Bayesian ANCOVA

MIcheleS

Hi everyone,

I am currently writing up a data analysis plan for the preregistration. We conduct a pilot intervention study and compare two groups. For both groups we have baseline data and follow-up. Groups are randomized and should not differ in baseline scores. To assess the treatment effect, I want to perform an ANCOVA analysis and calculate the Bayes factor. It seems straightforward in JASP but I still have some questions.

From what I understood, we should first define the prior distribution which could be a half-normal distribution in our case, as smaller effects are more likely than larger effects. By default, the prior is defined as r scale fixed effect =0.5, r scale random effect =1, and r scale covariate = 0.354. What does this exactly mean and how can I change it to a half-normal distribution?

Similarly, there are two options: compare to best model or null model. Which one should be preferred? And should the covariate be added to the null model?

Thanks for helping out!

EJ

Hi MIcheleS,

1. Is your covariate the baseline score? If the covariate is not something you are interested in evaluating (but it is something you feel is important to include in the model) then you might just as well add it to the null model.
2. The r scale values refer to the width of a Cauchy distribution. For the t-test we offer many more prior options (Normal, t, with locations away from 0) as well as one-sided tests. I would be severely tempted to see whether you could decompose the effect of interest in terms of a t-test.

Cheers,

E.J.