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

提案摘要：本提案的主要目的是为离散的空间/家族以及纵向数据开发新的和创新的参数和半参数相关模型，这些数据容易过度分散和缺失值。所提出的相关模型将用于推断数据的主要属性，如平均回归函数和数据中的变化。该提案将包括三个具体项目。第一个项目将处理空间计数和二进制数据的建模和推论。第二个项目的目的是开发纵向计数和可能存在过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有序纵向分类数据的动态混合模型。所有三个项目下这些模型的主要参数将通过使用所谓的高效GQL（广义准似然）或精确似然方法来估计，次要参数/函数（如非参数函数和相关指数参数）是否涉及第二个项目；第三个项目的相关参数和缺失机制参数将通过QL或矩量法进行估计。研究了主要参数/函数估计量的一致性、渐近效率和渐近正态性等渐近性质。这将需要中心极限定理(1)，适用于项目1下的空间模型中的模式相关变量，以及(2)适用于项目2下的半参数纵向混合模型中独立但不相同的多维变量，以及项目3下有或没有缺失值的动态混合模型。因此，本提案的主要性质是为选择相关的基本统计方法发展，如重复离散空间，离散过分散型半参数纵向和过分散纵向分类数据。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，因此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.