st: ML for logit/ologit

["Thomas Murray (Department of Economics)" <t.l.murray@bham.ac.uk>]

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 logittest
version 12.0
args lnf xb
tempvar lng
qui {
gen double 'lng' = ln(invlogit( 'xb')) if $ML_y1 == 1
replace 'lng' = ln(invlogit(-'xb')) if $ML_y1 == 0
replace 'lnf' = 'lng'
}
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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