Prior distribution regression analyses // different results using frequentist and Bayesian inference
I got the chance to revise the first paper in which I used Bayesian inference. It’s quite a while that I have been working with Bayesian inference. Now, having a little distance to my analyses, I am a little bit confused regarding the prior distribution and I am wondering if I have done a mistake in my analyses.
First, I only computed simple correlation analyses to present the correlations between the constructs (let me say construct A and construct B). I used the default prior distribution. Is that correct?
Second, I computed a regression analysis. Based on theory, I hypothesized that construct A will predict construct B. Again, as there were no previous data on the relationship between A and B, I used the default prior model probabilities (1/2 = 0.5). Now I am a little bit confused if I should have changed the prior width before conducting the analysis?
And one last question: I used both frequentist and Bayesian methods of inference. In a further exploratory regression analysis, I tested if construct A with four predictors (A1/A2/A3/A4) predicted construct B. Bayesian regression results showed that the model with the predictors A2 and A3 outperformed all other models. However, classical regression results did not reveal any significant predictors. One reviewer asked me to explain this result and I am wondering how to do that.
I would be very happy if someone could help me out!
Thank you very much!