An irt model to estimate differential latent change trajectories in a multi-stage, longitudinal assessment

Abstract

Repeated measures designs are widely used in educational and psychological research to compare the changes exhibited in response to a treatment. Traditionally, measures of change are found by calculating difference scores (subtracting the observed initial score from the final score) for each person. However, problems such as the reliability paradox and the meaning of change scores arise from using simple difference scores to study change. A new item response theory model will be presented that estimates latent change scores instead of difference scores, addresses some of the limitations of using difference scores, and provides a direct comparison of the mean latent changes exhibited by different groups (e.g. females versus males). A simulation-based test was conducted to ascertain the viability of the model and results indicate that parameters of the newly developed model can be estimated accurately. Two sets of analyses were performed on the Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K) to examine differential growth in math ability between 1) male and female students and 2) Caucasian and African American students from kindergarten through fifth grade.