Item Response Theory Models for Person Dependence in Paired Samples

Abstract

When paired samples (e.g., spouses, couples, twins, or siblings) are surveyed, the item responses of the paired samples may be locally dependent between the paired persons because the investigated latent traits often involve a relationship between the paired persons (e.g., marriage satisfaction). Standard item response theory (IRT) models fail to consider the dependence between paired persons and thus are not applicable. In this study, we developed new IRT models to account for person dependence and conducted simulation studies to evaluate the parameter recovery of the new models and the consequences for parameter estimation and test reliability when the dependence was ignored. Results showed that the parameters of the new models were recovered well with the freeware WinBUGS. Fitting the new models to data without the person dependence did little harm to parameter estimation, but ignoring the person dependence by fitting standard IRT models yielded a shrunken scale and underestimated test reliability. We provided an empirical example of marital satisfaction to demonstrate the implications and applications of the new models.