Testing the Assumption of Uncorrelated Errors for Short Scales by Means of Structural Equation Modeling

Abstract

It is shown that a minimal assumption should be added to the assumptions of Classical Test Theory (CTT) in order to have positive inter-item correlations, which are regarded as a basis for the aggregation of items. Moreover, it is shown that the assumption of zero correlations between the error score estimates is substantially violated in the population of individuals when the number of items is small. Instead, a negative correlation between error score estimates occurs. The reason for the negative correlation is that the error score estimates for different items of a scale are based on insufficient true score estimates when the number of items is small. A test of the assumption of uncorrelated error score estimates by means of structural equation modeling (SEM) is proposed that takes this effect into account. The SEM-based procedure is demonstrated by means of empirical examples based on the Edinburgh Handedness Inventory and the Eysenck Personality Questionnaire-Revised.