ANALYSIS OF COUNT DATA USING POWER VARIANCE FUNCTION

This paper considers two estimation methods for count data with a power variance function. One is the maximum likelihood method based on a negative binomial model with a power variance function which is not the standard application of a negative-binomial model. Another is the quasilikelihood/pseudolikelihood (QL/PL) estimating equation method. The QL/PL method is a robust method and is applicable to a more general exponential dispersion model with a power variance function. The asymptotic efficiency of the QL/PL estimates were calculated relative to the maximum likelihood estimates, and demonstrated that the mean parameter estimate is approximately fully efficient. If the power parameter of the variance is close to one, then the efficiency of the power parameter of the variance is close to one. It was also found that, in a negative-binomial model with power variance function, mean parameter estimates and variance parameter estimates are approximately asymptotically independnet. An example of data analysis using power variance function is given.