Parsing vector of parameters in Mata using Stata's `ml` command

[Alvaro Gutierrez]

I want to parse the parameter vector passed through the `ml` command to a Mata evaluator.

To make things concrete, I have a model with 4 regressors in which 1, one of them is fixed, and the other 3 are random. Additionally, each random effect can have a polynomial expansion (let's imagine a Taylor expansion).

For the example, take this data (not really relevant)

clear all
input id_ind    id_cs_of_ind_n    id_cs    alternative    x1    x2    x3 x_fix y 
1    1    1    1    -2.4 .08 0.5    0.5 1
1    1    1    2    1.1     -1.8 0.65    0.15 0
end

Now here are the macros that describe the problem. As we can see below, the first (`x1`), second (`x2`), and the third variable (`x3`) have polynomial expansions of order 1, 2, and 3, respectively. This information is contained in the macro `poly`.

// Macros available 
local fixed "x_fix"
local rand "x1 x2 x3"
local poly "1 2 3" 
local lhs "y"
local rhs `fixed' `rand' 
local kfix: word count `fixed'
local krnd: word count `rand'

mata: mata_kfix = strtoreal(st_local("kfix"))
mata: mata_krnd = strtoreal(st_local("krnd"))

Now I will use the ml command to call a mata evaluator (`eval_gf0`) (see below). I added the extra terms using the `/` expression. So you can see, for example, that `x3_3` represents the parameter of the third polynomial expansion of the random variable `x3`.

ml model gf0 eval_gf0()  (eq0: y = x_fix x1 x2 x3, noconst) /x2_2 /x3_2 /x3_3 

matrix init = (1,2,3,4,5,6,7) 
mat li init
ml init init ,copy
ml maximize  ,iter(0)

Here is the evaluator `eval_gf0` together with the desired objects.

// Evaluator used by the ml command.
mata:
void eval_gf0(/*string scalar B_s*/
  transmorphic scalar MM, real scalar todo, 
  real rowvector b, real colvector  lnfj, 
  S, H)
{

external mata_kfix
external mata_krnd

kfix = mata_kfix
krnd = mata_krnd

// Transposing the original vector into a column row.
B = b' 

// Total number of variables in equation 0
keq0 = kfix + krnd 

/* This recover the fixed parameter */
MFIX = B[|1,1\kfix,1|]

/*
  MFIX
  1
*/

/* This recovers the first term in the polynomial expansion for the three random variables. */
MPOLY_0 = B[|(kfix+1),1 \ keq0,1|]
/*
MPOLY_0
       1
    +-----+
  1 |  2  |
  2 |  3  |
  3 |  4  |
    +-----+

*/

/*

 Here I would like to create one matrix per polynomial order 
 and fill the missing spots with zeros when a given variable 
 does not have a polynomial of this order.

 For example, in this case, I should get the following: 

MPOLY_1  

         1
      +-----+ 
    1 |  0  | <-  this 0 is because there is polynomial of order 2 for x1
    2 |  5  |
    3 |  6  |  
      +-----+

      
MPOLY_2 
 
         1
      +-----+ 
    1 |  0  | <-  this 0 is because there is polynomial of order 3 for x1
    2 |  0  | <-  this 0 is because there is polynomial of order 3 for x2
    3 |  7  |
      +-----+
  
*/

exit(777) 

}
end

Any idea or hint about how to perform such operations? Thank you in advance.

PS1: When replicating this into Stata you need to put the evaluator BEFORE invoking it using the `ml` command.

PS2: Crossposted at Stackoverflow