158
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Markov Poisson regression models for discrete time series. Part 1: Methodology

Pages 855-869 | Published online: 02 Aug 2010

  • AKAIKE , H. Information theory and an extension of the maximum likelihood principle . Proceedings of Second International Symposium on Information Theory . Edited by: PETROY , B. N. and CSAKI , F. pp. 267 – 281 . Budapest : Akademia Kaido .
  • AKAIKE , H. 1974 . A new look at the statistical model identification . IEEE Transactions on Automatic Control , AC-19 : 716 – 723 .
  • ALBERT , P.S. 1991 . A two-state Markov model for a time series of epileptic seizure counts . Biom , 47 : 1371 – 1381 .
  • BAUM , L. E. , PETRIE , T. , SOUTLES , G. and WEISS , N. 1970 . A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains . The Annals of Mathematical Stat , 41 : 164 – 171 .
  • DEMPSTER , A. P. , LAMB , N.M. and RUBIN , D. B. 1977 . Maximum likelihood from incomplete data via the EM algorithm (with discussion) . Journal of the Royal Statistical Society, Se , 39 : 1 – 38 .
  • EFFRON , B. and TIBSHIRANI , R. J. 1993 . An Introduction to the Bootstrap , New York : Chapman & Hall .
  • KAUFMANN , H. 1987 . Regression models for nonstationary categorical time series: Asymptotic estimation theory . The Annals of Stat , 15 : 59 – 67 .
  • LEROUX , B. G. 1989 . “ Maximum-likelihood Estimation for Mixture Distribution and Hidden Markov Models ” . University of British Columbia . PhD Dissertation,
  • LEROUX , B. G. 1992 . Maximum-likelihood estimation for hidden Markov models . Stochastic Processes and Their Applic , 40 : 127 – 143 .
  • LEROUX , B. G. and PUTERMAN , M. L. 1992 . Maximum penalized likelihood estimation for independent and Markov dependent mixture models . Biom , 48 : 545 – 558 .
  • LIANG , K. Y. and ZEGER , S. L. 1986 . Longitudinal data analysis using generalized linear models . Biom , 73 : 13 – 22 .
  • MACDONALD , I. and ZUCCHINI , W. 1997 . Hidden Markov and Other Models for Discrete-valued Time Series , London : Chapman & Hall .
  • MCCULLAGH , P. and NELDER , J. A. 1989 . Generalized Linear Models, , 2nd edn , London : Chapman & Hall .
  • MCLACHLAN , G. J. and BASFORD , K. E. 1988 . Mixture Models , New York : Marcel Dekker .
  • NASH , J. C. 1990 . Compact Numerical Methods for Computers , Bristol : Adam Hilger .
  • OCHI , Y. and PRENTICE , R. L. 1982 . Likelihood inference in correlated probit regression . Biom , 71 : 531 – 543 .
  • SCHWARZ , G. 1978 . Estimating the dimension of a model . The Annals of Stat , 6 : 461 – 464 .
  • STIRATELLI , R. , LAIRD , N. and WARE , J. 1984 . Random effects models for serial observations with binary responses . Biom , 40 : 961 – 971 .
  • TEICHER , H. 1961 . Identifiability of mixtures . The Annals of Mathematical Stat , 32 : 244 – 248 .
  • TEICHER , H. 1963 . Identifiability of finite mixtures . The Annals of Mathematical Stat , 34 : 1265 – 1269 .
  • VENASLES , W. N. and RIPLEY , B. D. 1994 . Modern Applied Statistics with S-Plus , New York : Springer .
  • WANG , P. 1994 . “ Mixed Regression Models for Discrete Data ” . University of British Columbia . PhD Dissertation,
  • WANG , P. and PUTERMAN , M. L. 1999 . Markov Poisson regression models for discrete time series. Part 2: Applications . Journal of Applied Stat , 26 : 871 – 882 .
  • WANG , P. , PUTERMAN , M. L. , COCKBURN , L. and NHU , L. 1996 . Mixed Poisson regression models with covariate dependent rates . Biom , 52 : 381 – 400 .
  • WANG , P. , COCKBURN , L. and PUTERMAN , M. L. 1998 . Patent data analysis, A mixed Poisson regression model approach . Journal of Business and Economics Stat , 16 : 27 – 41 .
  • ZEGER , S. L. 1988 . A regression model for time series of counts . Biom , 75 : 621 – 629 .
  • ZEGER , S. L. , LIANG , K. Y. and SELF , S. G. 1985 . The analysis of binary longitudinal data with time independent covariates . Biom , 72 : 31 – 38 .
  • ZEGER , S. L. and QAQISH , B. 1988 . Markov regression models for time series: A quasi-likelihood approach . Biom , 44 : 1019 – 1031 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.