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st: Re: Matrix Algebra


From   "Michael Blasnik" <michael.blasnik@verizon.net>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Matrix Algebra
Date   Mon, 7 Oct 2002 07:42:34 -0400

I should have looked in the manual before suggesting using aweight.  The
manual states that the weights are normalized when using aweights with mat
accum.  You can use pweights instead and get the answer you seek.

Michael Blasnik


----- Original Message -----
From: "Alfonso MIranda" <ecrgw@csv.warwick.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, October 07, 2002 5:00 AM
Subject: st: Matrix Algebra


> Note: Apologies if this mail comes out twice.
>
>
> Dear Statalisters,
>
> I am trying to estimate a count model with endogenous switching as
> proposed by Terza(1998). It involves the use of a two-step method of
> moments estimator. First stage is done using a probit and second stage is
> done using non-linear least squares. I basically have coded all but the
> correction for the covariance matrix. For calculating such a matrix I have
> to create an intermediate matrix that has the following general form:
>
> Y = A'*W*A
>
> A is nxk matrix and W is a nxn diagonal matrix with regression's
> squared errors in the diagonal and zeros elsewhere. Lets say that I have
> variables a1 a2 a3 forming matrix A. And that the squared errors are saved
> as variable res2. I have more than 20,000 observations in my dataset.
>
> Since it is not possible to create matrices of 20,000x20,000 in Stata, I
> was very kindly suggested by Michael Blasnik to use the weighting feature
> of matrix accum for calculating matrix Y. Basically he suggested to use:
>
> .mat accum a1 a2 a3 [aw=res], noc
>
> In order to check that this solution is correct I drop observations after
> estimating my model, and residuals, and kept only 200 observations. Then,
> as also kindly suggested by Nick Cox, I calculate matrix A and W in the
> following way:
>
> .mkmat a1 a2 a3, matrix(A)
> .local n = _N
> .matrix W = J(`n',`n',0)
> .forval i=1/`n' { W[`i',`i']=res2[`i'] }
> .matrix mymat = A'*W*A
> .matrix list mymat
>
> .symmetric mymat[3,3]
>              a1          a2         a3
>       a1  62054.362
>       a2  60504.697  60504.697
>       a3  1004.4707  1004.4707  1004.4707
>
>
> This matrix is what I want but with large data it cannot be calculated
> using Nick's suggestion. Now, using the weighting feature of matrix accum
>
>  .matrix accum H = a1 a2 a3 [aw=res2], noc
> (sum of wgt is   2.4974e+03)
> (obs=200)
>
> .matrix list H
>
> symmetric H[3,3]
>             a1         a2          a3
>      a1  4969.5487
>      a2  4845.4456  4845.4456
>      a3  80.441821  80.441821  80.441821
>
> Clearly, mymat and H are different. Jiang, Tao very kindly suggested an
> alternative which would be:
>
> .sca m=10000
> .matrix accum Z= a1 a2 a3 [fw=res2+m], noc
> .matrix accum Z2= a1 a2 a3, noc
> .matrix Z=Z1-m*Z2
>
> however, since res2 is not a integer number, frequency weights cannot be
> estimated. I did what Jiang, Tao suggested using analytic weigths:
>
> sca m=10000
> matrix accum Z1=   g1c g1cat g1ind [aw=res2+m], noc
> (sum of wgt is   2.0002e+07)
> (obs=200)
>
> matrix accum Z2= a1 a2 a3, noc
> (obs=200)
> matrix Z=Z1-m*Z2
>
>  matrix list Z
>
> symmetric Z[3,3]
>            a1          a2           a3
>   a1   -4.670e+08
>   a2   -4.438e+08  -4.438e+08
>   a3   -4512856     -4512856     -4512856
>
> Which is also different to maymat. It seems then that all suggested
> strategies do not yield the matrix that I need. Does anyone has other
> idea?
>
> Many thanks,
>
> Alfonso Miranda
> University of Warwick


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