# [R] How to force two regression coefficients to be equal but opposite in sign?

Greg Snow Greg.Snow at imail.org
Fri Jun 6 19:39:27 CEST 2008

```One simple way is to do something like:

> fit <- lm(y ~ I(x1-x2) + x3, data=mydata)

The first coeficient (after the intercept) will be the slope for x1, the slope for x2 will be the negative of that.  This model is nested in the fuller model with x1 and x2 fit seperately and you can therefore test for differences.

Hope this helps,

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
(801) 408-8111

> -----Original Message-----
> From: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] On Behalf Of Woolner, Keith
> Sent: Friday, June 06, 2008 10:07 AM
> To: r-help at r-project.org
> Subject: [R] How to force two regression coefficients to be
> equal but opposite in sign?
>
> Is there a way to set up a regression in R that forces two
> coefficients
>
> to be equal but opposite in sign?
>
>
>
> I'm trying to setup a model where a subject appears in a pair of
>
> environments where a measurement X is made.  There are a total of 5
>
> environments, one of which is a baseline.  But each observation is for
>
> a subject in only two of them, and not all subjects will appear in
>
> each environment.
>
>
>
> Each of the environments has an effect on the variable X.  I want to
>
> measure the relative effects of each environment E on X with a model.
>
>
>
> Xj = Xi * Ei / Ej
>
>
>
> Ei of the baseline model is set equal to 1.
>
>
>
> With a log transform, a linear-looking regression can be written as:
>
>
>
> log(Xj) = log(Xi) + log(Ei) - log(Ej)
>
>
>
> My data looks like:
>
>
>
> #    E1   X1   E2    X2
>
> 1    A   .20   B    .25
>
>
>
> What I've tried in R:
>
>
>
> env <- c("A","B","C","D","E")
>
>
>
> # Note: data is made up just for this example
>
>
>
> df <- data.frame(
>
>                 X1 =
> c(.20,.10,.40,.05,.10,.24,.30,.70,.48,.22,.87,.29,.24,.19,.92),
>
>                 X2 =
> c(.25,.12,.45,.01,.19,.50,.30,.40,.50,.40,.68,.30,.16,.02,.70),
>
>                 E1 =
> c("A","A","A","B","B","B","C","C","C","D","D","D","E","E","E"),
>
>                 E2 =
> c("B","C","D","A","D","E","A","B","E","B","C","E","A","B","C")
>
> )
>
>
>
> model <- lm(log(X2) ~ log(X1) + E1 + E2, data = df)
>
>
>
> summary(model)
>
>
>
> Call:
>
> lm(formula = log(X2) ~ log(X1) + E1 + E2, data = df)
>
>
>
> Residuals:
>
>       1       2       3       4       5       6       7
> 8       9
> 10      11      12      13      14      15
>
>  0.3240  0.2621 -0.5861 -1.0283  0.5861  0.4422  0.3831
> -0.2608 -0.1222
> 0.9002 -0.5802 -0.3200  0.6452 -0.9634  0.3182
>
>
>
> Coefficients:
>
>             Estimate Std. Error t value Pr(>|t|)
>
> (Intercept)  0.54563    1.71558   0.318    0.763
>
> log(X1)      1.29745    0.57295   2.265    0.073 .
>
> E1B         -0.23571    0.95738  -0.246    0.815
>
> E1C         -0.57057    1.20490  -0.474    0.656
>
> E1D         -0.22988    0.98274  -0.234    0.824
>
> E1E         -1.17181    1.02918  -1.139    0.306
>
> E2B         -0.16775    0.87803  -0.191    0.856
>
> E2C          0.05952    1.12779   0.053    0.960
>
> E2D          0.43077    1.19485   0.361    0.733
>
> E2E          0.40633    0.98289   0.413    0.696
>
> ---
>
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>
>
> Residual standard error: 1.004 on 5 degrees of freedom
>
> Multiple R-squared: 0.7622,     Adjusted R-squared: 0.3343
>
> F-statistic: 1.781 on 9 and 5 DF,  p-value: 0.2721
>
>
>
> ----
>
>
>
> What I need to do is force the corresponding environment coefficients
>
> to be equal in absolute value, but opposite in sign.  That is:
>
>
>
> E1B = -E2B
>
> E1C = -E3C
>
> E1D = -E3D
>
> E1E = -E1E
>
>
>
> In essence, E1 and E2 are the "same" variable, but can play two
>
> different roles in the model depending on whether it's the first part
>
> of the observation or the second part.
>
>
>
> I searched the archive, and the closest thing I found to my situation
>
> was:
>
>
>
> http://tolstoy.newcastle.edu.au/R/e4/help/08/03/6773.html
>
>
>
> But the response to that thread didn't seem to be applicable to my
>
> situation.
>
>
>
> Any pointers would be appreciated.
>
>
>
> Thanks,
>
> Keith
>
>
>
>
>         [[alternative HTML version deleted]]
>
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