I am performing model selection using the anova() function in R. Model 1 is a 'baseline' model involving an interaction of the experimental manipulandum as the predictors. Each subsequent model involves the addition of a time-invariant predictor (i.e. some participant characteristics that were measured but not manipulated) as a main-effect covariate to the previous model. Thus, to my understanding, each model is nested within the subsequent model. The output is as follows:
Model df AIC BIC logLik Test L.Ratio p-value
1 11 1319.522 1353.349 -648.7610
2 12 1320.547 1357.450 -648.2737 1 vs 2 0.974570 0.3235
3 13 1314.144 1354.121 -644.0720 2 vs 3 8.403558 0.0037
4 14 1314.880 1357.932 -643.4398 3 vs 4 1.264430 0.2608
5 15 1316.872 1363.000 -643.4361 4 vs 5 0.007398 0.9315
6 16 1318.314 1367.517 -643.1569 5 vs 6 0.558260 0.4550
7 17 1320.067 1372.345 -643.0334 6 vs 7 0.247131 0.6191
According to the p-values in the final column the addition of the new predictor in model 3 delivers the only significant improvement in model fit over the baseline model.
My question is what tests does the anova()
function perform by default to arrive at the p-value for each test? Is it chi-squared based on change in residual sums of squares, or is it based in some way on log-Likelihood/ Information Criteria/Deviance statistics? The help page for this function doesn't give a lot of detail about the method used to derive this p-value and as far as I can tell there are a lot of different ways to compare models.