As you might probably know, brms allows you to enter the priors in conjunction with the predictors, so if you know what effects (in terms of log(odds) or betas) were associated with your predictors, you can enter them as priors.

The main challenge, however seems to be to convert your prior data into a format in line with logistic regression. What exactly do you mean by "I have data from a previous experiment (analysed with frequentist methods) on the same equation (EC~ BT), but on individual dogs."?

Technically-speaking, there's no such thing as a "correct" prior. Priors are plausibilities for model parameters. If you have data from a previous experiment, you can use these to help you decide on sensible constraints for the priors. It depends on what your goal is in modeling. Do you simply want a model that fits the data as closely as possible - or - do you want a model that can be used to make accurate predictions in future samples? If the former, you can use the exact mean/SD from the posterior. If the latter, you'll want to leave more uncertainty in the priors. Using too restrictive priors can result in overfitting and overconfidence in the model's predictive power.

Sven Greving: Thank you for your reply. What I meant was this. We had previously done a choice test experiment and checked for the same responses. That is, if Box type (A or B or C) influences Eating response (Yes/No). We did the choice test on individual dogs. So, if a dog is presented with the three choices, do they show preference for eating from a particular box. We analysed the data using Goodness of fit tests (Chi square test of independence). Now we are doing the same choice test but on groups of dogs. So my question was two fold:

(a) Can I use the data on choice from the previous experiment to act as priors in the current one? (b) If yes, how do I convert the data that I have into prior values (i.e, values for alpha and beta. I assume the prior will have beta distribution.Correct me if I am wrong)?

(c) Do I run my existing data through a bayesian glm using non informative or weakly informative priors (say, alpha=1, beta=1) and then use the posterior that I get as priors for my current data?

Does the above info helps? Apologies, I am new to bayesian statistics and using R to solve it and my lack of knowledge might get in the way of explaining things properly

Blaine Tomkins : Thank you for your reply. Yes, you are right of course. I am new to Bayesian statistics and my lack of knowledge gets in the way of correctly explaining things. My modelling goal is causal analysis and not predictive. As my dependent variable is of Yes/No type and my independent variable is categorical (nominal) with three levels (A/B/C), I was under the assumption that this is not normal distribution and thus mean/SD won't apply here. Was I wrong?

Rohan Sarkar In Bayesian data analysis, you're ultimately deriving probabilities. Even though your outcome variable is binary, there is some probability p that dogs will respond "yes" to (i.e., choose) the food in each of the 3 box conditions. The model becomes:

Y ~ Binomial(1, p)

where Y is the relative number of counts of 'yes' responses and p is the probability of a 'yes' response on any particular trial. Your ultimate goal is to estimate p (*technically the logit(p)), and p (assuming it's unimodal) has a mean falling somewhere between 0 and 1. It also has a standard deviation. This is where looking to previous data helps.

If the data are not normally distributed, you'll want to use a modeling approach that doesn't require a normal distribution, such as MCMC. It's a good idea to familiarize yourself with the logic and math in Bayesian analysis, and maybe work through a few simple tutorials to get a better grasp of things.

After rereading your initial question, I think it is reasonable to use your individual dogs' data and use it as priors (I already suggested that but was unaware that you already proposed modelling the data using a bayesian model). I however do not see the added value of using bayesian models with uninformative priors as compared to plain logistic regression.

Sven Greving : After thinking for a while, I realize that we have no clue whether group dynamics or hierarchy might have a role in influencing food choice. This might cause the overall food choice of a group to be different from an individual dog (where no such effects are at work). So maybe my previous idea won't work.

I will be carrying out a series of experiments building on the current one. And I plan to use bayesian modelling in all the subsequent ones too. So I am starting with this one even if its uninformative priors. Is that not an optimum choice, so to speak?

For uninformative priors, is beta (alpha=1, beta=1) a good choice for this particular dataset?

Sounds reasonable, all of it

Sven Greving : Thank you for taking the time to help me out. Much appreciated.