ml for nonlinear function

[Henry Strawforrd]

I have this log-likelihood function from a censored maximisation problem

with data on y_i, x_i, and z_i and want to have parameter estimates of \sigma, \lambda, \gamma_0, and \gamma_1. I wrote the following evaluator

cap program drop censored_likelihood
program define censored_likelihood
    version 17.0
    args lnf sigma lambda gamma0 gamma1 y x z
    tempvar m epsilon
    local y "$ML_y1"
    gen double `m' = (1 + (`lambda' - 1) * `x' * (`gamma0' - exp(-`gamma1' * `z')))
    gen double `epsilon' = `y' - `m'
    qui replace `epsilon' = 0 if `y' == 0
    
    gen double Iy0 = (`y' == 0')
    gen double Iy010 = (`y' > 0 & `y' < 10)
    gen double Iy10 = (`y' == 10)
    
    
    replace `lnf' = -0.5 * ln(2*c(pi)*`sigma'^2) - (`y'-`m')^2/(2*`sigma'^2)  ///
                + Iy0   * ln(normal(-`m'/`sigma')) ///
                + Iy010 * ln(normal((10-`m')/`sigma') - normal(-`m'/`sigma')) ///
                + Iy10  * ln(1 - normal((10-`m')/`sigma'))
    mlsum `lnf'
    
end

and then I don't get how to initialize it. How can I give the non-linear function and parameters to the ml model function?

Here is example data

set seed 12553
clear
set obs 1000
gen y = runiformint(0,10)
gen x = runiformint(0,1)
gen z = abs(rnormal() * 50)

[Joseph Coveney]

I have this log-likelihood function . . . and want to have parameter estimates of \sigma, \lambda, \gamma_0, and \gamma_1. I wrote the following evaluator . . . and then I don't get how to initialize it. How can I give the non-linear function and parameters to the ml model function?

Those are handled by ml model as constants in their own equations, separate from that of the predictors.

Take a look at Example 2 on pp. 1601–2 of the entry for ml — Maximum likelihood estimation in the user's manual, particularly in the bottom half of p. 1601 where alternative ways in which to specify these constant parameters are shown.

You can see another example in the StataCorp FAQ "How do I estimate a nonlinear model using ml?" here.

[Henry Strawforrd]

Thanks! I wrote it like this now and at least it does something. Is the y = x z correct or will that give y = a +bx + cz?

ml model lf censored_likelihood (b1: y = x z, nocons) (lambda:) (gamma0:) (gamma1:) (sigma:)
ml check
ml maximize

[Joseph Coveney]

Is the y = x z correct or will that give y = a +bx + cz?

The latter.

And it will feed the linear predictor to your sigma parameter. You need to rearrange your evaluator command's argument list to match the order in which ml model will feed things to it.

You might want to read through the user's manual's lf examples again, as well as the example in the company's FAQ, working through them slowly until you've got the gist of things.

I also recommend the book that's mentioned in the help file. I really didn't feel comfortable that I could program these things until I'd gone through the book.

[Henry Strawforrd]

Thanks! I am looking through both while trying to do this, but being a bit overwhelmed by the quantity and not finding very related passages to my problem.