Latent growth modeling of IRT versus CTT measured longitudinal latent variables

Latent growth models are often used to measure individual trajectories representing change over time. The characteristics of the individual trajectories depend on the variability in the longitudinal outcomes. In many medical and epidemiological studies, the individual health outcomes cannot be observed directly and are indirectly observed through indicators (i.e. items of a questionnaire). An item response theory or a classical test theory measurement model is required, but the choice can influence the latent growth estimates. In this study, under various conditions, this influence is directly assessed by estimating latent growth parameters on a common scale for item response theory and classical test theory using a novel plausible value method in combination with Markov chain Monte Carlo. The latent outcomes are considered missing data and plausible values are generated from the corresponding posterior distribution, separately for item response theory and classical test theory. These plausible values are linearly transformed to a common scale. A Markov chain Monte Carlo method was developed to simultaneously estimate the latent growth and measurement model parameters using this plausible value technique. It is shown that estimated individual trajectories using item response theory, compared to classical test theory to measure outcomes, provide a more detailed description of individual change over time, since item response patterns (item response theory) are more informative about the health measurements than sum scores (classical test theory).