Title: The Ordered Latent Transition Analysis Model for the Measurement of Learning
Description: Several statistical models have been developed in educational measurement to determine and track the performance of students in longitudinal studies. An example of a model designed for such purpose is the latent transition analysis (LTA) model. The LTA model (Graham, Collins, Wugalter, Chung, & Hansen 1991) is a type of autoregressive model specifically designed to model transitions between class membership from Time t to Time t+1. The model however makes no assumption of ordering of the latent statuses and the transition probabilities. This project extends the LTA model by using the ordering technique proposed by Croon (1990) to introduce inequality constraints on the response probabilities of the LTA model. This new approach, referred to as the ordered latent transition analysis (OLTA) model, ensures ordering of the students' learning levels (known as statuses under LTA), and the transition probabilities. Simulation study was conducted in order to determine the adequacy of parameter recovery by OLTA as well as to evaluate the performance of the information criterion (AIC and BIC) in selecting the appropriate number of levels in the model.

The simulation results showed good parameter recovery overall. Additionally, the AIC and BIC performed comparably well in selecting the correct transition model, but the AIC outperformed the BIC for the selection of optimal number of levels. An example of OLTA analysis of empirical data on reading skill development is presented.