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# st: How to maximize an approximated likelihood

 From Feddag Mohand-Larbi To statalist@hsphsun2.harvard.edu Subject st: How to maximize an approximated likelihood Date Mon, 08 Apr 2013 10:04:56 +0200

```Dear Statausers,

I am wondering to know how to maximize an approximated likelihood
depending on three parameters: the difficulty parameter as matrix, the
mean of the latent traits and its variance.

The function wrotten in Stata where the approximation is obtained by
Gauss-Hermite quadrature is given as follows:

qui gen proba=.
qui gen x=.
forvalues i=1/`nbobs' {
local int2=1
local u=RaschDepLoc[`i',1]
local v=`diff'[1,1]
local int1 "exp(`u'*(x-`v'))/(1+exp(x-`v'))"
forvalues j=2/`nbitems' {
local t=`diff'[`j',1]
local r=RaschDepLoc[`i',`=`j-1'']
local s=RaschDepLoc[`i',`j']
local int2
"`int2'*exp(`s'*(x-`t'+`d'*`r'))/(1+exp(x-`t'+`d'*`r'))"
}
local int="`int1'*`int2'"
qui gausshermite `int', mu(`mu') sigma(`sigma') display
qui replace proba=r(int) in `i'

}
gen lik=log(proba)*`nbobs'

where nbobs is the number of individuals, nbitems is the number of
items, RaschDepLoc is the matrix of data of order (nbobs*nbitems), diff
is the vector of difficulties parameters, mu and sigma^2 are the mean
and the variance of the latent traits.

I don't know how to write this function in order to use ml model lf myfunction (? =?)
and ml maximize

best

Dr Feddag

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```