Bayesian ANOVA - P(M|data) higher for the null model
Hi!
I have results from a Bayesian ANOVA suggesting that the null model fits the data better than the model with my independent variable. Specifically, the P(M|data) = 0.790 for the null model and = 0.210 for the alternative model.
I guess the reason is as follows: If the effect of the independent variable on the dependent variable is very small, the data may not provide strong evidence in favor of including it in the model and the null model, which assumes no effect of the independent variable, might have a higher posterior probability. (I find no differences between groups in frequentist ANOVA and no correlations/effects in regression analysis, so the explanation would make sense).
Is my guess correct? Also, is there any textbook or article that would provide a more detailed discussion?
Thanks in advance! 😀
Comments
Indeed, small effects in the sample are more likely to arise from the null model than from the alternative model. Some discussion on this is at https://pure.uva.nl/ws/files/52486656/s41593_020_0660_4.pdf
EJ