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 and fitting a second-order latent growth curve model. However, latent growth modeling with full information maximum likelihood (FIML) estimation becomes computationally challenging when the observed response data are categorical. This study first discusses some possible options that researchers can take regarding model specification and estimation (e.g., limited-information and various FIML estimators) to circumvent the challenge. To explore the utility of a stochastic Newton-Raphson type of algorithm (i.e., Metropolis Hastings-Robbins Monro; MH-RM) implemented primarily for multidimensional item response model, a re-parameterized latent growth model is also introduced. The viability of each option is examined via Monte-Carlo simulations. Insights on the pros and cons of these options and the conditions under which they are applicable are provided for researchers.