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# Re: st: FW: ML for logit/ologit

 From Yuval Arbel To statalist@hsphsun2.harvard.edu Subject Re: st: FW: ML for logit/ologit Date Wed, 16 Nov 2011 11:57:21 +0200

```Dear Thomas,

Several years ago I came across the same problem with estimation of
non-linear functions in STATA. The solution I found is to use MATLAB
for these objectives of non-linear functions. I believe that compared
to STATA, MATLAB will give you a much better flexibility to define
non-linear functions.

2011/11/16 Thomas Murray (Department of Economics) <t.l.murray@bham.ac.uk>:
> Dear all,
>
>
> 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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>

--
Dr. Yuval Arbel