Methods and Applications of Longitudinal Data Analysis

Appendix C

Quasi-likelihood functions and properties

The term quasi-likelihood function was initially introduced by Wedderburn (1974). While providing a way of allowing for overdispersion in statistical analysis, quasi-likelihood estimating equations are mostly applied for grouped binary or count data. In theories underlying this model, the quasi-likelihood function is shown to have similar properties to the log-likelihood function. Briefly, in this perspective, only relationship between the mean and the variance is specified in the form of a variance function.

Suppose we have independent observations Y_i (i = 1, …, N) with expectation μ_i and variances V(μ_i), where V(·) is some known function. Let each observation μ_i be some known function of parameters ...