How to interpret results of Bayesian regression

[Linh Nguyen]

Hi everyone,

Stata has an example of how to do Bayesian regression (https://www.stata.com/features/overview/bayes-prefix/)

However, they don't show how to interpret results from this regression (shown in the attached picture).

Can anyone help me to interpret the results?

The mean of math3 is 0.607 impies that the mean of the effect of math3 on math5 is 0.607, isn't it? But, what does it mean?

Thanks in advance!

[Carlo Lazzaro]

Linh:
the issue is that frequentist 95% CI tells you that, should you repeat the same analysis many times on a random sample of the same size drawn from the same population, 95 out of 100 times the CI will include the real value of the population parameter you're interested in. This does not mean that the real value of the population parameter has a 95% probability of falling in between the 95%CI bounds.
This happens because, according to the frequentist paradigm, the population parameters are not random, but fixed and unknown,

[Linh Nguyen]

Hi Carlo,

When we use OLS, we can conclude that math3 has a significantly positive effect on math5. Particularly, when math3 increase by 1 point, math5 will increase by 0.608 points.

However, what conclusion can we make regarding the effect of math3 on math5 when we use Bayes?

[Carlo Lazzaro]

Linh::
you can make the same conclusion.
More demanding issues are related to Bayesian model averaging (ie, comparing informative vs non-informative priors) and predictive distributions.
See, if interested, https://www.wiley.com/legacy/wileychi/koopbayesian/, pages 46-54.

[Linh Nguyen]

Thank you so much, Carlo. You are so quickly as usual.