具有隨機效應及測量誤差之對數線性模型的參數估計方法

The Estimation of the Log-Linear Model with Measurement Errors and Random Effects

丁怡皓(Yi-Hao Ting)

指導教授 ： 黃逸輝

淡江大學/理學院/數學學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00824

摘要

在自變數有測量誤差時,具有隨機效用的廣義線性模式的分析相當困難，主要原因是將隨機效用積分後的分配已不再是廣義線性模式，使得傳統上處理測量誤差的條件分數法或是校正分數法難以應用。本文主要探討對數線性在有測量誤差和隨機效用時的模型中，提出使用延伸校正QVF(quasilikelihood and variance function)的估計法，並與 Naive 、迴歸校正法及部分條件分數法三者作模擬比較。

關鍵字

測量誤差 ； 隨機效應 ； 對數線性模型 ； 延伸校正QVF估計法

並列摘要

There are not many literatures discuss the statistical inference when
the measurement error and random effect exist in the generalized linear
model. The main reason is that the distribution after integrating the random
effect is no longer a generalized linear model, hence the conventional
conditional score or corrected score are difficult in application. This
paper discussed the estimation method when measurement error and random
effect coexist in the log-linear model, the estimation was done by an
extended corrected QVF score. We compare the efficient of the methods of
Naive, regression calibration and partially conditional score with the
proposed method by simulation studies.

並列關鍵字

Measurement error ； Random effect ； Log-linear model ； Extended corrected QVF score

參考文獻

Chan, Jennifer S.K. and Kuk, Anthony Y.C. (1997). Maximum Likelihood Estimation

for Probit-Linear Mixed Models with Correlated Random Effects. Biomet-

Novick, S. J. and Stefanski, L. A. (2002). Corrected score estimation via complex

variable simulation extrapolation. Journal of the American Statistical Associa-

Schall, R. (1991). Estimation in Generalized Linear Models with Random Effects.