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st: FW: ML for logit/ologit


From   "Thomas Murray (Department of Economics)" <t.l.murray@bham.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: FW: ML for logit/ologit
Date   Wed, 16 Nov 2011 09:44:59 +0000

Dear all,

Does anyone have any advice about the problem described below?

Many Thanks,

Tom Murray

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Thomas Murray (Department of Economics)
Sent: 15 November 2011 16:28
To: statalist@hsphsun2.harvard.edu
Subject: st: ML for logit/ologit

Dear Statalisters,

I need to use the ML function to create a program for an ordered logit  log likelihood function.  Before writing the code for the ologit model I've been trying to practice with a computationally simpler logit regression.  This is what I've written so far:

program define logit2_lf
version 10.1
args lnf xb
tempvar lnlj
qui {
gen double `lnlj' = ln(invlogit( `xb')) if $ML_y1 == 1
replace `lnlj' = ln(invlogit(-`xb')) if $ML_y1 == 0
replace `lnf' = `lnlj'
}
end

However, the model I wish to estimate is not simply y = a + bx.

I want to estimate the following: y = a + b((x^(1-ρ)-1)/(1-ρ))

where ρ is a parameter to be determined.

I have been trying to incorporate this into the logit code above (by replacing the xb function) along the lines of:

program drop logittest
program define logittest
version 12.0
args lnf b1 x rho
tempvar lng
qui {
gen double `lng' = ln(invlogit(`b1'*((`x'^(1-`rho')-1)/(1-`rho')))) if $ML_y1==1 replace `lng' =  ln(invlogit(-`b1'*((`x'^(1-`rho')-1)/(1-`rho')))) if $ML_y1==0 replace `lnf' = `lng'
}
end

ml model lf logittest ( y = x)
ml max

However I get the error 'unknown function ^()' - it doesn't like my attempted manipulation of x using powers.

My question - is it possible to impose this particular form of x into a logit (or ordered logit) function?  Am I just making a computational mistake in my programming language?

Many thanks in advance of any help offered.

Tom Murray,
University of Birmingham

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