A note on composite likelihood inference and model selection

A composite likelihood consists of a combination of valid likelihood objects, usually related to small subsets of data. The merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models, even when the use of standard likelihood or Bayesian methods is not feasible. In this paper, we aim to suggest an integrated, general approach to inference and model selection using composite likelihood methods. In particular, we introduce an information criterion for model selection based on composite likelihood. We also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well-known Old Faithful geyser dataset. Copyright 2005, Oxford University Press.

[1]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[2]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  Adelchi Azzalini,et al.  Maximum likelihood estimation of order m for stationary stochastic processes , 1983 .

[5]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[6]  E. Carlstein.  The Use of Subseries Values for Estimating the Variance of a General Statistic from a Stationary Sequence , 1986 .

[7]  A. V. Vecchia.  Estimation and model identification for continuous spatial processes , 1988 .

[8]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[9]  R. Shibata.  Statistical aspects of model selection , 1989 .

[10]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[11]  A. Bowman,et al.  A look at some data on the old faithful geyser , 1990 .

[12]  B. Leroux.  Maximum-likelihood estimation for hidden Markov models , 1992 .

[13]  N. Hjort,et al.  Topics in Spatial Statistics , 1992 .

[14]  Bing-Yi Jing,et al.  On Sample Reuse Methods for Dependent Data , 1996 .

[15]  Adrian Pagan,et al.  Estimation, Inference and Specification Analysis. , 1996 .

[16]  ON SAMPLE REUSE METHODS FOR SPATIAL DATA , 1997 .

[17]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

[18]  C. Heyde,et al.  Quasi-likelihood and its application , 1997 .

[19]  Michael A. West,et al.  Bayesian forecasting and dynamic models (2nd ed.) , 1997 .

[20]  S. Lele,et al.  A Composite Likelihood Approach to Binary Spatial Data , 1998 .

[21]  David J. Nott,et al.  Pairwise likelihood methods for inference in image models , 1999 .

[22]  Patrick J. Heagerty,et al.  Weighted empirical adaptive variance estimators for correlated data regression , 1999 .

[23]  James K. Lindsey,et al.  On the use of corrections for overdispersion , 1999 .

[24]  Patrick J. Heagerty,et al.  Window Subsampling of Estimating Functions with Application to Regression Models , 2000 .

[25]  Erik T. Parner,et al.  A Composite Likelihood Approach to Multivariate Survival Data , 2001 .

[26]  P. Donnelly,et al.  Approximate likelihood methods for estimating local recombination rates , 2002 .

[27]  D. Renard.  Topics in Modeling Multilevel and Longitudinal Data , 2002 .

[28]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[29]  M. Peruggia.  Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.) , 2003 .

[30]  R. Henderson,et al.  A serially correlated gamma frailty model for longitudinal count data , 2003 .

[31]  Geert Molenberghs,et al.  A pairwise likelihood approach to estimation in multilevel probit models , 2004, Comput. Stat. Data Anal..

[32]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .

[33]  Øivind Skare,et al.  Pairwise likelihood inference in spatial generalized linear mixed models , 2005, Comput. Stat. Data Anal..

[34]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[35]  Cristiano Varin,et al.  Pairwise likelihood inference for ordinal categorical time series , 2006, Comput. Stat. Data Anal..