In this thesis, we present an overview of generalized linear models (GLMs) for binary and count data with missing covariates when the missing data mechanism is nonignorable. We use the maximum likelihood method to estimate the parameters in GLMs. We study a set of ML estimating equations for fitting regression models to binary and Poisson data with missing covariates.

Simulations were carried out to observe the behaviour of the MLEs under both correctly specified and misspecified structures. Our simulation study shows that the ML method generally provides unbiased and efficient estimators under correctly specified models, whereas a misspecified model provides biased and inefficient estimators. It also indicates that for small sample size, the empirical coverage probabilities of the parameter estimates are a bit apart from the nominal 95% level. Also, the average lengths of the confidence intervals for the regression parameters tend to be smaller for larger sample size.