Any way to speed up a time-varying logistic regression?

Just to add to @stevebronder’s comment. This is not even a non-informative prior if you apply the inverse logit (plogis in R) to the prior, you can think of this as your prior information about the intercept on the probability that your outcome is 1.

plot(density(plogis(rnorm(100000,rnorm(1, 0, 25), 1/rgamma(1, 0.01, 0.01)))))

The priors are basically saying that the model is really sure that you either have mostly 1 or mostly 0 for a given time. With a binomial model, my rule of thumb for my work in social sciences is that a regression coefficient of 10 (when predictors are standardized) is basically the same as infinity. I adjust my priors so that there is little probability mass above 5 and below -5.

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