長期資料分析之模型診斷

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 學位論文 > Item 987654321/32935

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题名:	長期資料分析之模型診斷
其它题名:	Model diagnostics in longitudinal data analysis
作者:	余佳燕;Yu, Jia-yan
贡献者:	淡江大學數學學系碩士班張玉坤;Chang, Yue-cune
关键词:	長期資料;樣本自我相關函數;樣本偏自我相關函數;Longitudinal Data;Sample Autocorrelation Function;Sample Partial Autocorrelation Function
日期:	2008
上传时间:	2010-01-11 03:00:17 (UTC+8)
摘要:	在臨床相關之生物醫學的療效評估研究中，同一個體需在不同時間點重複觀測，形成所謂的長期縱貫性之相依資料。處理此類相依資料的統計分析方法中，GEE方法之廣義線性模式或是混合效應模式是較常被用來探討各變項間之相關性。此方法提出雖已超過20年，但其相關之模型診斷問題，仍待積極研發。造成這種問題的主要原因之一，可能在於不同研究中同一個體之多筆重複觀測資料間的相依型態具有很大的差異性。因此，任何單一檢定方法，不能解決所有長期相依資料之模型診斷問題，導致此類的模型診斷變得更複雜。針對此問題，有學者提議需同時採用多種指標與方法，較為妥當。本文所提方法屬於殘差分析圖形判別法的一種。更具體的說，使用Box-Jenkins時間數列模式理論中的樣本自我相關函數(SACF)與樣本偏自我相關函數(SPACF)兩種函數圖形來判別所建構預測模型之殘差值是否具隨機性，必要時，再加上延伸的樣本自我相關函數(ESACF)來輔助模型診斷的進行。如果模型診斷結果顯示我們所建構的預測模型之殘差值不具隨機性，即表示建構的預測模型還有改善的空間。我們使用五組實際臨床資料，分別以固定效應及隨機效應建立預測模式後，以所提方法進行模型診斷，並與Yang & Chang(2006)的結果相互比較。結果發現，五組資料在固定效應模式之下，殘差值幾乎都不具隨機性。換言之，以固定效應模式對五組資料所建構的預測模型還不是最合適，仍有改善空間。因此考慮使用隨機效應模式來改善原先建構的預測模型。在隨機效應模式下，雖有部分模型診斷結果顯示殘差值仍不具隨機性，但並非所有診斷方法。因此，依本研究結果顯示，不同研究之相依資料因結構複雜，沒有單一的指標可以明確地做為所有相依資料模型診斷的依據。處理此類相依資料分析的模型診斷問題時，盡可能同時採用/參考多種診斷方法以達到相輔相成的效果。 In clinically biomedical research, to evaluate the treatment effects, each subject should be measured repeatedly at preset time points, which forms a longitudinal dependent data. To analyze these dependent data, the GEE methods’ generalized linear models and/or the mixed effects models are, relatively compare to all potential statistical methods, more commonly used method to explore the possible relationships within the collected variables. Although the GEE methods were proposed over two decades, the related model diagnostic procedures for longitudinal data are not yet fully formalized. One of the possible reasons to cause this kind of problem is mainly due to the tremendous variety of the types of dependency within the same subject’s repeated measurements. Therefore, it is impossible to find a single diagnostic procedure that can solve all kinds of model diagnostics of longitudinal studies, which makes the model diagnostic for longitudinal study become more complicated. Accordingly, Yang & Chang (2006) proposed the simultaneous usage of multiple diagnostic procedures. The method we proposed in this paper is kind of visualized residuals analysis. More specifically, we use two kinds of functional plots in time series analysis proposed by Box and Jenkins, named the sample autocorrelation function (SACF) and sample partial autocorrelation function (SPACF), to test the randomness of the residual values obtained from the final fitted model. The extended sample autocorrelation function (ESACF) plot will be used to assist model diagnosis whenever it is needed. The fitted model need to be improved if the results of diagnostic show that the residual values is not random. We used the proposed method to five real clinical studies data and compared the results to those shown in Yang and Chang (2006). We found that all those five residual values obtained from the fixed effects’ models were not random. In other words, those five fixed effect’s models were not fitted satisfactory and needed to be improved. With no extra variable available, we used the random effects’ models. Although there were still some diagnostic results’ showed that the residual values were not random,but not all of them, under the random effects’ models. Therefore, according to our findings, due to the heterogeneity of the within subject’s dependency among different studies, there is no single diagnostic procedure can be used to all kinds of dependent studies. We should use (refer to) all possible diagnostic procedures simultaneously in order to complement each other.
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