Date:         Wed, 6 Aug 1997 08:32:00 GMT
Reply-To:     m.fahey@junk.unsw.edu.au
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         Michael Fahey <solar.usnw.edu.au@ACSUSUN.ACSU.UNSW.EDU.AU>
Organization: University of New South Wales
Subject:      Re: design matrix specification in proc iml

Yes, I'm replying to my own post and I wrote:
 
>I have data from a two way nested mixed design and would like to use proc
>iml to specify the model.  In particular, it would be helpful if I could
>use SAS code to create the design matrices for the fixed and random effects
>from the raw data (or some transformation of it).  This would be much easier
>than manually specifying the design matrices for a large dataset.
 
>For example, consider the following (simplified) data to illustrate the
>problem.  To study a biomarker (Y) among people in different regions (R),
>2 or 3 subjects (S) were randomly sampled from 2 regions and 2 or 3
>measurements of the biomarker obtained from each individual.  Regions is a
>fixed factor and subjects a random factor nested within regions.  The data
>are unbalanced.  The 13 observations have been entered into a database as
>follows:
 
>R      S       Y
 
>1      1       14
>1      1       14
>1      1       15
>1      2       12
>1      2       13
>2      1       17
>2      1       17
>2      2       16
>2      2       17
>2      2       17
>2      3       14
>2      3       16
>2      3       16
 
>Briefly, the 13x1 vector of observations is represented by the 3rd column
>in the array of data above.  The 13x3 design matrix (X) for the fixed region
>effect requires a column of ones for the mean and two columns to specify the
>region effect.  It would look like this:
 
>X:
 
>1 1 0
>1 1 0
>1 1 0
>1 1 0
>1 1 0
>1 0 1
>1 0 1
>1 0 1
>1 0 1
>1 0 1
>1 0 1
>1 0 1
>1 0 1
 
 
>The 13x6 design matrix (Z) for the random nested effect due to subjects
>requires a row for each observation and a column for each possible
>combination of region.subject levels, including levels without data. The
>latter point is important and is illustrated by the 3rd column below, which
>contains only zeros, since there are only 2 subjects from region 1.
 
>Z:
 
>1 0 0 0 0 0
>1 0 0 0 0 0
>1 0 0 0 0 0
>0 1 0 0 0 0
>0 1 0 0 0 0
>0 0 0 1 0 0
>0 0 0 1 0 0
>0 0 0 0 1 0
>0 0 0 0 1 0
>0 0 0 0 1 0
>0 0 0 0 0 1
>0 0 0 0 0 1
>0 0 0 0 0 1
 
The following data step code creates variables that represent the above
matrices, is easily modified for larger matrices and can be read into
proc iml:
 
--
 
data design (keep=y x1-x3 z1-z6);
   set regions;
 
* design matrix for fixed effects;
 
array x(3);     /*  X is a Nx(I+1) matrix.  */
 
x1=1;           /*  A column of ones for the mean.  */
do i=1 to 2;
   x(i+1)=0;
   if region=i then x(i+1)=1;
end;
 
* design matrix for random effects;
 
array z(2,3);  /*  Z is a Nx(I*J) matrix.  */
 
do i=1 to 2;
   do j=1 to 3;
      z(i,j)=0;
      if region=i and subj=j then z(i,j)=1;
   end;
end;
 
proc print data=design;
   var y x1-x3 z1-z6;
run;
 
--
 
Replying to your own post is a bit like sending yourself a letter to cheer
yourself up...  Am I so down?  :-)
 
--
Michael Fahey         | Tel: +61-2-9828-6000
Epidemiology Unit     | Fax: +61-2-9828-6012
Liverpool Hospital    | Remove "junk." to reply to this message.