The Influence of Dimensionality on Parameter Estimation Accuracy in the Generalized Graded Unfolding Model

Abstract

The generalized graded unfolding model (GGUM) is an ideal point model of responding that is consistent with the Thurstonian theory of respondent behavior. Ideal point models have recently generated interest in the realms of attitude and personality assessment. One unclear aspect of applying ideal point models is the influence of multidimensionality on GGUM item and person parameters estimation accuracy. Using simulated data, the authors tested the influence of the balance, or ratio, of items loading onto two dimensions, the degree of bidimensionality and sample size on parameter estimation accuracy. The results suggest that bidimensionality and the proportion of items loading onto a second trait increases estimation error. The second trait was chosen in estimation when a large number of the items in the survey reflected a highly irrelevant second trait. Estimation error was greater for persons and items at the extreme ends of the continuum; positive estimates were biased upward and positive parameters downward. The results suggest that although the GGUM chooses another trait in estimation, in most cases conventional fit analyses and checks for item parameter extremity are likely to be successful in identifying items measuring another trait. Furthermore, the conditions in which the trait being estimated may not be clear should be rare in practice. The implications of these results for researchers who wish to apply these models to real-life data are discussed.