​Moptimize and Multiple equation models- Can I "trick" Moptimize in this way?

[Christophe Kolodziejczyk]

Hi

I am trying to estimate a finite mixture model with multiple equations by maximum likelihood.
I use Moptimize to find the optimum of the likelihood function.
The model takes the following form

equation	parameters	covariates	# of parameters
1	b1	X1	k1
2	u1		l1
3	b2	X2	k2
4	u2		l2
5	prob. associated with the u's

The u's are actually mass-points (a serie of constants) related to their counterpart equations containing the b's.
u1 are for example the mass-points for equation 1.


Although the paremeters for the u's have no covariates they form one group of parameters (in terms of the logic of the model).
Is it possible to treat this vector of parameters as an equation and to supply a fake matrice of
covariates which has the same number of columns as the parameter vector in order to trick moptimize?
Will it affect the way the numerical gradient and hessian are computed?
I want to avoid to loop over all the elements of u1 in order to feed the initial values and supply u1
once instead.

I am thinking of the following code

u1 = ....  // initial values
eq = 1
moptimize_init_eq_cons(M,eq,"off")
moptimize_init_eq_indepvars(M,eq,J(1,cols(u1),0))
moptimize_init_eq_coefs(M,eq,u1)

I use Stata 14.1 on Windows 2008 server.

Best
Christophe

[Jeff Pitblado (StataCorp)]

An alternative would be something like

u1 = ....  // initial values
moptimize_init_eq_n(M,cols(u1))
moptimize_init_coefs(M,u1)

While moptimize_init_coefs() is not documented, it is a convenience that we are using,
so it will not be going away. We will try to get it documented in the future.

[Christophe Kolodziejczyk]

Jeff
Thanks for your tip. It seems to be quite useful. In my case I could avoid the loop by just passing the entire vector of paramaters and the total number of equations.

I also tried to make a simple example which uses the approach I suggest and it seems to work.
In my problem I want to mix equations wich have covariates with equations which just contain parameters not related to covariates.

to be more precise I was thinking of something like

// pass the covariates x1 to equation 1
eq = 1
moptimize_init_eq_indepvars(M,eq,x1) // x1 is a matrix of covariates
moptimize_init_eq_coefs(M,eq,J(1,cols(x1)+1,0))

// pass the mass-points of equation 1 to equation 2
u1 = ....  // initial values
eq = 2
moptimize_init_eq_cons(M,eq,"off")
moptimize_init_eq_indepvars(M,eq,J(1,cols(u1),0))
moptimize_init_eq_coefs(M,eq,u1)

.


Best
Christophe