# Prior distribution regression analyses // different results using frequentist and Bayesian inference

Hello everybody,

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!

Alexa

## Comments

Hi Alexa,

Cheers, E.J.

E.J., thank you very much for this helpful and fast answer.

1. / 2. Ah, I understand. Actually, I wanted to present the correlation table just as “an overview” (as I assessed several constructs), but I didn’t want to test any hypothesis. Although, of cause, I assumed e.g., a positive relationship (directional H1) between A and B and a negative relationship between A and C (directional H1). The testing of the association between other constructs, e.g., between A and D was exploratory (uniform). Afterwards, I conducted the regression analysis (linear and multiple regression analyses) with the default prior (directional H1 as you said). (I hope that my description is understandable). Do you think in my case it is “OK” to conduct both correlation and regression analyses with the default prior or should I adjust the correlation analysis? I just quickly re-ran the correlation analysis and you are right, there are slightly different BF when testing a directional H1.

3. I will send you a part of the Tables via PM (because of unpublished data), I hope that this is OK.

Thank you!!