複合概似函數有效性之探討

Efficiency of the Composite Likelihood

陳婉貞(Wan-chen Chen)

指導教授 ： 鄒宗山

國立中央大學/理學院/統計研究所/博士(2013年)

摘要

近年來,複合概似函數方法 (Composite Likelihood) 引起高度關注。原因在於複合概似函數方法對於分析不易獲得聯合分布函數的相關性資料,既便利又有效。無庸置疑的,多維常態分配經常被當作建構複合概似函數的核心模式。
本論文納入多維負二項分配為核心模式來建構複合概似函數,對於相關性資料的迴歸分析,證明此核心模式所建構的複合概似函數相較於多維常態分配是更好的選擇。此外,多維負二項複合概似函數方法亦能得到更有效的迴歸參數估計量。
集群內相關性的估計對於改善有效性是有助益的。本文最後,根據錯誤的模型假設(如用二項分配模式配適相關二元資料或多項分配模式配適相關的有序資料)所導致Bartlett第二等式錯誤的性質，提出一個估計集群內相關性的新方法。此方法可應用於如:邏吉斯迴歸模型、對數迴歸模型、比例勝算迴歸模型或其他適當的連結函數,且可利用有提供naïve及sandwich共變異數矩陣的統計軟體來簡單的執行此估計方法。

關鍵字

複合概似函數 ； 多維負二項分配 ； 費雪訊息 ； Bartlett's 第二等式 ； 集群資料 ； 相關係數

並列摘要

The method of composite likelihood (CL) has attracted a lot of attentions in recent years. This expedient method is convenient for analyzing correlated data whose joint distribution is difficult to model or unattainable. Without surprises, multivariate normal has been the sole model utilized to fabricate composite likelihood functions
In this thesis we incorporate the multivariate negative binomial distribution as the core model to build up composite likelihoods. We will show that using the negative binomial model to formulate a composite likelihood might be a better choice for regression analysis of general correlated data. The negative binomial-based composite likelihood (NB-CL) will be demonstrated to be more efficient than the usual normal-based composite likelihood (NM-CL).
To further improve the efficiency, a sensible estimation of the intra cluster correlation (ICC) is often beneficial for this purpose. To this end, we introduce a new tool for inference making for ICC between correlated binary data and correlated ordinal data. The creation of this method is founded upon the violation of Bartlett’s second identity when adopting the binomial distributions to model cluster binary data and the multinomial distributions to model cluster ordinal data. The new methodology applies to any sensible link functions that connect the success probability and covariates. One can easily implement the procedure by using any statistical software providing the naïve and the sandwich covariance matrices for regression parameter estimates.

並列關鍵字

Composite likelihood ； Multivariate negative binomial distribution ； Fisher information matrix ； Bartlett's second identity ； clustered data ； Correlation coefficient

參考文獻

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