中華心理學刊 民 90，43 卷，1 期，35-44
Chinese Journal of Psychology 2001, Vol.43, No.1, 35-44
洪來發（國立中正大學心理學系） ； 王文中（國立中正大學心理學系）
摘要
母體分配的假設是個重要的議題。如果當初關於母體分配的假設不恰當，後績的統計推論都將失眞。本研究探討「White(1982)母體分配假設的訊息矩陣檢定法(information matrix test）及其相關的檢定法。鑑於該檢定法必須計算log-density之第三階偏導數以求得共變異矩陣，因此推演困難且繁雜，並不實用。Chesher(1983)與Lancaster(1984)提出人工迴歸式的簡單計算公式，不需計算∇D(θ) , 就能估算出White訊息矩陣統計檢定式等於樣本大小n乘以判定係數R2。由於該人工迴歸式不適用於∇D(θ)為0的情境，因此我們提出「適用於∇D(θ)爲0時，和Lancaster計算式不同的統計檢定式。由於訊息矩陣檢定法，牽涉到許多估計式，在尙無嚴謹理論佐證下，我們藉由模擬分析來評斷各檢定式之第一型誤差，結果顯示Lancaster人工迴歸檢定法傾向於過度拒絕虛無假設，White檢定法結果是三者中最令人滿意的，我們的檢定法結果介於兩者之間，這說明了我們的檢定法簡單有效。
關鍵詞： White訊息矩陣檢定、Lancaster人工迴歸式、有限樣本、母體分配
INFORMATION MATRIX TESTS FOR POPULATION DISTRIBUTION HYPOTHESIS IN FINITE SAMPLES
Lai - Fa Hung（Department of Psychology, National Chung-Cheng University）；Wen - Chung Wang（Department of Psychology, National Chung-Cheng University）
Abstract
This study attempts to explore the issues in hypothesis testing of population distributions, based on Whites' information matrix test (White, 1982). We point out that White's ▽D(θ) method requires the computation of the third derivatives of log-density for finding the covariance matrix, which is very labor-intensive and impractical. Chesher (1983) and Lancaster (1984) developed a simpler method of artificial regression where the computation is no longer needed. It is found that White's w is equal to sample size n multiplied by the coefficient of determination R2. However, their method is improper when ▽D(θ) = 0. Accordingly, we propose another estimator to correct the errors in the artificial regression. Without strong theoretical evidence, these three methods are compared through a simulation study in terms of type I error rates. The results show that the artificial regression method tends to over-reject the null hypothesis, White's method yields very satisfactory results. Our method is between these two methods in performance, indicating that our method is simple and effective.
Keywords：White information matrix test, Lancaster artificial regression, Finite samples, Population distributions
