不完整長期追蹤資料下經驗概似方法的模型選取準則

Model selection criteria based on empirical-likelihood for incomplete longitudinal data

丘富瑜(Fu-Yu Ciou)

指導教授 ： 陳怡如

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2022年)

https://doi.org/10.6846/TKU.2022.00562

摘要

不完整長期追蹤資料常見於公共衛生與生物醫學等科學領域，而加權廣義估計方程式 (WGEE) 廣泛應用於隨機遺失型態下的邊際模型分析。在統計資料分析中，模型選取是非常重要的議題，若干學者藉由加權廣義估計方程式應用於不完全長期追蹤二元資料分析提出模型選取訊息準則。然而這些準則不論是依據擬慨似或是經驗概似方法，根據模擬結果顯示其訊息準則表現與樣本數有關。本論文主要研究目的為提出不受樣本數限制，依據經驗概似方法適用於不完全長期追蹤二元或順序資料分析的模型選取訊息準則。藉由模擬研究以比較所提出的訊息準則與其他訊息準則之表現，並分別使用不完全長期追蹤二元與順序資料實例，以說明如何應用所提出的模型選取訊息準則。

關鍵字

赤池訊息準則 ； 貝氏訊息準則 ； 經驗概似 ； 多重插補 ； 加權廣義估計方程式

並列摘要

Incomplete longitudinal data are commonly encountered in the public health and biomedical sciences, and the weighted generalized estimating equations (WGEE) approach is widely applied for the analysis of marginal models under the missing at random process. Model selection is a crucial issue in statistical data analysis, and several information criteria for model selection, based on WGEE estimation in the analysis of incomplete longitudinal binary data, have been developed . However, the performances of those criteria either built on quasi-likelihood or empirical-likelihood may depend on the sample sizes according to simulation results. The main purpose of this article is to propose a stable model selection criterion based on empirical-likelihood, regardless of sample sizes, and applicable for simultaneously selecting the marginal model and a working correlation matrix in the analysis of incomplete longitudinal binary or ordinal data. The performance of the proposed criterion compared to the current criteria is presented by simulation studies. The utility of the proposed approach is further illustrated by two real applications involving incomplete longitudinal binary and ordinal data.

並列關鍵字

Akaike information criterion ； Bayesian information criterion ； empirical likelihood ； multiple imputation ； weighted generalized estimating equation

參考文獻

[1] Akaike, H. (1973). Information theory and an extension of the maximum likelihood

principle. In Proceedings of the Second International Symosium on Information

Theory, 267–281.

[2] Chen, C., Shen, B., Zhang, L., Xue, Y., Wang, M. (2019). Empirical-likelihoodbased criteria for model selection on marginal analysis of longitudinal data with

dropout missingness. Biometrics, 75, 950-965.