Quasilikelihood inferences in gamma AR(1) models for longitudinal data

Madan, Manish (2006) Quasilikelihood inferences in gamma AR(1) models for longitudinal data. Masters thesis, Memorial University of Newfoundland.

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Abstract

The statistical analysis of gamma data (exponential being a special case) is quite common in many biomedical or engineering research. The existing studies deal with this type of data either in the independence or time series set up. Independence, as the name suggests implies that the data at time point 't + 1' is independent of the data at time point 't', whereas the time series set up suggests dependence in the data collected at subsequent time points. -- It may however happen in practice that one collects the gamma responses repeatedly along with a set of multi-dimensional covariates, from a large number of independent individuals over a small period of time. In this set up, it is natural that the repeated gamma responses of an individual will be correlated. It is of interest to obtain consistent and efficient estimates for the effects of the covariates on the responses after taking the longitudinal correlation into account. -- In this thesis, we study an autoregressive order 1 (AR(1)) type longitudinal gamma model consisting of a regression vector, a scale, and a longitudinal correlation parameter. The likelihood and a generalized quasilikelihood (GQL) inferences are considered for the estimation of these parameters. It is argued that the likelihood approach is extremely complicated whereas the GQL approach appears to be much simpler which also provides consistent and highly efficient estimates. This is verified through a simulation study.

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