Many variables that are used in social and behavioural science research are ordinal categorical or polytomous variables. When more than one polytomous variable is involved in an analysis, observations are classified in a contingency table, and a commonly used statistic for describing the association between two variables is the polychoric correlation. This paper investigates the estimation of the polychoric correlation when the data set consists of misclassified observations. Two approaches for estimating the polychoric correlation have been developed. One assumes that the probabilities in relation to misclassification are known, and the other uses a double sampling scheme to obtain information on misclassification. A parameter estimation procedure is developed, and statistical properties for the estimates are discussed. The practicability and applicability of the proposed approaches are illustrated by analysing data sets that are based on real and generated data. Excel programmes with visual basic for application (VBA) have been developed to compute the estimate of the polychoric correlation and its standard error. The use of the structural equation modelling programme Mx to find parameter estimates in the double sampling scheme is discussed.

中文翻译：

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根据错误分类的数据估算多态相关性。

在社会和行为科学研究中使用的许多变量是序数分类变量或多变量变量。当一个分析中涉及多个变量时，观察结果会在列联表中分类，描述两个变量之间关联的常用统计数据就是多变量相关性。当数据集包含错误分类的观测值时，本文研究了多变量相关性的估计。已经开发出两种估计多态相关性的方法。一个假设与错误分类有关的概率是已知的，另一个假设使用双重抽样方案来获取有关错误分类的信息。开发了参数估计程序，并讨论了估计的统计属性。通过分析基于真实数据和生成数据的数据集，说明了所提出方法的实用性和适用性。已经开发了具有Visual Basic for Application（VBA）的Excel程序，以计算多色相关及其标准误差的估计值。讨论了使用结构方程建模程序Mx查找双采样方案中的参数估计值。