction between the expected event counts and predictors as a function of some underlying variables. We thus develop a Poisson autoregressive varying-coefficient model, which introduces autocorrelation through a latent process and allows regression coefficients to nonparametrically vary as a function of the underlying variables. The nonparametric functions for varying regression coefficients are estimated with data-driven basis selection, thereby avoiding overfitting and adapting to curvature variation. An efficient posterior sampling scheme is devised to analyse the proposed model. The proposed methodology is illustrated using simulated data and daily homicide data in Cali, Colombia.

[1]  Taeyoung Park,et al.  Partially Collapsed Gibbs Sampling for Linear Mixed-effects Models , 2016, Commun. Stat. Simul. Comput..

[2]  Xiyun Jiao,et al.  Metropolis-Hastings Within Partially Collapsed Gibbs Samplers , 2013, 1309.3217.

[3]  Taeyoung Park,et al.  Bayesian Analysis of Individual Choice Behavior With Aggregate Data , 2011 .

[4]  Patrick T. Brandt,et al.  Dynamic modeling for persistent event-count time series , 2000 .

[5]  Minjae Park,et al.  Analysis of binary longitudinal data with time-varying effects , 2017, Comput. Stat. Data Anal..

[6]  M. Clyde,et al.  Mixtures of g Priors for Bayesian Variable Selection , 2008 .

[7]  Jun S. Liu,et al.  The Collapsed Gibbs Sampler in Bayesian Computations with Applications to a Gene Regulation Problem , 1994 .

[8]  Qi Li,et al.  Efficient estimation of a semiparametric partially linear varying coefficient model , 2005, math/0504510.

[9]  Taeyoung Park,et al.  Bayesian variable selection in Poisson change-point regression analysis , 2017, Commun. Stat. Simul. Comput..

[10]  D. V. van Dyk,et al.  Searching for Narrow Emission Lines in X-ray Spectra: Computation and Methods , 2008, 0808.3164.

[11]  S. Zeger.  A regression model for time series of counts , 1988 .

[12]  D. V. Dyk,et al.  Partially Collapsed Gibbs Sampling and Path-Adaptive Metropolis–Hastings in High-Energy Astrophysics , 2011 .

[13]  Jianqing Fan,et al.  Efficient Estimation and Inferences for Varying-Coefficient Models , 2000 .

[14]  J. Puyana,et al.  Policies for alcohol restriction and their association with interpersonal violence: a time-series analysis of homicides in Cali, Colombia. , 2011, International journal of epidemiology.

[15]  H. Friedl.  Econometric Analysis of Count Data , 2002 .

[16]  A. Verhasselt.  GENERALIZED VARYING COEFFICIENT MODELS: A SMOOTH VARIABLE SELECTION TECHNIQUE , 2013 .

[17]  Robert Kohn,et al.  Nonparametric regression using linear combinations of basis functions , 2001, Stat. Comput..

[18]  K. B. Kulasekera,et al.  Generalized varying coefficient models with unknown link function , 2011 .

[19]  Taeyoung Park,et al.  Bayesian Semiparametric Inference on Functional Relationships in Linear Mixed Models , 2016 .

[20]  Damla Şentürk,et al.  Generalized varying coefficient models for longitudinal data , 2008 .

[21]  D. V. van Dyk,et al.  Partially Collapsed Gibbs Samplers: Illustrations and Applications , 2009 .

[22]  B. D. Finetti,et al.  Bayesian inference and decision techniques : essays in honor of Bruno de Finetti , 1986 .

[23]  Jianqing Fan,et al.  Profile likelihood inferences on semiparametric varying-coefficient partially linear models , 2005 .

[24]  B. McCabe,et al.  Analysis of low count time series data by poisson autoregression , 2004 .

[25]  Subir Ghosh.  Asymptotics, Nonparametrics, and Time Series , 2000 .

[26]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[27]  C. Lai,et al.  First‐order integer valued AR processes with zero inflated poisson innovations , 2012 .

[28]  M. Clyde,et al.  Model Uncertainty , 2003 .

[29]  Jae Won Lee,et al.  Bayesian nonparametric inference on quantile residual life function: Application to breast cancer data , 2012, Statistics in medicine.

[30]  Taeyoung Park,et al.  Efficient Bayesian analysis of multivariate aggregate choices , 2015 .

[31]  Taeyoung Park,et al.  Bayesian semi-parametric analysis of Poisson change-point regression models: application to policy-making in Cali, Colombia , 2012, Journal of applied statistics.

[32]  R. Kohn,et al.  Nonparametric regression using Bayesian variable selection , 1996 .