To fulfill the interests of developmentalists, growth models were developed to summarize the quantitative changes of variables of targets. As we acknowledged, the growth is poorly modeled as a linear function so that nonlinear curves are preferred instead to describe the trend of growth. In this study a list of growth models, with different degrees of complexity, were introduced, and they were applied to fit a dataset by using Mplus.
1. Ideally, the idea of nonlinear growth modeling can be directly incorporated into IRT models to describe the nonlinearity relationship between latent trait and categorical responses. However, the estimation of nonlinear growth curve of latent trait under the framework of IRT will require more responses (i.e., larger sample size, longer test length, and as many as time points for repeated measures) . The application of compound model presumably is limited to few empirical datasets because most collected datasets do not have sufficient information in respect of the intend-to-be-measured latent traits across time points.
2. The more complex the function, the less robust the model. The statement is especially vivid to describe what was done of this study. As being researchers, what are we seeking for? Just a model yields best fit after a series of model comparison?
3. All the functions of introduced models except Equation 1 are strongly restricted. Supposed a set of estimates for a growth model is obtained, do we have sufficient confidence to say that the model with given estimates has external validity to expect the next sample?