I am trying to develop a linear regression model for estimating stature from handprint measurements. I would like to employ the Bayesian approach and define informative priors from the previous studies. I have a data set with several predictors (several linear measurements) and stature measurements (as a target variable).
From previous studies, there is information on descriptive statistics (mean and sd) for the same variables and formulae of linear regression models. So, my question is, how can I use that information to extract the informative priors for my study? For example, I have this data for variable HL and Stature from the previous study:
mean (HL) = 17.94, SD (HL) = 0.94, mean (STATURE) = 178.5, SD (STATURE) = 7.05, range (STATURE) = (162.4–200.5)
stature estimation model = 69.723 +5 .567 x HL, SEE = 4.83, r = 0.73
how can I use them to construct prior and prior_intercept in my model
Model <- stan_glm(STATURE ~ HL, data = mydata, prior = ?, prior_intercept = ?)
Also, since there can be differences in the output variable (stature) in my population and the population from the previous study, is there any way to construct the prior for the target variable based on the results from the other studies. For example, if I know that the average stature in my population is 180 +/- 5 cm.
I was looking for explanations in various sources (e.g. http://mc-stan.org/rstanarm/articles/priors.html), but there are no guides how to construct informative priors from previous studies.