R help - May 2012 - setting parameters equal in lm

Forgive me if this is a trivial question, but I couldn't find it an answer
in former forums. I'm trying to reproduce some SAS results where they set
two parameters equal. For example:

y = b1X1 + b2X2 + b1X3

Notice that the variables X1 and X3 both have the same slope and the
intercept has been removed. How do I get an estimate of this regression
model? I know how to remove the intercept ("-1" somewhere after the
tilde).
But how about setting parameters equal? I have used the car package to set
up linear hypotheses:


X1 = rnorm(20, 10, 5); X2 = rnorm(20, 10, 5); X3 = rnorm(20, 10, 5)
Y = .5*X1 + 3*X2 + .5*X3 + rnorm(20, 0, 15)
data.set = data.frame(cbind(X1, X2, X3, Y))
linMod = lm(Y~X1 + X2 + X3, data=data.set)
require(car)
linearHypothesis(linMod, c("(Intercept)=0", "X1-X3=0"))

(forgive the unconventional use of the equal sign....old habit).
Unfortunately, the linearHypothesis is always compared to a full model
(where the parameters are freely estimated). I want to have an ANOVA
summary table for the reduced model. Any ideas? Thanks in advance for the
help!

-- 
Dustin Fife
PhD Student
Quantitative Psychology
University of Oklahoma

	[[alternative HTML version deleted]]

I don't know how it ties into the tools car gives you, but one (quick
and dirty) way to do this is to simply regress on

Y ~ aX2 + b(X1+X3)

or in R code something like:

lm(Y ~ X2 + I(X1+X3), data = data.set)

which gives a linear model you can play around with. Note the I()
function [that's the capital letter immediately preceding J] which
tells R to interpret that term "AsIs"

Hope this helps,
Michael

On Mon, May 28, 2012 at 11:14 PM, Dustin Fife <fife.dustin at gmail.com>
wrote:
> Forgive me if this is a trivial question, but I couldn't find it an
answer
> in former forums. I'm trying to reproduce some SAS results where they
set
> two parameters equal. For example:
>
> y = b1X1 + b2X2 + b1X3
>
> Notice that the variables X1 and X3 both have the same slope and the
> intercept has been removed. How do I get an estimate of this regression
> model? I know how to remove the intercept ("-1" somewhere after
the tilde).
> But how about setting parameters equal? I have used the car package to set
> up linear hypotheses:
>
>
> X1 = rnorm(20, 10, 5); X2 = rnorm(20, 10, 5); X3 = rnorm(20, 10, 5)
> Y = .5*X1 + 3*X2 + .5*X3 + rnorm(20, 0, 15)
> data.set = data.frame(cbind(X1, X2, X3, Y))
> linMod = lm(Y~X1 + X2 + X3, data=data.set)
> require(car)
> linearHypothesis(linMod, c("(Intercept)=0", "X1-X3=0"))
>
> (forgive the unconventional use of the equal sign....old habit).
> Unfortunately, the linearHypothesis is always compared to a full model
> (where the parameters are freely estimated). I want to have an ANOVA
> summary table for the reduced model. Any ideas? Thanks in advance for the
> help!
>
> --
> Dustin Fife
> PhD Student
> Quantitative Psychology
> University of Oklahoma
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Hello,

Your model is equivalent of

y = b1(X1 + X3) + b2X2

(plus error)

So, use I() to add X1 and X3. You don't need to create an extra variable 
X13 <- X1 + X3. See the help page for it. The point on function formula.

?I

linMod2 = lm(Y ~ -1 + I(X1  + X3) + X2, data=data.set)
summary(linMod2)
# The same.
linMod3 = lm(Y ~ 0 + I(X1  + X3) + X2, data=data.set)
summary(linMod3)

With set.seed(1) your common slope is

coef(linMod2)
I(X1 + X3)         X2
  0.4237869  3.3626984

Also, I find it better to put 'library', 'require', etc as the
first
lines of code.

Hope this helps,

Rui Barradas

Em 29-05-2012 04:14, Dustin Fife escreveu:
> Forgive me if this is a trivial question, but I couldn't find it an
answer
> in former forums. I'm trying to reproduce some SAS results where they
set
> two parameters equal. For example:
>
> y = b1X1 + b2X2 + b1X3
>
> Notice that the variables X1 and X3 both have the same slope and the
> intercept has been removed. How do I get an estimate of this regression
> model? I know how to remove the intercept ("-1" somewhere after
the tilde).
> But how about setting parameters equal? I have used the car package to set
> up linear hypotheses:
>
>
> X1 = rnorm(20, 10, 5); X2 = rnorm(20, 10, 5); X3 = rnorm(20, 10, 5)
> Y = .5*X1 + 3*X2 + .5*X3 + rnorm(20, 0, 15)
> data.set = data.frame(cbind(X1, X2, X3, Y))
> linMod = lm(Y~X1 + X2 + X3, data=data.set)
> require(car)
> linearHypothesis(linMod, c("(Intercept)=0", "X1-X3=0"))
>
> (forgive the unconventional use of the equal sign....old habit).
> Unfortunately, the linearHypothesis is always compared to a full model
> (where the parameters are freely estimated). I want to have an ANOVA
> summary table for the reduced model. Any ideas? Thanks in advance for the
> help!
>