Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T02:01:37.517Z Has data issue: false hasContentIssue false
  • English
  • Français

A robust algorithm for estimating regression and dispersion parameters in non-stationary longitudinally correlated Com–Poisson data

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  01 March 2016

Naushad Mamode Khan
Naushad Mamode Khan*
Affiliation:
University of Mauritius, Reduit, Mauritius email [email protected]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In recent years, Com–Poisson has emerged as one of the most popular discrete models in the analysis of count data owing to its flexibility in handling different types of dispersion. However, in a stationary longitudinal Com–Poisson count data set-up where the covariates are time independent, estimation of regression and dispersion parameters based on a generalized quasi-likelihood (GQL) approach involves some major computational difficulties particularly in the inversion of the joint covariance matrix. On the other hand, in practical real-life longitudinal studies, time-dependent covariates leading to non-stationary responses are more frequently encountered. This implies that further computational problems will now arise when estimating parameters under non-stationary set-ups. This paper overcomes this problem by approximating the inverse of the ill-conditioned covariance matrix in the GQL approach through a multidimensional conjugate gradient method. The performance of this novel version of the GQL approach is then assessed on simulations of AR(1) stationary and AR(1) non-stationary longitudinal Com–Poisson counts and on real-life epileptic seizure counts. However, there is not yet an algorithm to generate non-stationary longitudinal Com–Poisson counts nor a GQL algorithm to estimate the parameters under non-stationary set-ups. Thus, the paper also provides a framework to generate non-stationary AR(1) Com–Poisson counts along with the construction of a GQL equation under non-stationary set-ups.

MSC classification

Primary: 65C60: Computational problems in statistics
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 25 - 36
Copyright
© The Author 2016 

References

Castillo, J. and Perez-Cassany, M., ‘Weighted Poisson distributions for overdispersion and underdispersion situations’, Ann. Inst. Statist. Math. 50 (1998) 567–585.CrossRefGoogle Scholar
Jowaheer, V. and Sutradhar, B., ‘Analysing longitudinal count data with overdispersion’, Biometrika 89 (2002) 389–399.Google Scholar
Jowaheer, V. and Sutradhar, B., ‘Fitting lower order nonstationary autocorrelation models to the time series of Poisson counts’, WSEAS Trans. Math. 4 (2005) 427–434.Google Scholar
Mamode Khan, N. and Jowaheer, V., ‘Comparing joint estimation and GMM adaptive estimation in COM–Poisson longitudinal regression model’, Comm. Statist. Simulation Comput. 42 (2013) 755–770.Google Scholar
McKenzie, E., ‘Autoregressive moving-average processes with negative binomial and geometric marginal distributions’, Adv. Appl. Probab. 18 (1986) 679–705.CrossRefGoogle Scholar
Prentice, R. and Zhao, L., ‘Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses’, Biometrics 47 (1991) 825–839.CrossRefGoogle ScholarPubMed
Shmueli, G., Minka, T., Borle, J. and Boatwright, P., ‘A useful distribution for fitting discrete data’, J. R. Stat. Soc. Ser. C Appl. Stat. 54 (2005) 127–142.CrossRefGoogle Scholar
Sutradhar, B. and Das, K., ‘On the efficiency of regression estimators in generalised linear models for longitudinal data’, Biometrika 86 (1999) 459–465.Google Scholar
Thall, P. and Vail, S., ‘Some covariance models for longitudinal count data with overdispersion’, Biometrika 46 (1990) 657–671.CrossRefGoogle ScholarPubMed
Wang, Y. and Carey, V., ‘Working correlation structure misspecification, estimation and covariate design: implications for generalized estimating equations performance’, Biometrika 90 (2003) no. 1, 29–41.Google Scholar