11.4 - Testing the Significance of the Carry-over Effect

To test for the overall significance of carry-over effects, we can drop the carry-over covariates (\(x_1\) and \(x_2\) in our example) and re-run the ANOVA. Because the reduced model is a subset of the full model that includes the covariates, we can construct a likelihood ratio test.

\(\Delta G^2=(-2logL_{Reduced})-(-2logL_{Full})\)

with \(df_{Reduced}-df_{Full}\) degrees of freedom

The -2logL values are provided in the SAS Fit Statistics output for each model. For our example, the SAS output for the Full model with carry-over covariates is:

Fit Statistics
-2 Res Log Likelihood 122.5
AIC (smaller is better) 130.5
AICC (smaller is better) 132.6
BIC (smaller is better) 132.5

and for the reduced model without the carry-over covariates is:

 
Fit Statistics
-2 Res Log Likelihood 136.5
AIC (smaller is better) 144.5
AICC (smaller is better) 146.4
BIC (smaller is better) 146.4

So,

\(\Delta G^2 =136.5-122.5=14\)

and with

\(\chi^2_{.05, 2}=5.991\)

we conclude that there are significant carry-over effects.