Parametric and/or Semi-parametric Dynamic Mixed Models for Discrete Spatial and/or Longitudinal Data

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Summary of the Proposal : The main purpose of this proposal is to develop new and innovative parametric and semi-parametric correlation models for discrete spatial/familial as well as longitudinal data subject to over-dispersion and missing values. The proposed correlation models will be exploited for the inferences about the primary properties of the data such as the mean regression function and variation in the data. The proposal will contain three specific projects. The first project will deal with modeling and inferences for spatial count and binary data. The purpose of the second project is the development of semi-parametric dynamic mixed models for longitudinal count and binary data with possible over-dispersion. The third project will deal with dynamic mixed models for both nominal and ordinal longitudinal categorical data with or without missing values. The primary parameters of these models under all three projects will be estimated either by using the so-called efficient GQL (generalized quasi-likelihood) or exact likelihood approaches, whether secondary parameters/functions such as the non-parametric function and correlation index parameter involved in the second project; and the correlation and missing mechanism related parameters in the third project will be estimated by QL or moment approaches. The asymptotic properties such as consistency, asymptotic efficiency and asymptotic normality of the estimators of main parameters/functions will be studied. This will require the central limit theorems (1) for patterned correlated variables in spatial models under project 1, and (2) for independent but nonidentical multidimensional variables both in semi-parametric longitudinal mixed models under project 2, and in dynamic mixed models with or without missing values under project 3. Thus, the primary nature of this proposal is the fundamental statistical methodological developments for selected correlated such as repeated discrete spatial, discrete over-dispersed type semi-parametric longitudinal, and over-dispersed longitudinal categorical data. Because these types of correlated data arise in natural and physical sciences, bio-statistical, social-science and econometric research fields, the proposed methodological research will benefit graduate students and researchers in Canada and elsewhere engaged in theoretical and/or applied research in these areas. **