| Poisson and negative binomial regression are widely used in analyzing count data or count data with extra-Poisson variation in the fields of epidemiology, medical research and biology. Numerous methods have been suggested for dealing with these kinds of problems. However, most of these methods have only been applied to the models with the assumption that all the covariates were measured without error. However, ignoring the measurement error structure would cause biases in the estimation of parameter and hence lead to inaccuracy in the analysis.;In this thesis, the measurement error is taken into consideration. We consider the Poisson model with measurement error in covariate. Five estimators are derived for this specific model based on the existing methods and a new estimator is proposed. Biases, asymptotic variances and efficiencies of the estimator derived from the quasi-likelihood and the proposed estimator are studied and compared.;These two proposed estimators for Poisson model are extended and derived for the case when the response follows negative binomial distribution. Two hypothesis tests for testing the Poisson assumption are proposed for the model with measurement error in the covariate. Their conclusion provides statistical evidence for choosing between Poisson and negative binomial models.;For the case of misspecification on covariate, an expression for the asymptotic bias caused by the misspecification is given. With this expression, we can have a better insight of the factors that affect the accuracy of the estimation when the covariate is misspecified. |
