With repeatedmeasurement, the within-person covariance matrix is assumed identity in common.The study proposed a more complex model to include the series autocorrelationfor accounting for the error terms. With random errors considered, the bias offixed effects or random effects of interest can be reduced relatively. Two typeof serial-correlation processes: autoregressive (AR) and moving average (MA)are combined together to take those nuisance errors into account. The aim ofthe study is to examine the effect of misspecification of serial correlation. Thelinear growth curve model was introduced firstly. Only two-level structure wasstudied. One is for the time serial, the other is for within-person errors. Thenthe model ignoring the serial correlation (VC), model with autoregressive model(AR(1)), model with moving average (MA(1)), model with conbined strategy(ARMA(1,1)), and unstructured model (UN) were used as true model to generatedata and fit interchangedly the data generated from different models.
AR(1)model assumes the present observation is a linear function of previousobservation only. MA(1) model assumes the present error has a linearcorrelation with previous error. ARMA model can design a serial time-pointcovariance matrix of error via formula (6) and (7). UN model is theconventional MANOVA without conceptually considering serial correlation. In simulationstudies, the magnitude of correlation, sample size, series length, andcovariance specification were manipulated. Criteria such as relative bias, empiricalType 1 error rates, fit indexes (RLRT, AIC, AICC, and BIC), and effect sizeswere used for different purposes.
Thefixed effects were estimated well under each model. Exception is that Un modelwhen sample size is small. Even if the true model (ARMA) was used to estimatevariance components, better estimation were obtained when sample size is relativelylarge. Among fit indexes, AIC seems performing well when sample size is 200,serial length was 8, and moving average parameter was -.3.
Qs:
1. The oo multipliedwith x1i in formula (2b) should be corrected as o1.
2. In UN model, it uses the samenotation t which is previouslydefined as time.
3. The estimation problem for UNmodel, I think, may result from a lack of optimization of search maximum pointof likelihood, rather than due to too many parameters needed to estimate unlessthe model was overly-parameterized.
4. When sample size is 200, theauthor suggests that UN model seems an alternative choice to fit serialcorrelation data. But we will ignore the underlying processes when data weregenerated from other models such as ARMA.
5. Variance components cannot beestimated well even true model was used. Is it institute this is resulted fromsmall sample size? Even 200 sample size is used.