Examples of homogenous covariance structures are Compound Symmetry (CS), Variance Component (VC), Toeplitz (TOEP), and First- order Autoregressive (AR(1)).
Covariance structures investigated in this study were CS, UN, AR(1), TOEP, CSH, ARH(1), TOEPH, and UNR., respectively.
In the study, the major attention has been paid to statistically test performance of candidate covariance structures structures such as: Compound Symmetry (CS), Heterogenous Compound Symmetry (CSH), Unstructured (UN), Huynth Feldth (HF), First-Order Autoregressive (AR(1)), Heterogenous First-Order Autoregressive (ARH(1)), First-Order Ante-Dependence ANTE(1), Toeplitz (TOEP) and Heterogenous Toeplitz (TOEPH) specified for the missing repeated measures with two fixed factors, region (7 levels) and time (18 levels) using mixed model.
In harmony with 20% missing data, the worst performance was again obtained by TOEP. Of the tested covariance structures, the estimates of fixed effects and goodness of fit criteria for HF, TOEPH, and UN were not estimated due to infinite likelihood and non-positive definite Hessian matrix.
"Preah Mohaksatr Samdech Mae, Samdech Sanghareach teang pi thvay preah phloeng buon loek min chheah, loek ti bram Samdech Techo buong suong som, toep
thvay preah phloeng chheah" [The king, the queen-mother, and both supreme patriarchs light the fire four times without it starting; the fifth time Samdech Techo prays, then the fire starts].
The best repeated measures analysis using mixed models such as homogeneous variance-covariance models ((Compound Symmetry (CS), First-Order Autoregressive_AR(1) and Toeplitz (TOEP
)) and heterogeneous variance-covariance models ((Unstructured (UN), Heterogeneous Compound Symmetry (CSH), Huynh-Feldt (HF) and First-Order Ante-dependence (ANTE(1))) were performed according to Akaike's Information Criterion (AIC).
Se probaron ocho estructuras de la matriz de varianzas-covarianzas: 1) sin estructura (UN), 2) componentes de varianza (VC), 3) autoregresiva de primer orden (AR(I)), 4) simetria compuesta (CS), 5) Toeplitz (TOEP
), 6) autoregresiva de primer orden heterocedastica (ARH(1)), 7) simetria compuesta heterocedastica (CSH) y 8) Toeplitz heterocedastica (TOEPH).
Twelve variance and covariance matrix structures were tested, as follows: Variance Component (VC), Compound Symmetry (CS), Unstructured (UN), First-order Autoregressive (AR ), Heterogeneous First-order Autoregressive (ARH ), Heterogeneous Compound Symmetry (HCS), Toeplitz (TOEP
), First-order Autoregressive Moving Average (ARMA [1,1]), Ante-dependence First-order (ANTE), Unstructured Correlation (UNR), Banded Main Diagonal (UN ), and Huynh-Feldt (H-F).
Also, compound symmetry (CS), toeplitz (TOEP
), first-order autoregressive (AR(1)), homogeneous variance-covariance models and unstructured (UN), heterogeneous compound symmetry (CSH), heterogeneous toeplitz (TOEPH), heterogeneous first-order autoregressive (ARH(1)), first-order ante-dependence (ANTE(1)) and unstructured correlation (UNR) heterogeneous variance-covariance models were performed in order to determine the variance-covariance structure between the repeated measures.
O mesmo aconteceu com a estrutura TOEP
, ao se inverter tais suposicoes.
In general linear mixed model, nine covariance structures (CS, CSH, UN, HF, AR( ), ARH(1), ANTE(1), TOEP
and TOEPH) were applied.