Goodness-of-Fit Tests for The Proportional Odds Regression Models via Global Odds Ratio

以全域勝算比方法所建構之等比優勢迴歸模型適合度檢定統計量

林國欽(Kuo-Chin Lin)

《智慧科技與應用統計學報》 10卷2期 (2012/12) Pp. 1-10

https://doi.org/10.29807/JTITAS.201212.0001

摘要

長期追蹤順序資料廣泛應用於社會學及生物醫學研究中。整體模型適配之檢定問題是在長期追蹤類別型資料分析中，不可避免的重要研究議題。本文章將利用全域勝算比當作資料相關測量方式，針對等比優勢迴歸模型提出兩個新的適合度檢定統計量，檢定統計量以皮爾森卡方型式及非權重殘差平方和方式呈現。Lin（2010）提出的適合度檢定統計量方法係考慮各種不同的相關矩陣結構下而得，本研究的結果可視為以上方法更一般化的延伸。在大樣本條件下，新檢定統計量之抽樣分配係用近似常態分配分析。本研究同時提出各種條件之模擬計算，主要目的為比較新方法與現有方法的檢定力表現及型I誤差比較。最後，我們應用一筆長期追蹤順序實驗資料之模型適配檢驗，來闡述新方法的應用性。

關鍵字

廣義估計方程式 ； 全域勝算比 ； 適合度檢定 ； 長期追蹤順序資料

並列摘要

Studies involving longitudinal ordinal responses are widely applied in the social and biomedical sciences research. The overall test for model adequacy is an essential issue in longitudinal categorical data analysis. This article proposes two alternative goodness-of-fit tests in terms of Pearson chi-squared and unweighted sum of square residual for the proportional odds regression models based on the global odds ratio as a measure of association. Our method can be regarded as an extension of the method proposed by Lin (2010) considering four major variants of working correlation structures. For large samples, the distributions of the two test statistics are approximated by the standard normal distribution based on the asymptotic means and variances. In simulation studies, the type I error rate and the power performance comparison between the proposed tests and the current tests are presented for various sample sizes. The application of the proposed tests is illustrated by a real data set.

並列關鍵字

GEE ； global odds ratio ； goodness-of-fit ； longitudinal ordinal data