本計畫之目的是提出一個新的半母數(semi-parametric)方法來分析相關性資料。此方法結合了兩種估計函數，其中一個估計函數是適用於獨立的資料，另外一個估計函數則是納入了資料相關性的部分。本計畫的靈感來自Tsou (2008a, 2008b)兩篇論文。此兩篇論文是使用多元負二項(multivariate negative binomial)模型來分析相關性的個數資料。其中，多元負二項的迴歸參數的分數函數(score function)可以拆解成兩個部分: 其中一個部分為卜瓦松模型的分數函數，另外一個部分為以群內總和為反應變數，且包含了相關性的參數的估計函數。這兩個估計函數皆為不偏估計函數。在不知道相關性資料真正的分配情況下，本計畫將探索這種＂複合估計函數(composite estimating equations)＂用於分析相關性資料迴歸參數的效果。我們會探討複合估計函數迴歸參數估計量的大樣本性質，例如漸進常態與有效性。計畫中也將比較複合估計函數，廣義估計方程式(generalized estimating equations)及複合概似函數(composite likelihood)在參數估計及估計量的大樣本性質上表現的差異。 The aim of this project is to establish a new semi-parametric means of analyzing correlated data. The idea is to combine two estimating equations, one for dependent data and one for accommodating the nature of within-cluster association existing in data. This project is inspired by the work of Tsou (2008a, 2008b), where the multivariate negative binomial model was used to analyze general correlated count data. The score function based on this working model is composed of two parts. The first one is simply a score function from Poisson and the second is an estimating function utilizing cluster total as response. Both functions are unbiased. We explore the usefulness of this “composite estimating equations＂ method for analyzing correlated data whose underlying distributions need not to be known. The performance of the composite estimating equations will be investigated in terms of asymptotic properties, such as the asymptotic normality and the efficiency. Comparisons to the generalized estimating equations (GEEs) and the composite likelihood method will also be made. 研究期間：10008 ~ 10107
