Date:         Tue, 27 Oct 2009 10:25:15 -0700
Reply-To:     Dale McLerran <stringplayer_2@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: PROC GLM parameterization XXXX
In-Reply-To:  <d18436ce0910270526x5ca2d1a2s23f379eb6651e76f@mail.gmail.com>
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Dan,

The model which you want to estimate is

  Y = mu + D1*(X=1) + D2*(X=2) + ... + Dk*(X=k)

where mu is the grand mean, which in the observed
sample is simply Ybar.  We can rewrite this equation
as:

  Y - mu = D1*(X=1) + D2*(X=2) + ... + Dk*(X=k)

or

  y - Ybar = D1*(X=1) + D2*(X=2) + ... + Dk*(X=k)

Note that this latter equation does not have any
intercept.  By rewriting the equation as shown above
we are able to obtain the model which you wish to
estimate, but only by constructing a new response
variable Ynew = Y - Ybar and modeling Ynew without
an intercept term.

Hence, the steps required to fit this model are as
follows:

1) Compute the grand mean of the response variable
   among observation that will be used for fitting the
   regression model - i.e., observations that do not
   have missing values for any of the predictor
   variables.

2) Construct a new response variable as Ynew = Y - Ybar

3) Employ Ynew as your response in PROC GLM and specify
   the NOINT option.


Of course, the model which we estimate with the GLM
procedure does not have mu on the right hand side.
But that is a trivial problem since you already know
the sample estimate of mu.

HTH,

Dale

---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@NO_SPAMfhcrc.org
Ph:  (206) 667-2926
Fax: (206) 667-5977
---------------------------------------


--- On Tue, 10/27/09, Dan Abner <dan.abner99@GMAIL.COM> wrote:

> From: Dan Abner <dan.abner99@GMAIL.COM>
> Subject: PROC GLM parameterization XXXX
> To: SAS-L@LISTSERV.UGA.EDU
> Date: Tuesday, October 27, 2009, 5:26 AM
> Hello,
>
> How can I obtain an effect or deviation parameterization of
> a model
> estimated in PROC GLM as opposed to the default reference
> group
> parameterization?
>
> In other words, I want a parameterization of the model
> where the intercept
> is the grand mean and cofficients for discrete groups are
> deviations from
> the grand mean.
>
> Thank you,
>
> Dan
>