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

提案摘要：该提案的主要目的是为离散的空间/家族数据以及受过度分散和缺失值影响的纵向数据开发新的和创新的参数和半参数相关模型。建议的相关模型将被用来推断数据的主要属性，如平均回归函数和数据中的变化。该提案将包含三个具体项目。第一个项目将处理空间计数和二进制数据的建模和推断。第二个项目的目的是开发用于纵向计数和可能过度分散的二进制数据的半参数动态混合模型。第三个项目将处理有或没有缺失值的名义和顺序纵向分类数据的动态混合模型。无论第二个方案是否涉及非参数函数和相关指数参数等次要参数/函数，这些模型在所有三个方案下的主要参数都将使用所谓的有效GQL(广义拟似然)或精确似然方法估计，而第三个方案中与相关和缺失机制相关的参数将使用QL或矩方法估计。研究主要参数/函数估计量的相合性、渐近有效性和渐近正态等渐近性质。这将需要中心极限定理(1)在项目1的空间模型中的模式相关变量，和(2)在项目2的半参数纵向混合模型中和项目3的动态混合模型中独立但不相同的多维变量的中心极限定理。因此，本建议的主要性质是对选定的相关数据的基本统计方法的发展，例如重复的离散空间、离散的超离散类型的半参数纵向分类数据和过度分散的纵向分类数据。由于这些类型的相关数据出现在自然科学和物理科学、生物统计学、社会科学和计量经济学研究领域，拟议的方法研究将使加拿大和其他地方从事这些领域理论和/或应用研究的研究生和研究人员受益。

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. **