The multilevel generalized graded unfolding model

The generalized graded unfolding model (GGUM; Roberts, Donoghue, & Laughlin, 2000) has been applied to attitude data to unfold persons’ and items’ locations. It assumes that all persons are sampled randomly from the same distribution (i.e., simple random sampling). In practice, sampled data may have a multilevel structure, for example, repeated measures nested within a person, persons nested within a family, or students nested within a school. It is likely that data sampled from the same cluster (e.g., students from the same school) are more homogenous than data sampled from different clusters (e.g., students from different schools). To account for such a multilevel structure, we developed the multilevel generalized graded unfolding model (MGGUM). We proposed to use Markov chain Monte Carlo Bayesian methods that were implemented in WinBUGS (Lunn, 2000) for parameter estimation of the MGGUM. A series of simulations were conducted. The results showed that the parameters can be recovered fairly well; and statistics of model comparison could correctly select the MGGUM over the GGUM. An empirical example of political attitude was given.