在長期性資料分析裡，邊際效應的GEE 方法以及混合效應模型是經常被用來探 討疾病與某些預後因子之間的相關性。但是，相關的模型診斷方法還沒有被廣泛地探 討。潛在的主要原因是個體內相依資料之共變異的多樣性，以及重複測量次數的差異很 大。Yang 與Chang（2006）延續Chang（2000）的觀點，建議考量此種共變異的多樣 性，應用多重指標有其必要性。當個體的殘差值集滿足可交換性時可視模型具適切性的 情況下，我們發現Yang 與Chang（2006）的大部份指標會拒絕模型的適切假設；其原 因是把殘差值集以序列型態來做探討所造成的。在過去的研究裡，我們將殘差值集以陣 列型態建構一個統計量稱為H U （這樣的檢定統計量可以讓具可交換性的模型被拒絕的 錯誤機會被控制。），在列向量滿足相互獨立，且列向量具可交換性的條件下，該統計 量的漸近分布為具有自由度(k1)2的卡方分布。在本研究裡，我們延續該研究，探討統 計量H U 在非可交換性下的漸近檢定力。並探討在不同對立假設下，從列秩矩陣的邊際 分布情形，並輔以其他指標，歸納出建構模型時的相關訊息。
In longitudinal data analysis, the generalized estimating equation (GEE) method and/or mixed-effects models are employed very often for exploring the relationship between disease and some pathogenic factors. The related model diagnostic procedures are not yet widely studied. The potential causes of major problems are the high variety of the dependence within subjects and/or the number of repeated measurements. Yang and Chang (2006) suggested that multiple quantitative indexes for model diagnostics are needed to take into account this variety which followed the viewpoint of Chang (2000). Sometimes, however, one regards the fitted model is well when the individual’s residuals satisfy the property of exchangeability. We find that some of those indexes in Yang and Chang (2006) reject the hypothesis. In the past research, we had developed a test which was called H U through the array of the residual sets (The probability of false rejection when the current model satisfies the property of exchangeability will be controlled by the proposed test). Under the conditions of independent between the exchangeable row vectors, the asymptotic distribution of the statistic UH is according to chi-square 2 distribution with (k1)2 degrees of freedom. In this research, we study the asymptotic power of the statistic H U under the condition of un-exchangeability which was followed by that study. Also, under the alternative hypothesis, we study the marginal distributions of the array and other auxiliary indexes to generalize the information of the model fitting.
