Handling missing data in item response theory. Assessing the accuracy of a multiple imputation procedure based on latent class analysis

A critical issue in analyzing multi-item scales is missing data treatment. Previous studies on this topic in the framework of item response theory have shown that imputation procedures are in general associated with more accurate estimates of item location and discrimination parameters under several missing data generating mechanisms. This paper proposes a model-based multiple imputation procedure for multiple categorical items (dichotomous, multinomial or Likert-type) which relies on the results of latent class analysis to impute missing item responses. The effectiveness of the proposed technique is assessed in the estimation of item response theory parameters using a range of ad hoc measures. The accuracy of the method is assessed with respect to other single and multiple imputation procedures, under different missing data generating mechanisms and different rate of missingness (5% to 30%). The simulation results indicate that the proposed technique performs satisfactorily under all conditions and has the greatest potential with severe rates of missingness and under non ignorable missing data mechanisms. The method was implemented in R code with a function that calls scripts from a latent class analysis routine.