對數線性混合效用測量誤差模型之ㄧ致性估計

A Consistent Estimation in Log-Linear Mixed Measurement Error Models

張瑞君(Jui-Chun Chang)

指導教授 ： 黃逸輝

淡江大學/理學院/數學學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00564

摘要

將隨機效用引進迴歸模型裡，反應變數之間就會具有相關性。因此當模型包括隨機效用時，也就是所謂的混合模型，便可以用來模式化具有相關性反應變數的資料。在大多數的混合模型裡，以概似函數為基礎的推論通常是可行的，然而當迴歸模型裡有任何共變數受限於測量誤差時，統計推論的工作就會變得困難，因為在大部分的測量誤差問題裡概似函數是無界的也通常是不可行的，尤其是在自變數是未知參數的時候。因此至今只有少數的文獻討論處理有測量誤差的混合模型。就作者所知，在對數線性混合效用模型且自變數受限於測量誤差時，目前尚未有人提出一個具有一致性的估計方法。在本篇論文裡，我們將利用準變異數函數與校正分數的概念，在傳統加法性的測量誤差假設下，提出一種具有一致性的估計方法，而我們的模擬研究也顯示這個估計函數的表現是不錯的。

關鍵字

改正分數 ； 對數線性模型 ； 測量誤差 ； 混合效用 ； 準變異數函數

並列摘要

By introducing the random effect into a regression model, the correlation between responses raises consequently. Thus when a model includes random effects, which is called a mixed model, can be suitable for modeling correlated responses. In most mixed models, the likelihood-based inferences are usually applicable. However, when any covariate in the regression model are subject to measurement error, the statistical inference becomes difficult for the reason that the likelihood approach is not feasible in most measurement error problems, especially for the functional cases. For this difficulty, there are only few literatures dealing with the mixed model with measurement error nowadays. Furthermore, to the best knowledge of the author, there is no consistent estimation for the log-linear mixed effect model when measurement error presents. In this thesis, inspired by the quasi-variance function and the corrected score, we construct estimating function for log-linear mixed model with classical additive measurement error. It is shown that the estimation is consistent and our simulation study indicates that the proposed estimating function works satisfactory.

並列關鍵字

Corrected score ； Log-linear model ； Measurement errors ； Mixed effects ； Quasi-variance function

參考文獻

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