# [R] penalized maximum likelihood estimation and logistf

Tue Mar 9 18:22:02 CET 2010

```Let us look at a piece of the relevant code from "logistf" package:

iter <- iter + 1
XW2 <- crossprod(x, diag(pi * (1 - pi))^0.5)
Fisher <- crossprod(t(XW2))
covs <- solve(Fisher)
H <- crossprod(XW2, covs) %*% XW2
if (firth)
U.star <- crossprod(x, y - pi + diag(H) * (0.5 -
pi))
else U.star <- crossprod(x, y - pi)
delta <- as.vector(covs %*% U.star)
mx <- max(abs(delta))/maxstep
if (mx > 1)
delta <- delta/mx

First, note that this is inside an iterative loop.  The Fisher information matrix is first formed, and then it is inverted to get `covs'.  This is where it can get troublesome.  It is very likely in your case that the `Fisher' information matrix is ill-conditioned, and hence `covs' cannot be computed.  Consequently, the steplength `delta' for the Newton method cannot be determined.

Ravi.

____________________________________________________________________

Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619

----- Original Message -----
From: xiaoyan yu <xiaoyan.yu at gmail.com>
Date: Tuesday, March 9, 2010 11:26 am
Subject: [R] penalized maximum likelihood estimation and logistf
To: r-help at r-project.org

> Hi, I got two questions and would really appreciate any help from here.
>  First, is the penalized maximum likelihood estimation(Firth Type Estimation)
>  only fit for binary response (0,1 or TRUE, FALSE)? Can it be applied
> to
>  multinomial logistic regression?
>  If yes, what's the formula for LL and  U(beta_i)? Can someone point
> me to
>  the right reference?
>  Second, when I used *logistf *on a dataset with binary response, I
> got the
>  following error msg:
>  "Error in if (mx > 1) delta <- delta/mx :
>    missing value where TRUE/FALSE needed"
>
>  What does this msg mean? does it mean the dataset includes missing response?
>  I  checked my dataset several times and didn't find anything other
> than TRUE
>  or FALSE for the response. Please shed light on this.
>
>  Thanks,
>  Xiaoyan
>
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>
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