Estimating the polychoric correlation from misclassified data

Abstract

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.

Noninferiority testing for matched‐pair ordinal data with misclassification

“…Our proposed method was inspired by the work of Yiu and Poon, but there are several notable differences. Yiu and Poon focused on parameter estimation of the polychoric correlation between two categorical variables with misclassification, whereas we are interested in a noninferiority test for two correlated categorical variables. Consequently, the model parameterization and the parameter estimation procedure differ from those of Yiu and Poon .…”

“…Yiu and Poon focused on parameter estimation of the polychoric correlation between two categorical variables with misclassification, whereas we are interested in a noninferiority test for two correlated categorical variables. Consequently, the model parameterization and the parameter estimation procedure differ from those of Yiu and Poon . The proposed alternative parameterization can facilitate the noninferiority test, but SE estimation must be revisited because the method proposed by Yiu and Poon is no longer applicable.…”

Sample size determination for disease prevalence studies with partially validated data

“…This data collection method that results in partially validated data is sometimes called doublesampling, [3][4][5] although in a more rigorous sense the term double-sampling would be better applied when there is an intention to further sample subjects from those who might have specific responses in the screening tests. 6 The analysis of partially validated data has long been an important research topic due to its wide applications.…”

“…Morvan et al 13 proposed two methods to assess the accuracy of the screening procedure and corrected estimations in two-phase surveys of prevalence disease. Yiu and Poon 5 proposed a latent variable approach to analyze ordinal categorical data with double-sampling, and proposed various estimation methods that could be implemented by widely available software programs. Poon and Wang 14 considered a multivariate model and developed an EM-type algorithm to analyze the model.…”

Bayesian Analysis of Multivariate Probit Models with Surrogate Outcome Data

“…Assuming a monotone misclassification pattern, Eickhoff and Amemiya (2005) used the Expectation-Maximization (EM) algorithm (Dempster, Laird, & Rubin, 1977) to estimate the model parameters in a latent normal variable model. Yiu and Poon (2008) considered a twodimensional latent variable normal model and used a minimum chi-square approach to find the correlation of the two variables. Poon and Wang (2010) established an analytic framework for the multivariate structure of ordinal categorical variables with misclassified data, and provided a unified EM algorithm to estimate the thresholds and the parameters in a latent normal model.…”