Missing item responses in latent growth analysis: Item response theory versus classical test theory

In medical research, repeated questionnaire data is often used to measure and model latent variables across time. Through a novel imputation method, a direct comparison is made between latent growth analysis under classical test theory and item response theory, while also including effects of missing item responses. For classical test theory and item response theory, by means of a simulation study the effects of item missingness on latent growth parameter estimates are examined given longitudinal item response data. Several missing data mechanisms and conditions are evaluated in the simulation study. The additional effects of missingness on differences in classical test theory- and item response theory-based latent growth analysis are directly assessed by rescaling the multiple imputations. The multiple imputation method is used to generate latent variable and item scores from the posterior predictive distributions to account for missing item responses in observed multilevel binary response data. It is shown that a multivariate probit model, as a novel imputation model, improves the latent growth analysis, when dealing with missing at random (MAR) in classical test theory. The study also shows that the parameter estimates for the latent growth model using item response theory show less bias and have smaller MSE’s compared to the estimates using classical test theory.