Testing Significance of Tetrachoric Correlation Coefficient Matrix of Binary Variables

檢定雙生變數四分相關係數矩陣之顯著性

林定香(Ting-Hsiang Lin)

《管理科學與統計決策》 5卷1期 (2008/03) Pp. 46-50

https://doi.org/10.6704/JMSSD.2008.5.1.46

摘要

四分相關係數常用來測量2x2的列聯表中，兩個假設存在著潛在常態分配的雙生變數間的相關關係。研究者經常需要多個雙生變數的相關係數矩陣以執行更先進的統計技術，譬如多變量分析、因素分析、或結構方程模式。然而，多數軟體無法產生四分相關係數矩陣。我們寫了一個程式來達成此目標。演算法以Divgi的方法爲起始值，並使用了四分相關數列展開式及高斯求積分法，並以32點求積法以避免可能的無數次疊代的問題。我們並考慮估計值的絕對值是否超出預設的邊界值，程式並考慮稀少及負的次數分配。我們討論演算的流程及寫了計算四分相關係數矩陣及漸進標準誤差的程式。本程式並且可以執行四分相關係數顯著性的假設檢定。

關鍵字

四分相關係數 ； 四分相關數列展開式 ； 32點求積法 ； 雙生變數

並列摘要

The tetrachoric correlation coefficient is often used in a 2x2 contingency table to measure the relationship of two binary variables assuming that each variable has an underlying continuous normal distribution. Researchers often demand a correlation matrix of more than two variables to perform more advanced statistical techniques such as multivariate analysis, factor analysis, or structural equation modeling. However, most software lacks the ability to do so. We implemented a program to achieve the goal. The algorithm used Divgi's method as starting values, and exercised tetrachoric series expansion and Gaussian quadrature with a 32-point quadrature adjustment to avoid possibly infinite number of iterations. The program also takes sparse and negative frequencies into consideration. We discussed the algorithm calculating the tetrachoric correlation coefficient matrix and their asymptotic standard errors. The program also performs hypothesis testing for significance of tetrachoric correlation coefficients.

並列關鍵字

tetrachoric correlation ； tetrachoric series expansion ； 32-point quadrature ； binary variables

參考文獻

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