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Thread Subject:
nonlinear index of logit regression

Subject: nonlinear index of logit regression

From: C F

Date: 11 Feb, 2009 23:29:02

Message: 1 of 2

I'm trying to estimate parameters in a logit regression, but the index of the regression is not linear in the parameters. Generally, i'm trying to estimate Pr(y=1)=G(H(XB)). I presume the logistic toolbox in matlab takes the H function to be the identity function. G is the cdf of the logisitic dist'n. In my case, H is a nonlinear function. Any ideas on how to estimate my 3 beta parameters?

THanks

Subject: nonlinear index of logit regression

From: Peter Perkins

Date: 12 Feb, 2009 16:45:16

Message: 2 of 2

C F wrote:
> I'm trying to estimate parameters in a logit regression, but the index of the regression is not linear in the parameters. Generally, i'm trying to estimate Pr(y=1)=G(H(XB)). I presume the logistic toolbox in matlab takes the H function to be the identity function. G is the cdf of the logisitic dist'n. In my case, H is a nonlinear function. Any ideas on how to estimate my 3 beta parameters?

CF, I don't know what the "logistic toolbox" is. You may be referring to GLMFIT in the Statistics Toolbox, though. I'll assume you are. You haven't said anything at all about what H is, so it's a little hard to give any advice. I can only assume that it is fully known and involves no parameters that need to be estimated.

It's conceivable that you could merge G and H into a single function (the "inverse link function") and take advantage of the last part of the following from "help glmfit":

       'link' - the link function to use in place of the canonical link.
          The link function defines the relationship f(mu) = x*b
          between the mean response mu and the linear combination of
          predictors x*b. Specify the link parameter value as one of
             - the text strings 'identity', 'log', 'logit', 'probit',
               'comploglog', 'reciprocal', 'loglog', or
             - an exponent P defining the power link, mu = (x*b)^P for
               x*b > 0, or
             - a cell array of the form {FL FD FI}, containing three
               function handles, created using @, that define the link (FL),
               the derivative of the link (FD), and the inverse link (FI).

It's also possible that you're better off just using the brute force of something like FMINCON and maximize the negative log-likelihood.

Hope this helps.

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