病例對照研究中多元羅吉斯迴歸模型的資訊矩陣適合度檢定

An information matrix goodness-of-fit test of the multinomial logistic regression model in case-control studies

張琇雅(Hsiu-Ya Chang)

指導教授 ： 陳麗菁

淡江大學/商管學院/統計學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00307

摘要

在多元反應變數的病例對照研究中，常使用多元羅吉斯迴歸模型來探討疾病與風險因子之間的關係。將模型重參數化後發現，多元羅吉斯迴歸模型會等價於多組雙樣本半參數化模型，且病例組與對照組的密度函數比值取對數後會與資料呈線性關係。本文以此為基礎建構半參數最大概似估計量。為了檢測多元羅吉斯迴歸模型的適合度，本文推廣White(1982)及Zhang(2001)的概念，針對病例對照資料提出以資訊矩陣為基礎的適合度檢定統計量，並使用拔靴法計算該檢定統計量之p值。透過模擬研究，比較該檢定統計量之型一誤比率與檢定力。最後將所提出的適合度檢定應用於兩組實務資料做為範例。

關鍵字

拔靴法 ； 病例對照研究 ； 適合度檢定 ； 資訊矩陣檢定 ； 多元羅吉斯迴歸 ； 半參數最大概似估計量

並列摘要

For multinomial response in case-control studies, the multinomial logistic regression model is popularly used to infer the relationship between disease and risk factors. After reparameterisation, the assumed the multinomial logistic regression model is equivalent to several two-sample semiparametric models in which the log ratio of case to control density function is linear in data. Based on this finding, the semiparametric maximum likelihood estimator is constructed. In order to detect the goodness-of-fit of the multinomial logistic regression model, this thesis extends the idea of White(1982) and Zhang(2001) to propose an information matrix based goodness-of-fit statistic based on case-control data. A bootstrap procedure is presented to evaluate the p-value of the proposed test. Power and size comparisons are performed through some simulations. Finally, this thesis illustrates the information-matrix-based test by analyzing two real datasets.

並列關鍵字

Bootstrap method ； case-control study ； goodness-of-fit test ； information matrix test ； multinomial logistic regression ； semiparametric maximum likelihood estimator

參考文獻

許育愷 (2014)。病例對照研究中多元羅吉斯迴歸模型的適合度檢定。淡江大學統計學系應用統計學研究所碩士論文。

Louviere, J. J., Hensher, D. A., and Swait, J. D. (2000). Stated choice methods: analysis and applications. Cambridge University Press.

Bull, S. B., and Donner, A. (1987). The efficiency of multinomial logistic regression compared with multiple group discriminant analysis. Journal of the American Statistical Association, 82, pp. 1118-1122.

Chernoff, H., and Lehmann, E. L. (1954). The use of maximum likelihood estimates in χ^2 tests for goodness of fit. The Annals of Mathematical Statistics, 25, pp. 579-586.

Efron, B. (1979). Bootstrap methods: another look at the jackknife. The annals of Statistics, pp. 1-26.