Unfolding IRT Models for Likert-Type Items With a Don't Know Option.

Attitude surveys are widely used in the social sciences. It has been argued that the underlying response process to attitude items may be more aligned with the ideal-point (unfolding) process than with the cumulative (dominance) process, and therefore, unfolding item response theory (IRT) models are more appropriate than dominance IRT models for these surveys. Missing data and don't know (DK) responses are common in attitude surveys, and they may not be ignorable in the likelihood for parameter estimation. Existing unfolding IRT models often treat missing data or DK as missing at random. In this study, a new class of unfolding IRT models for nonignorable missing data and DK were developed, in which the missingness and DK were assumed to measure a hierarchy of latent traits, which may be correlated with the latent attitude that a test intended to measure. The Bayesian approach with Markov chain Monte Carlo methods was used to estimate the parameters of the new models. Simulation studies demonstrated that the parameters were recovered fairly well, and ignoring nonignorable missingness or DK resulted in poor parameter estimates. An empirical example of a religious belief scale about health was given.