Many issues in psychology and educational research involved analysis of within-participant across time, such as development psychology and growth rates of skill learning. Those longitudinal studies often used autoregression model for statistic and illustration. Another method for expressing time series effect is multilevel linear model. Further, it was important to consider the correlation between the residuals of within-participant across time-points. This studies reviewed five methods to model this within-participant covariance structure Σ. The first was a most commonly method, VC, which assume there are no autocorrelation in the structure. Second was AR(1) , which modeled the adjacent score deviation. Third was MA(1), which mentioned the function of adjacent errors. Forth was ARMA(1,1), which combined AR(1) with MA(1) and modeled correlation among three units of time point error. Finally, the unstructured model (UN) which estimates all pair covariance parameters of the time-point residuals. This study simulated data by ARMA(1,1) and investigated the estimation of multilevel growth model parameters by those methods. The result presented that VC and AR(1) estimated variance components poorly at times. ARMA(1,1) still estimated variance biased across many conditions. The UN had better performance when sample size was large.
My common mentions two points. One is this simulation study although help us understanding more about the specification correctly and incorrectly at within-participant covariance structure, it seems difficulty to design a study using real data to demonstrate these results. Since the model fit indices cannot be confident, we don't have a criteria to evaluate the appropriation level of the practice data was expressed by hypothetical model. Another common is I am surprise that specification occasion still had biased estimation across many conditions. Maybe using more parameters , such as UN method, expresses data better because the model is more complex.