st_view in optimization

[Nhan Nguyen]

Hi all

I have a column vector (let call that X) that contains rows(X) i.i.d variables with Geometric distribution in Stata. I try to use optimize to find the parameter (let call that p) that maximizes the likelihood function of the sample.

Here is my codes:

mata mata clear
mata:
    x = st_view(x=0,.,"X",0)
    void MLE_geo_dtype(todo,p,x,ll,g,H)
    {
        ll = rows(x)*ln(p)+(sum(x)-rows(x))*ln(1-p)
        if (todo>=1) {
            g = rows(x)/p-(sum(x)-rows(x))/(1-p)
            if (todo==2) {
                H = (-rows(x)/p^2)-(sum(x)-rows(x))/((1-p)^2)
            }
        }
    }
    S = optimize_init()
    optimize_init_evaluator(S, &MLE_geo_dtype())
    optimize_init_evaluatortype(S,"d2")
    optimize_init_params(S,0.5)
    optimize_init_argument(S,1,x)
    p = optimize(S)
end

I know in advance that the sample was created with p = 0.3 (I checked the mean and variance of the sample, and it surely was created by Geometric distribution with the chance of success is 0.3). What surprised me are: first, the

p=optimize(S)

returns the true parameter for p is 0.5 (which is the initial value set for p and it is wrong). Second, the column vector x, which is a view on X, contains no value despite the fact that X has not changed. I know this is the setup of g-type optimization, but I want to learn whether d-type could work with extra parameter like the g-type.

Can anyone help me to explain this.

Thank you

[Joseph Coveney]

I'm unfamiliar with the syntax:

x = st_view(x=0,.,"X",0)

and it seems to return an empty matrix. The help file says that st_view() is a subroutine (void function).

Try running this to see what I mean:

version 17.0

clear *

// seedem
set seed 1058123613

quietly set obs 250

generate byte x = rgeometric(0.3)

mata:
mata set matastrict on

// Unfamiliar syntax
X2 = st_view(X2=0, ., "x", 0)
isview(X2)
eltype(X2)
orgtype(X2)
nonmissing(X2)
rows(X2)
cols(X2)

// Familiar syntax
st_view(X=(.), ., "x")
isview(X)
orgtype(X)
orgtype(X)
nonmissing(X)
rows(X)
cols(X)

void function geodist(
    real scalar todo,
    real scalar p,
    real matrix X,
    real scalar ll,
    real rowvector g,
    real matrix H) {

    assert(isview(X))

    ll = rows(X) * ln(p) + ( sum(X) - rows(X) )  * ln(1-p)

    if (todo >= 1) {
        g = rows(X) / p - ( sum(X) - rows(X) ) / (1-p)
        if (todo == 2) {
            H = ( -rows(X) / p^2 ) - ( sum(X) - rows(X) ) / ( (1-p)^2 )
        }
    }
}

S = optimize_init()
optimize_init_evaluator(S, &geodist())
optimize_init_evaluatortype(S,"d2")
optimize_init_params(S, 0.5)
optimize_init_argument(S, 1, X)
p = optimize(S)

p

end

exit

[Nhan Nguyen]

Thank you Joseph, it worked.

I am quite new to mata and sometimes get confused with the syntax.

May I ask one more question related to your function geodist? If I want to redefined the mata function geodist or remove it after using optimize. What should I do because when I code mata mata drop geodist(), I cannot drop the function as Mata said that it is in use. So it leaves me the one option to clear the entire memory of mata using mata clear.

[Joseph Coveney]

You have to drop S first.

S is described in the help file as a "problem-description handle", which implies that it's persistent.

Because S has a pointer to your evaluator function, Mata balks at dropping your evaluator function until the pointer to it is set to NULL, which will happen during destruction of S.

So, after your done with things, you can

mata drop S // First, before dropping the evaluation functioni
mata drop geodist()

[Joseph Coveney]

If I want to redefined the mata function geodist

If you want to keep S otherwise intact, then as an alternative to what I show above you can just change out the pointer that S has to a placeholder (dummy) evaluator.

That will allow you to drop your evaluator function, rewrite it, and then swap it back in for the placeholder.

Like the following:

void function dummy() {}

optimize_init_evaluator(S, &dummy())

mata drop geodist()

[Nhan Nguyen]

Thank you for your explanation Joseph.

It is really helpful. Those are not written in the help file of optimize function so I kept messing around.