迴歸模式無重複觀測值缺適性檢定的簡便法

Abstract

一個迴歸模式之適當與否，有賴於缺適性檢定，而傳統之缺適性檢定 ，只能對有重複觀測值之情形作檢定，對於無重複觀測值之情形，雖然有 不少學者針對此問題進行探討，但至今仍無定論。以往學者大多以近鄰之 概念將觀測值分組，並將分組後之觀測值視為重複觀測值，然後以重複觀 測值缺適性檢定方法進行檢定；而本研究提出一與傳統方法截然不同之概 念，利用虛擬變數表示分組後之迴歸模式，並作重合性檢定，以此檢定結 果便可得知該迴歸模式是否有缺適性情形存在，而分組係以殘差散佈圖作 為依據，並以敏感度分析評估分組方式之強勢性(robustness)。本研究並 對所提之方法與其他學者之方法作比較分析，包括模擬分析與實例分析， 以確定本方法不僅簡單易懂，同時兼顧正確性。 Assessment of the adequacy of a regression model has been extensively carried out by using lack-of-fit test. However, the classical lack-of-fit testis useful only when replications are available. Therefore, some methods for testing lack-of-fit in regression without replication, but there still existsome restrictions. Most of the works group observations based on "near neighbor", within which observations are viewed as replicates, and then theclassical lack-of-fit test is applied. In this thesis, we provide a quitedifferent concept by introducing dummy variables for separate groups of observations into a regression model, and then testing for coincidence forevaluating lack-of-fit. Residual plots are examined to help determine suitable cutoff points to form different groups. Sensitivity analysis is performed to evaluate the robustness regarding where the cutoff point are located. We alsocompare the proposed method with other methods in terms of simulation and anempirical example. We conclude that the proposed method is simple easy-to-use,and accurate.