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  • Firth bias correction multilevel logistic regression model

    Hello, does anyone have advice on how to implement Firth's penalized maximum likelihood estimation method in a multilevel logistic regression model in Stata? I have data from a study with 32 clusters (hospitals). I've tried using melogit but am running into the issue of perfect prediction for a few of the variables. I was able to run the firthlogit Stata module successfully - but it does not have a way to account for the clustered study design (I think?) Thank you for any advice you have, I appreciate it.

  • #2
    Originally posted by Beth Jimenez View Post
    . . . does anyone have advice on how to implement Firth's penalized maximum likelihood estimation method in a multilevel logistic regression model in Stata? . . . it does not have a way to account for the clustered study design (I think?)
    No guarantees, but you can try something like clustered bootstrapping or jackknifing.

    The approach is inspired by the information in this thread, especially Enrique Pinzon's post there.

    The tactic is to take the direct analogue of this GEE multilevel model
    Code:
    xtgee . . . , i(. . .) family(binomial) link(logit) corr(independent) vce(jackknife, mse)
    with -firthlogit-, as in the following illustration.
    Code:
    version 17.0
    
    quietly webuse bangladesh, clear
    
    // Conventional GEE with HC3 clustered-robust standard errors
    xtgee c_use i.urban c.age i.children, i(district) family(binomial) link(logit) ///
        corr(independent) vce(jackknife, mse)
    
    // Direct analogue using -firthlogit-
    jackknife _b[1.urban] _b[age] _b[1.children] _b[2.children] _b[3.children] ///
        _b[_cons], eclass cluster(district) mse: firthlogit c_use i.urban c.age i.children
    
    exit
    You can also look into fitting a Bayesian multilevel regression model (bayes: melogit) with regularizing prior distributions on the troublesome variable's coefficient, but that will require more effort.

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    • #3
      Thank you so much, Joseph Coveney, your suggestions are much appreciated!!

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