Semiparametric likelihood methods for longitudinal data with nonignorable nonresponse

This dissertation deals with longitudinal data analysis with missing values in the responses. We focus on semiparametric estimation of the model parameters. The proposed estimators don't require specifications of the data model or the missing probability model or both. Throughout the dissertation we assume that the nonresponse doesn't depend on the covariate which is always observed.;First for a sequential longitudinal model, we propose a pseudo likelihood estimator for the model parameters without specifying the missing probability model. We assume that the missingness is current-value dependent, which means whether or not the current outcome variable is observed depends on the current value of the response. The proposed estimator is robust to misspecification of the missing probability model and is computationally easier due to absence of nuisance parameters indexing the missing probability models; In addition, it utilizes all data points, completely or incompletely observed. Hence it is more efficient than alternative estimators.;Second, without specifying the missing probability model, we consider a more general missing mechanism that the missingness of the response not only depends on the current value of the response, but also depends on all previous response values, given that the previous responses are observed. That is, the missingness is non-future dependent.;Third, we consider an empirical likelihood approach that generates a parameter estimator without specifying either the missing probability or the response model. We assume that the mean function of the current outcome variable, given the covariate and previous outcome variables, is parametric indexed by the unknown parameters. We assume the missingness is non-future value dependent.;Simulations and data analysis examples are provided to demonstrate the finite sample properties of the estimators in terms of empirical bias, standard errors and coverage probabilities.