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I was wondering how I could incorporate a prior to form a posterior distribution for multiple logistic regression.

More specifically, I am working with basketball data, where the response variable is binary (whether a player made the shot or not) and the explanatory variables are the distance from the basket and the defensive ratings of the opposing 5 players. I am able to generate multiple seasons worth of these shot logs for each player from the past, and wanted to know how I could take previous seasons of data into account when I also have a current season's worth of data.

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  • $\begingroup$ In what sense is this* multivariate*? Do you have multiple response variables? $\endgroup$ Mar 15, 2016 at 8:41
  • $\begingroup$ Is that what multivariate means? Sorry I meant to say that there are multiple explanatory variables, but the response variable is either 0 or 1 $\endgroup$ Mar 16, 2016 at 17:19

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This article discusses Bayesian logistic regression nicely. Basically, you have the flexibility to parametrize estimation however you see fit, but using a model which is linear on the log odds scale makes sense for many reasons. Furthermore, using a normal prior for log odds ratios should give you very approximately normal posteriors.

To do the sequential analysis, estimate the "prior" for this season by doing a first-pass Bayesian logistic regression for past seasons using a non-informative normal prior for that model.

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  • $\begingroup$ Thanks for the response Adam. But what if my covariates are continuous and not discrete? $\endgroup$ Mar 19, 2016 at 22:00
  • $\begingroup$ @kleiza don't put a prior on your covariates. We generally think of them as "fixed" or given in regression modeling. $\endgroup$
    – AdamO
    Mar 19, 2016 at 22:02

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