st: Problem using/understanding "mlmatbysum"

[Mike Brewer <mike_b@ifs.org.uk>]

Dear list - or at least, those who have used mlmatbysum, which I imagine 
is a very small subset of the list,

I am trying to use mlmatbysum to code up a d2 maximum likelihood 
estimator for a panel data model where my data does not meet the 
linear-form restriction (the data is 1 observation per time period per 
person).

The model is not a conventional panel data model, but, as the book 
"Maximum Likelihood Estimation with Stata" suggests (section 4.5.3),
the Hessian matrix is such that the within-equation submatrices involve 
some observation-level outer-product matrices:

Sum over i=1...N of { sum over t=1..T_i of (d_it x1it'x1it) }

and some group-level outer-product matrices:

Sum over i=1...N of {
  (Sum over t=1..T_i of a_it)
x (Sum over t=1..T_i of b_it x1it')
x (Sum over t=1..T_i of b_it x1it)   }

and:

Sum over i=1...N of {
  (Sum over t=1..T_i of a_it)
x (Sum over t=1..T_i of b_it x1it')
x (Sum over t=1..T_i of c_it x2it)  }


If that makes any sense written in plain text!

i=1...N indexes people (the group index) and t indexes observations 
within a group (time), and there are T_i observations for individual i 
(see p117 of "Maximum Likelihood Estimation with Stata").

The manual advises using "mlmatbysum" to create matrices which are:

Sum over i=1...N of
{ (Sum over t=1..T_i of a_it)
x (Sum over t=1..T_i of b_it x1it')
x (Sum over t=1..T_i of b_it x1it) }

or:

Sum over i=1...N of
{ (Sum over t=1..T_i of a_it)
x (Sum over t=1..T_i of b_it x1it')
x (Sum over t=1..T_i of c_it x2it) }

But I am failing to implement this correctly, and am hoping for some tips.

I am 99% sure that I have written down the 2nd derivatives in my model 
correctly, as d2debug confirms that I have the Hessian correct in all of 
my pairs of equations except where I have to use "mlmatbysum".

Furthermore, if I artificially constrain my model so that all of the 
equations have only a single variables in them (with no constant) - and 
so all of the sub-matrices are really scalars - then I can correctly 
code the negative hessian by using terms formed with "egen ... sum(..), 
by($MY_panel)" and an "mlmatsum" command. I cannot manage to code the 
equivalent using mlmatbysum.

So all I can think of is that I am using the mlmatbysum command 
incorrectly.

Does anyone have any general tips or experience to share?

What I am finding is that the values for the negative Hessian that I 
code using mlmatsum are many many many orders of magnitude larger than 
the numerical ones produced by d2debug (ie N is 1000, Ti is 20 on 
average, the mean of the relevant X variable is 10, d2debug says the 
correct value might be -1000, but my code using mlmatbysum says -10^9).

many thanks, Mike


--
Mike Brewer
Programme Director, Direct Tax and Welfare
Institute for Fiscal Studies, www.ifs.org.uk, 020 72914800

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