Mixed Design Bayesian ANOVA and Model Averaged R2

jlwoodard

I have done a series of mixed-design Bayesian ANOVAs and have been puzzled by the large magnitudes of the Model Averaged R2 values. Typically, in models where the Null Model has the largest BF-M (e.g., 5.2), and there is no evidence of Group, Time, or Group x Time effects, I am seeing very large Model Averaged R2 values on the order of .35 to .8. I'm trying to get a better sense of what the Model Averaged R2 represents and how to interpret it. I think the large magnitudes in the absence of main or interaction effects is what is confusing me. Thank you very much in advance for any help!

pchs0114

Hi,

The Model Averaged R^2 in Bayesian analysis signifies the proportion of variance in the dependent variable that can be accounted for by the predictors across all contemplated models. This is calculated by averaging the R^2 values from all the models, with each being weighted by their probability considering the data and the model priors.

This, however, doesn't necessarily mean that individual predictors in the model are significant. It measures how efficiently any possible model can explain the data. Therefore, it's entirely feasible to get a high model averaged R^2 even when no individual predictors are significant.

In your case, a high BF-M for the null model suggests that the data are better explained without any predictors, notwithstanding the high model averaged R^2. A high model averaged R^2 and absence of significant predictors can coexist, particularly in intricate models or with small sample sizes.

Hope this helps.

EJ

If you could send a concrete data set that would help. Also, comparison to the classical methodology could be useful.