I have more questions than answers, I'm afraid. I could speculate on many of these answers, but my speculations are likely to be wrong.
Most Bayesian analyses put prior distributions on the unknown parameters. But the independent variables are not unknown parameters. They are known. So why would you or how would you even try to place a prior distribution on X1 through X6? Typically, you place priors on beta1 through beta6 (and beta0, of course). And (as far as I can tell) there is no good reason to make the prior on beta1 any different than the prior on beta6.
What is the definition of "most associated"? There are several competing definitions and your approach may be different depending on what mathematical definition you use for most associated.
Why do you care which variable is most associated with the outcome? I'm not sure that picking a "most associated" variable has any practical value. Picking a set of variables that does the best job of predicting seems like a far more interesting question than picking a single best variable.
Why do you want a Bayesian approach? The classical logistic regression model has a pseudo-R squared measure that might be exactly what you want. Why muddy the waters with a Bayesian model? What does a Bayesian model give you that a classical model doesn't?
Steve Simon, blog.pmean.com
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Hello All,
I am conducting a “factor comparison” study to determine which factors are most associated with a dependent variable (success, y = 1). I have six independent variables and one binary dependent variable. I am using a logistic regression to do the analysis under the Bayesian framework.
My question: Is there a way to determine which factor is most associated with the dependent variable that does not involve either transforming/standardizing the IV (not desirable because I do not want normal priors on the variables. They are naturally non-negative so I’d rather keep a beta distribution as their prior) or exponentiating the coefficient to get to the odds (rather than the log odds)? Interpreting the odds is also not preferable because the conclusion compares different levels of that particular IV, not across IVs.
Second question: If I just compared “the magnitude of the mean of each of the coefficients” as one suggested to me, would it only be appropriate if each of the variables were standardized? What if one of the IV were an indicator variable? Would the interpretation of the mean of the coefficient be the same? In my opinion, the mean would just be an estimate of the percentage of records that had that particular criterion.
PS – Here’s a bit more info about the variables:
- Y = dependent variable (1 = success)
- X1-X4 = independent variables (positive percentages, bounded between 0 and 100). I put a beta prior on each of these.
- X5 = IV5 (indicator, I put a binary prior on this. X5 ~ bin(0.5))
- X6 = IV6 (positive ratio that has a lower bound at 0 but no upper bound, put an exponential prior on this)
Considering this, if mean(b3) > mean(b5) across my iterations, can I argue that X3 is more associated with the success of Y than is X5? How would the interpretation change if say X2 was included as a covariate and it was found to have a positive influence on Y?
Any help you give would be greatly appreciated.
Ray
PS – If you need actual variables, please email me and I’ll provide additional concrete details.
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Raymond Mooring
Senior Statistical Consultant
Analysis Made Easy
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