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On a Unified Generalized Quasi–likelihood Approach for Familial–Longitudinal Non‐Stationary Count Data
Author(s) -
SUTRADHAR BRAJENDRA C.,
JOWAHEER VANDNA,
SNEDDON GARY
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00607.x
Subject(s) - mathematics , count data , covariate , statistics , correlation , generalized estimating equation , quasi likelihood , longitudinal data , random effects model , estimation , regression , data set , regression analysis , generalized method of moments , econometrics , panel data , data mining , computer science , meta analysis , medicine , geometry , management , economics , poisson distribution
. In this paper, conditional on random family effects, we consider an auto‐regression model for repeated count data and their corresponding time‐dependent covariates, collected from the members of a large number of independent families. The count responses, in such a set up, unconditionally exhibit a non‐stationary familial–longitudinal correlation structure. We then take this two‐way correlation structure into account, and develop a generalized quasilikelihood (GQL) approach for the estimation of the regression effects and the familial correlation index parameter, whereas the longitudinal correlation parameter is estimated by using the well‐known method of moments. The performance of the proposed estimation approach is examined through a simulation study. Some model mis‐specification effects are also studied. The estimation methodology is illustrated by analysing real life healthcare utilization count data collected from 36 families of size four over a period of 4 years.