Interpretation of Bayesian 3-way Repeated Measures ANOVA?

jmbostwick

Hello all! I'm looking for help understanding the output for this 3-way RM ANOVA (output attached, along with the traditional ANOVA as well). I have been asked to provide BF01 values for "all nonsignificant effects (using p < 0.05) and interactions", and so that is what I'm trying to do. I have three such interactions; SCD x MM, SCD x Key, and SCD x Key x MM. I've put a box around the first model (which includes only the significant effects) and the three lines that I believe indicate the models I'm looking for.

This analysis was run using the "compare to best model" option in JASP. My understanding is that the BF01 for a given model can be roughly interpreted as the odds that the best model is a better fit than the given model. For instance, the model in Box 2 has a BF01 value of 2.064, meaning the best model is about twice as likely as the model in Box 2. Is that a generally correct interpretation? And, is that interpretation still appropriate for looking at a three-way interaction?

Mostly, I'm just nervous. This is the first time I've used these analyses in a paper headed towards potential publication and I don't feel solid on my understanding of the way to run and/or interpret more complex higher-level interactions. The sources I've found universally stop their discussion of interpretation at 2-way ANOVAs (so, if anyone knows of a source that discusses 3-way ANOVAs, I'd be eternally grateful!).

Please let me know if I can provide more information to help get answers to these questions. Thank you for reading and replying!

EJ

Dear jmbostwick,

1. "My understanding is that the BF01 for a given model can be roughly interpreted as the odds that the best model is a better fit than the given model. For instance, the model in Box 2 has a BF01 value of 2.064, meaning the best model is about twice as likely as the model in Box 2. Is that a generally correct interpretation?"

This is correct only when you assume the models to be equally likely a priori. The BF generally indicates relative predictive success, so the degree to which the data are more likely to occur under one model than the other. For a blog post on the topic see https://www.bayesianspectacles.org/the-single-most-prevalent-misinterpretation-of-bayes-rule/

2. Otherwise, I think your interpretation is correct.

Cheers,

E.J.