The random-threshold generalized graded unfolding model

Theoretical Articles Background: It has been argued that ideal point models could be more appropriate for describing responses to attitude items or Likert items than dominance models. In recent years, unfolding models have been developed to fit responses of attitude items, including the hyperbolic cosine model (Andrich, 1988, 1989; Andrich & Luo, 1993), the PARELLA model (Hoijtink, 1991) and the generalized graded unfolding model (GGUM; Roberts, 1998; Roberts, Donoghue, & Laughlin, 2000, 2002; Roberts & Laughlin, 1996). Among them, the GGUM appears to be the most popular. Theoretical Articles Aims: Likert items require respondents to make a subjective judgment on rating labels (e.g., strongly disagree, disagree, agree, and strongly agree), which often depends on personal preference (Wang, Wilson, & Shih, 2006). To account for such an individual difference in the personal preference, we extend the GGUM to the so-called random-threshold generalized graded unfolding model (RTGGUM) by adding a set of random-effect parameters to the GGUM, one for each threshold. We use MCMC procedure and Gibbs sampling algorithm provided by software WinBUGS to estimate parameters and conduct a simulation study to ascertain parameter recovery. Theoretical Articles Arguments: The proposed RTGGUM has an advantage of accounting for individual difference in personal preference on rating labels in Likert items. Its parameters can be well recovered using WinBUGS. When there is individual difference in personal preference, fitting a model assuming no such an individual difference (i.e., the GGUM) will yield a biased parameter estimate and an overestimation of test reliability. In contrast, fitting a model that assumes such an individual difference to data without that difference will yield a fairly accurate parameter estimate and a close to zero estimate for the variance of thresholds. In other words, it does no harm to apply the RTGGUM even when data do not contain any individual difference in personal preference. Theoretical Articles RASCH: The slope parameters in the GGUM can be set at a constant. We extend the GGUM to the RTGGUM by adding a set of random-effect parameters to the GGUM, one for each threshold. Theoretical Articles Conclusions: The results of the simulation support our hypotheses. The parameters of the RTGGUM can be well recovered from WinBUGS. This study not only sheds new light on theoretical issues of developing unfolding models for attitude tests but also provides practitioners clear guidelines for applying such techniques.