Ordinal Factor Analysis of Graded-Preference Questionnaire Data

Abstract

We introduce a new comparative response format, suitable for assessing personality and similar constructs. In this "graded-block" format, items measuring different constructs are first organized in blocks of 2 or more; then, pairs are formed from items within blocks. The pairs are presented 1 at a time to enable respondents expressing the extent of preference for 1 item or the other using several graded categories. We model such data using confirmatory factor analysis (CFA) for ordinal outcomes. We derive Fisher information matrices for the graded pairs, and supply R code to enable computation of standard errors of trait scores. An empirical example illustrates the approach in low-stakes personality assessments and shows that similar results are obtained when using graded blocks of size 3 and a standard Likert format. However, graded-block designs might be superior when insufficient differentiation between items is expected (due to acquiescence, halo, or social desirability).