electing the best unbalanced repeated measures model
Guillermo Vallejo & M. Paula Fernández &
Pablo E. Livacic-Rojas & Ellián Tuero-Herrero
This study examined the performance of selection criteria available in the major statistical packages（R/Splus lme(),SAS Proc Mixed, SPSS/PASW mixed, and Stata xtmixed,） for both mean model and covariance structure. The simulation study was conducted. The results show that no single criterion can be uniformly recommended, however the AIC and HQIC had the best overall performance among the procedures examined. The REML2-based information criteria performed comparably to the ML-based information criteria, performance of criteria was worse under REML1 than ML. Overall the consistent criteria (BIC, CAIC, and HQIC) performed better than their efficient counterparts (AIC and AICC) when the covariance patterns used to generate the data were relatively simple
Comments：
It is useful for future model chosen.
1 will the parameter values of the covariance patterns used to generate the data affect the results?
2 what is the recovery about the parameters？
3 The author distinguished the REML1 and REML2，however the results in the table only provides one of them for the other one is poor. I think the subscripts should be includes in reporting the result since they are different.
4 in the results the author mentioned averaging across the covariance structures, total sample size, number of repeated measurements, and methods of estimation, then we can get overall success. Does that means to simply average all the rates together?
Simulation:
Two different mean models：
(1) a full model with a common intercept, a dummy variable indicating membership in one
of two groups, a continuous covariate that took equallyspaced values in each group, and an additional group ×
slope interaction;
(2) a reduced model with a common intercept, a linear trend, and an additional group covariate.
4 covariance structures:
(a) first-order autoregressive covariance pattern (AR), (b) first-order autoregressive covariance pattern with variance heterogeneity within subjects (ARH), (c) Toeplitz covariance pattern with variance heterogeneity within subjects (TOEPH), and (d) unstructured covariance pattern (UN).
Repeated measures: t = 4 or t = 8
sample sizes:
n = 30 (n1 = n2 = 15),
n = 60 (n1 = n2 = 30),
n = 120 (n1 = n2 = 60).
Power：.40, .60, and .80
Two population distributions:
The multivariatenormal distribution with univariate skew and kurtosis equal to zero (γ1 = γ2 = 0)
A moderately skewed distribution with shape parameters equivalent to those of an exponential distribution (γ1 = 2 and γ2 = 6)
Estimators
ML estimation
REML estimation：REML1 &REML2
This process was repeated 5,000 times for each condition using a SAS macro