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
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