This study examined effect of misspecification of autoregressive moving average process under multilevel linear growth curve models.
Five alternatives for modeling serial correlation were introduced, 1) variance components VC, assuming no autocorrelation is present; 2) stationary autoregressive models AR, representing the most recent observation in a series as a function of previous observations; 3) moving average models MA, representing the most recent observation in a series as a function of previous errors in a series; 4) autoregressive moving average models ARMA, combining the autoregressive and moving average processes; 5) unstructured models UN, freely estimating the t(t+1)/2 parameters.
True model in this study is ARMA, and fitting models include VC, AR, ARMA and UN.
Four factors are manipulated in this study:
1) autocorrelation of the AR process, by .5 and .8;
2) correlation of the MA process, by .3 and -.3;
3) sample size by 30 and 200;
4) series length by 5 and 8.
So take all factors together, there are totally 16 different conditions.
Results show that, the fixed effects accurately estimated under all conditions, even when the serial correlation is mismodeled. Type I error for the fixed effects will increased under the UN model when the sample size is small. Additional research by the authors showed that, the UN specification will perform well if the sample size is sufficient large, at least 100. That is, increase of type I error is not a serious problems for the specification of UN.
However, results suggest that, estimates of the variance component can be biased even when the model is correctly specified.
According to the simulation results, two suggestions for applied researchers were provided:
1) not rely on testing variance components to decide whether explanatory varianbles should be added;
2) not trying out different covariance matrixes and rely on the fit indexes to indicate the correct model.
UN is not advised to use if the sample size is small. And the performance of UN under large sample size calls for further research.
Q:
1. Given the data is generated using ARMA, why even use the true model, the estimation of variance component is still biased?
2. in page 279, what does the last sentence mean? “The estimates of the ARMA autocorrelation parameters however, though, as sample size and series length increased.”