st: RE: Could Not Find Idempotent Matrix Inverse

 From "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: Could Not Find Idempotent Matrix Inverse Date Mon, 1 Nov 2004 08:46:49 -0600

The only idempotent matrix that is not singular is the identity matrix. All
others won't have an inverse.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of BASSOLE
Sent: Sunday, October 31, 2004 12:49 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Could Not Find Idempotent Matrix Inverse

Dear all,
I trying to program to make estimate multi-way error components models with
unbalanced data structures. My program is based on Peter DAVIS (2002)
article on
Journal of Econometric. When I want to make the inverse of Idempotent matrix
(Qhhvv), STATA return the error message "Matrix has missing value". But,
before
making the invers, I check the missings values in the matrix and no missing
values are present. After this  I decide to calcul the determinant of this
matrix, and here STATA return dot, instead of the value of determinant. I
dont
know why. Before send the mail I make the same program in TSP, and here I
have
not see the programe for calculate the inverse of the same matrix (Qhhvv).
/*Create the orthogonal projection matrices for each variances component*/;
*For Household*;
mkmat idm1-idm346, matrix(hh);
mat Phh = hh*(inv(hh'*hh))*hh';
mat Qhh = INN - Phh;
*For Villages*;
mkmat codevillage1-codevillage58, matrix(vv);
mat Pvv = vv*(inv(vv'*vv))*vv';
mat Qvv = INN - Pvv;
/*Apply Lemma 1 (p.70) in Davis(2002)*/;
*Here, X1 are households and X2 villages*;
mat Qhhvv   = Qhh*vv;
mat Qhhvv = Qhh*vv;
mat PQhhvv = Qhhvv*inv(Qhhvv'*Qhhvv)*Qhhvv';
matrix has missing values
r(504);
Does anybody know the solution to this problem?

Léandre BASSOLE
CERDI-CNRS
65 Boulevard F. Mitterrand
Boite Postale 320
63009 Clermont-Ferrand CEDEX 1
FRANCE
Tel : 04 73 17 74 00
Fax : 04 73 17 74 28

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