True Scale Correlations for Ordinal Categorical Items

Japan Women’s University Journal:

The Graduate School of Integrated Arts and Social Sciences, 2018, March, No. 24, 71-82.

Yasuharu Okamoto

Abstract

This study proposes hierarchical nonlinear models to estimate the correlation coefficients for the true values of the concepts,

each of which is measured using an ordinal categorical item scale.

For continuous items, the correction formula for correlation attenuation is well known

and refers to when the correlation coefficient of the observed scores is smaller than that of the true concept values.

However, for ordinal categorical items, this correction formula does not hold.

In this study, direct Bayesian methods were employed in the proposed models for ordinal categorical items

and were successfully applied to hypothetical data sets. The proposed methods do not need a parallel item assumption.