From the very beginning, the authors argued that the uncorrelated assumption of errors of multilevel growth curve models which often employed in repeated measurements. And then, the authors review four different models for serial correlation (autoregressive models, moving average models, autoregressive moving average models and unstructured models) in details after introduced the linear growth curve model. Some issues of making the correlation assumptions in practice also rise, as well as the model fit indices. To guide the practices, the authors investigate the parameter recovery and model fit indices under the following factors: autoregressive parameters, moving average parameter, sample size and series length. Then the results of each parameters included in the model was presented. First of all, the fixed effects were well recovered, even if the analysis model was underspecified. For the random effect, most of the models were poor estimated under many conditions which conducted in this study. By so doing, some important implications were draw for practitioners. Further study directions also proposed at the end of this paper.
An interesting phenomenon of this study is that the true model (ARMA) can not be well recovered but an augmented model (UN) can, in many conditions.