On Modeling the Double and Multiplicative Binomial Models as Log-Linear Models

In this paper we have fitted the double binomial and multiplicative binomial distributions as log-linear models using sufficient statistics. This approach is not new as several authors have employed this approach, most especially in the analysis of the Human sex ratio in [1]. However, obtaining the estimated parameters of the distributions may be problematic, especially for the double binomial where the parameter estimate of π may not be readily available from the Log-Linear (LL) parameter estimates. Other issues associated with the LL approach is its implementation in the generalized linear model with covariates. The LL uses far more parameters than the procedure that employs conditional log-likelihoods functions where the marginal likelihood functions are minimized over the parameter space. This is the procedure employed in SAS PROC NLMIXED. The two procedures are essentially equivalent for frequency data. For models with covariates, the LL uses far more parameters and the marginal likelihood functions approach are employed here on three data set having covariates.