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Re: reg_sweep

From: John Darrington
Subject: Re: reg_sweep
Date: Thu, 26 Aug 2010 12:57:28 +0000
User-agent: Mutt/1.5.18 (2008-05-17)

On Wed, Aug 25, 2010 at 05:37:49PM -0400, Jason Stover wrote:
     On Wed, Aug 25, 2010 at 02:43:07PM +0000, John Darrington wrote:
     > 1. The comment says:
     >   /*
     >    LAST_COL is considered to be the final column in the augmented matrix,
     >    that is, the column to the right of the '=' sign of the system.
     >    */
     >   If I understand the theory correct, this should read "to the LEFT of 
the = sign" ??
     I was thinking of it this way:
     Suppose A is an n by n matrix, x an n by 1 vector, and y an n by 1
     vector. The values of A and y are known. reg_sweep solves the system
         A x = y
     for x. This is done by forming an augmented matrix
     a_{11} a_{12} ... a_{1n} | y_1
     a_{21} a_{22} ... a_{2n} | y_2
     ........................ | ..
     a_{n1} a_{n2} ... a_{nn} | y_n
     and using Gaussian elimination. I thought I had coded reg_sweep to
     assume LAST_COL was the column corresponding to the vector y above,
     which is on the right-hand side of Ax = y.

Right.  My confusion arose because earlier in the comment, the 
equation is formulated with Y on the left: "Y = Xb + Z".
     > 2. Results from my initial experiments suggest that:
     >    a) In order to  do a factorial anova, we would need to run reg_sweep 
N times where
     >       N is this number of factor variables.
     No, it should only require one call of reg_sweep on the covariance matrix.
     Unless there is more than one dependent variable, one call to reg_sweep
     should suffice. 
     >    b) We need to add another variable to reg_sweep to tell it which 
variable we're currentl
     >       interested in.
     I don't understand what you mean by "which variable we're currently
     interested in." Do you mean the dependent variable? Anyway, reg_sweep
     is meant to be dumb: It just runs Gaussian elimination.
     It sounds like you are using it wrong, though there is a chance it
     needs updating. I can help if you send some sample code.

I'm starting with a simple univariate anova, using my rapidly hacked up version 

  glm Y by X1 X2.

In my glm implementation I have the following code:
    gsl_matrix *cm = covariance_calculate_unnormalized (cov);

    dump_matrix (cm);

    reg_sweep (cm, 0);

    dump_matrix (cm);

I can see that before the sweep operatotr, the Corrected Total is in CM(0,0)
I can also see that after the sweep operator, CM(0,0) contains 
(CorrectedTotal - SumOfSquaresForX1).  How do I get the sum of squares for X2? 
The only way I can see it is to re-arrange the rows/columns of CM such that X2 
the first factor and re-run reg_sweep.


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