Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time. When the response data are categorical, item response theory (IRT) model can be used as the measurement model of a second-order latent growth model (referred to as LGM-IRT) to measure change. However, application of the LGM-IRT model in practice is limited due to complications caused by model parameterization, estimation, and panel attrition. This research first explores parameterization methods of the LGM-IRT for different statistical packages, then compares the performance of three estimation algorithms for the LGM-IRT under various data conditions via two simulation studies. The preliminary results of the simulation are presented and discussed.