If JMP were fitting a model of the form:
Y = A0 + A1*(X1-X1center) + A2*(X2-X2center) +
A12*(X1-X1center)*(X2-X2center)
then A0 would agree with your calculations. However JMP is really fitting a
model of the form:
Y = A0' + A1*X1 + A2*X2 + A12*(X1-X1center)*(X2-X2center)
from which you can see (and verify) that
A0' = A0 - A1*X1center -A2*X2center
In general A0' won't have an interesting interpretation I think.
Michael
-----Original Message-----
From: jmp-l-owner@lists.biostat.wustl.edu
[mailto:jmp-l-owner@lists.biostat.wustl.edu] On Behalf Of Michael Bailey
Sent: Sunday, May 10, 2009 9:56 PM
To: jmp-l@lists.biostat.wustl.edu
Subject: Re: [jmp-l] intercept in jmp 7, "fit model?"
Thanks. But please trust me, I'm not making an elementary error. I
know that if you center the variables, the intercept will change from
the non-centered situation. To summarize the problem, when jmp centers
the variables (as it does via default), one gets a different intercept
than when i do the centering myself.
On May 10, 2009, at 8:49 PM, Friedman, Emil wrote:
> Let's consider a simpler example. Imagine the two equations:
>
> y = b0 + b1*X versus y = b'0 + b'1(X-Xbar)
>
> where Xbar is the mean of the X's.
>
> The two equations will make identical predictions if
>
> b1 = b'1 and b0 = b'0 - b'1*Xbar
>
> but b0 will not equal b'0 so the two approaches will give us
> different intercepts.
>
> It's like going from Fahrenheit to Celcius. The intercept on the
> Celcius scale is at freezing point of water. The intercept on the
> Fahrenheit scale is at (I've forgotten but I think it was whatever
> the coldest achievable temperature was for the guy who invented it.)
>
> Does that help?
> ----------------------------------------------
> Emil M Friedman, PhD
> www.statisticalconsulting.org <http://www.statisticalconsulting.org/>
> emilfriedman@sbcglobal.net
> efriedman@mannkindcorp.com
> 65 Cables - Unit 6
> Waterbury, CT 06710
> 216-287-0821 (cell)
> MannKind Biopharmaceuticals
> (Non-Clinical) Statistician
> One Casper Street
> Danbury, CT 06810
> 203-790-2507 (office)
>
> ________________________________
>
> From: jmp-l-owner@lists.biostat.wustl.edu on behalf of Michael Bailey
> Sent: Sun 5/10/2009 5:55 PM
> To: jmp-l@lists.biostat.wustl.edu
> Subject: Re: [jmp-l] intercept in jmp 7, "fit model?"
>
>
>
> Thanks to Al Best for his suggestion. However, I cannot find any
> information about the intercept. I understand about centering
> continuous predictors in a polynomial context. The regression
> coefficients all make sense. What doesn't make clear sense is the
> value of the Y intercept.
>
> For example, if I use a sample data set (Facsalarydummyexamp.jmp)
>
> (Download:
>
http://www.psych.northwestern.edu/psych/people/faculty/bailey/Facsalarydummy
examp.jmp)
> if I regress Salary on Merit, Years, and their interaction, using
> the cross button in the "fit model" box, I get 55.305 for the
> intercept. If, however, I do this by first creating deviation scores
> by hand and then creating a product of deviation variables for the
> interaction term, I get exactly the same value for the regression
> coefficients--except for the intercept, which is now 50.499. I have no
> idea where that number comes from.
>
>
>
> On May 10, 2009, at 3:19 PM, Al Best wrote:
>
>> center polynomials
>
> Michael Bailey
> jm-bailey@northwestern.edu
>
>
>
>
> <winmail.dat>
Michael Bailey
jm-bailey@northwestern.edu
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