This study mainly introduced five models to describe the characteristic of the growth process in developmental psychology research. The interpretation and assumption of those five models were illustrated separately in each section. They are linear growth model, quadratic growth model, latent basis growth model, additive nonlinear latent growth, and multiplicative nonlinear latent growth curves. For investigating the best adequate model, The author use a real data to fit each model above. the result showed that the multiplicative nonlinear model had the best model-data fitness and could capture the reasonable interpretation of developmental theory.
1) I think of how to calculate the RMSEA in Table 1. In the real data analysis, the true parameters are not able to be obtained. What value approximating the true vale should be compared with the estimated parameter? Then I search the formula at internet:
√(χ2 - df)
__________
√[df(N - 1)]
I am curious how could this index represent the root mean square error.
2) How to extent those model to IRT model should be considered. In those model, the dependent variable is height, a kind of continuous data. When the y observed variable is the categorical data, we could substitute the ability in IRT model for the y. Although the large sample size should be needed to estimate the more parameter, we can expect the model to be revised step by step and then obtain more applicable model in the future.