Measurement Models, Estimation, and the Study of Change

Abstract

The study of change is based on the idea that the score or index at each measurement occasion has the same meaning and metric across time. In tests or scales with multiple items, such as those common in the social sciences, there are multiple ways to create such scores. Some options include using raw or sum scores (i.e., sum of item responses or linear transformation thereof), using Rasch-scaled scores provided by the test developers, fitting item response models to the observed item responses and estimating ability or aptitude, and jointly estimating the item response and growth models. We illustrate that this choice can have an impact on the substantive conclusions drawn from the change analysis using longitudinal data from the Applied Problems subtest of the Woodcock–Johnson Psycho-Educational Battery–Revised collected as part of the National Institute of Child Health and Human Development's Study of Early Child Care. Assumptions of the different measurement models, their benefits and limitations, and recommendations are discussed.

Keywords:

• change
• growth
• item response model
• longitudinal
• measurement

Notes

¹Latent scores can be estimated and plotted against age at testing when conducting simultaneous estimation; however, the estimated scores are influenced by the growth model chosen to represent the data. Thus, they are not independent from the fitted growth curve.

^aItem response theory and exponential growth model were simultaneously estimated.

^aItem response theory and exponential growth model were simultaneously estimated.

*Significant parameter at p < .05.