Table 2.
Comparative Fit of Models with Different Covariance Structures for School Effects over Time.
| Stable | Dynamic | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Intercept | Intercept + Slope | UN* | Toeplitz | SB(4) | SB(3) | SB(2) | CS | AR | ARMA | ||
| Parameters | 5 | 7 | 25 | 10 | 9 | 8 | 7 | 6 | 6 | 7 | |
| Model 1: Includes Cohort, Grade and Cohort × Grade Effects | |||||||||||
| −2LL | 52267.9 | 52190.2 | 52090.1 | 52109.2 | 52110.2 | 52131.3 | 52131.3 | 52142.2 | 52122.8 | 52122.7 | |
| AIC | 52277.9 | 52204.2 | 52140.1 | 52129.2 | 52128.2 | 52147.3 | 52145.3 | 52154.2 | 52134.8 | 52136.7 | |
| BIC | 52287.5 | 52217.7 | 52188.4 | 52148.5 | 52145.5 | 52162.8 | 52158.9 | 52165.8 | 52146.4 | 52150.2 | |
| Model 2: Includes Cohort, Grade, Cohort × Grade, Socioeconomic Status and Attitude Effects | |||||||||||
| −2LL | 52045.0 | 51967.6 | 51866.2 | 51883.1 | 51883.8 | 51904.9 | 51905.0 | 51917.2 | 51897.1 | 51897.1 | |
| AIC | 52055.0 | 51981.6 | 51916.2 | 51903.1 | 51901.8 | 51920.9 | 51919.0 | 51929.2 | 51909.1 | 51911.1 | |
| BIC | 52064.6 | 51995.1 | 51964.5 | 51922.5 | 51919.2 | 51936.4 | 51932.5 | 51940.7 | 51920.7 | 51924.6 | |
*
Estimated group-effects covariance matrix was non-positive definite.
Note: Parameters refers to the number of unique variance/covariance parameters estimated in the model, −2LL is the log-likelihood of the model multiplied by a factor of −2 (i.e., the model deviance), AIC is Akaike’s Information Criterion, BIC is Bayes’ Information Criterion. Bolded entries indicate best fit. Covariance structures were specified as defined in Table 1: UN = unrestricted, Toeplitz = fully banded Toeplitz, SB(t) = Stabilizing banded – stabilizing at lag t, CS = compound symmetric, AR = first-order autoregressive, and ARMA = first order autoregressive moving average.