Psychology Ph.D. Dissertations


Applications of Differential Functioning Methods to the Generalized Graded Unfolding Model

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)



First Advisor

Michael J. Zickar, PhD

Second Advisor

Scott Highhouse, PhD (Committee Member)

Third Advisor

John Tisak, PhD (Committee Member)

Fourth Advisor

James Albert, PhD (Committee Member)


This study examined the utility of two popular item response theory (IRT)-based methods of identifying differential item functioning (DIF) to a new and relatively unique parametric IRT model, the generalized graded unfolding model (GGUM). Specifically, the Likelihood Ratio (LR) and Differential Functioning of Items and Tests (DFIT) methods of DIF were applied to the GGUM. Although the LR and DFIT approaches to identifying DIF have seen application to traditional IRT models, these models all relied on the assumption of monotonicity, or that persons higher on the latent trait continuum (e.g., attitude, personality) are more likely to endorse positively worded items than those lower on the continuum. However, recently researchers have used the GGUM to show the advantages of instead making an ideal point assumption, which implies that a person is most likely to endorse an item when the item is closer to them on the latent continuum (i.e., when the statement reflects their level of attitude or personality). Given the recent surge in interest toward ideal point models, and more specifically, the GGUM, it is pertinent to determine whether methodologies useful in application to traditional IRT models are transportable to this new and unique model. Further, the accuracy of the methods has yet to be compared directly in the current literature using any IRT model. This investigation intends to fill these current gaps in knowledge. In this investigation, Monte Carlo simulations were conducted to simulate unfolding response data under varying conditions of DIF and sample size. In generating response data, items were simulated to have certain types of DIF (e.g., DIF due to differences in item locations versus DIF due to differences in item sensitivity), to have varying number of items showing DIF (i.e., 2, 5, or 8 DIF items in a 20-item survey), and varying levels of balance in the size of the two groups being compared (i.e., completely balanced versus one group with a considerably smaller sample size). Thus, the “truth” of whether an item showed DIF was known. Using the generated data, DIF analyses were conducted to determine the accuracy of the LR and DFIT approaches by determining the rate at which they were able to correctly identify items simulated to have DIF and correctly return null results for items that were not simulated to have DIF. Findings suggested that the two approaches differ greatly in terms of accuracy. The LR approach showed greater utility in terms of returning true positives and true negatives. Although the DFIT procedure performed only slightly poorer in the case where only two items were simulated to have DIF, as the number of items having DIF increased, the difference between the two approaches became much larger. These results indicate that the LR approach may be more appropriate for analyzing data resulting from an ideal point response process and is perhaps a more effective method than the DFIT approach. Although further research may find that the use of empirical adjustments recently suggested for the DFIT approach may render it more effective than found in this study, these methods are difficult to implement for most researchers and software for conducting such adjustments is not currently available. Therefore, the LR approach appears to be the more sensible and efficient method of studying DIF in GGUM data for the time being.