So a friend ran some linear model using "lm" in R and a particular binary categorical variable had a non-statistically-significant coefficient. Then he ran the anova table on that model output and it gave that same variable a statistical significance. Now, neither of us thinks statistical significance is particularly of interest, we're both Bayesian. But the lm model has a Bayes with flat prior interpretation, is there any useful Bayesian interpretation to the ANOVA table? #bayes #bayesian
Ultimately this is exploratory to see if the data is worth building a principled Bayesian model for... so I told him to just run the same formula from the lm model through #brms to get a quick and dirty bayes-interpretable output. #statistics #bayes #frequentist #anova
Having thought about it a while I'm going to guess the most likely outcome is that the #brms posterior will show correlations or nonlinear dependencies between the coefficients, and this results in different p values for the ANOVA calculations vs the marginals from the coefficients in the lm output. Will circle back after he gets brms output and see if my intuition was right.