Rich and (Judd and McClelland) give
the right approach.
But I'm not sure about what [EMAIL PROTECTED] means about
"estimated a non-linear
model".
I think he really means a LINEAR
MODEL!
You can start with the ASSUMED LINEAR MODEL ( 4 PARAMETERS- 2
SLOPES AND 2 INTERCEPTS).
Then you can impose any meaningful restrictions that are
implied by your natural language statement
of you hypotheses.
1. If your hypotheses imply that b1-b2 =0, then
impose that restriction AND OBTAIN A RESTRICTED LINEAR MODEL and use the F
statistic to compare the TWO MODELS.
2. If your hypotheses imply that a1-a2 = 0 AND b1-b2 =
0, then impose those restrictions and do the same as in 1.
You can impose ANY LINEAR RESTRICTIONS of interest and
that makes sense to you.
That's the power of the REGRESSION/LINEAR MODELS
approach.
-- Joe
**********************************
Joe H. Ward, Jr.
167 East Arrowhead Dr.
San Antonio, TX 78228-2402
Phone: 210-433-6575
Fax: 210-433-2828
Email: [EMAIL PROTECTED]
http://www.northside.isd.tenet.edu/healthww/biostatistics/wardindex
==============================
Health Careers High School
4646 Hamilton Wolfe Road
San Antonio, TX 78229
**********************************
Joe H. Ward, Jr.
167 East Arrowhead Dr.
San Antonio, TX 78228-2402
Phone: 210-433-6575
Fax: 210-433-2828
Email: [EMAIL PROTECTED]
http://www.northside.isd.tenet.edu/healthww/biostatistics/wardindex
==============================
Health Careers High School
4646 Hamilton Wolfe Road
San Antonio, TX 78229
**********************************
----- Original Message -----
From: "Rich Ulrich" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, October 08, 2003 9:46 AM
Subject: Re: coefficients
>
> > Hello,
> >
> > Given the data of two sectors, I estimated a non-linear model and I got the
> > coefficients of both sectors. Let say that the coefficient of the model in
> > the first sector is a1 and b1 and second sector a2 and b2. Is there any way to
> > test the difference between b1 and b2 or to test whether b1-b2=0 or not. Your
> > help is highly appreciated.
> >
>
> You name four parameters, above.
>
> The conventional solution is to pool the data and fit
> just two parameters; then you compare the fit with 2
> to the fit with 4 (or the sum of the two fittings, each done
> with 2). Or, might think of this as having 3, as another
> model. In OLS, the residual has a different Sum of Squares,
> and degrees of freedom, depending on the model.
> You define an F-test by subtraction
>
> It works rather similarly for Maximum Likelihood models,
> where the difference is log-likelihoods (times minus 2) is
> tested by chisquared, with d.f. determined by the difference
> in the number of parameters.
>
> It is pretty simple to set up with dummy variables, for
> linear models and ordinary least squares.
>
> try
> Judd and McClelland, "Data analysis, a model comparison
> approach."
>
> --
> Rich Ulrich, [EMAIL PROTECTED]
> http://www.pitt.edu/~wpilib/index.html
> "Taxes are the price we pay for civilization."
> .
> .
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