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Description:
Generalized linear and nonlinear mixed effects models have been used in many fields of application, such as psychology, medicine, and engineering, etc. There are multiple observations within subjects over time. Hence, the structure of the data in these models is longitudinal. This means that data within each subject are correlated and between the subjects are uncorrelated. In this dissertation, we treat the binary and ordinal mixed effects regression model, where the response variable includes two or more than two levels, respectively. Moreover, a nonlinear longitudinal Poisson regression model is considered to test the ability of the subjects. For estimating the model parameters, we intend to use the maximum likelihood estimator of the parameters due to its well behaved asymptotic properties; however, because the form of the log-likelihood function does not have a closed form, we have to choose an alternative estimation method. The quasi maximum likelihood estimation method is a suitable suggestion for this aim. To determine this estimate, it is required to build the quasi log-likelihood function. This function depends on the marginal first and second order moments of the response variable. These moments do not have an explicit closed form in the binary and ordinal mixed effects models, either, and have to be approximated, too. In contrast to that in the longitudinal Poisson regression model the required moments have an explicit analytical Under sufficient conditions for the quasi maximum likelihood estimate of the parameters, we aim to achieve the D-optimum designs for the experimental settings. Therefore, we construct the quasi Fisher information matrix and establish the corresponding D-optimality criterion. In the binary and ordinal mixed effects models, the quasi Fisher information matrix lacks the analytical form. Hence, we approximate it for particular cases of the models. On the other hand, in the longitudinal Poisson regression model, the quasi Fisher information matrix has the closed form and can be ...