I am playing with the a 1-way anova with and without the "-1" option.
I have a simple cooked up example below but it behaves the same on a more
complex real example.
From what I can tell:
1) the estimated means of the different levels are correctly estimated
either way (although reported as means with the -1 and as contrasts without
the -1 as expected)
2) the residuals are identical (in this contrived example they differ
slightly due to numeric instability but in a more real-world example they
truly are identical)
3) BUT the r2/F/p-value are different (in my real-world example they are
drastically different)
How can a model that gets the same parameter estimates on the same data
leading to the same residuals get different r2/F/p-value?
I suspect it depends on the difference in the model.matrix (see below) but
this just confused me how it got the same parameter estimates without
really clearing up why the r2's are different.
Any help on this is greatly appreciated!
> x<-as.factor(c(1,1,1,2,2,2))
> y<-c(1.1,1.0,0.9,2.0,2.1,1.9)
> summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5 6
1.000e-01 -4.980e-16 -1.000e-01 8.538e-18 1.000e-01 -1.000e-01
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.00000 0.05774 17.32 6.52e-05 ***
x2 1.00000 0.08165 12.25 0.000255 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1 on 4 degrees of freedom
Multiple R-Squared: 0.974, Adjusted R-squared: 0.9675
F-statistic: 150 on 1 and 4 DF, p-value: 0.0002552
> summary(lm(y~x-1))
Call:
lm(formula = y ~ x - 1)
Residuals:
1 2 3 4 5 6
1.000e-01 5.027e-16 -1.000e-01 4.405e-20 1.000e-01 -1.000e-01
Coefficients:
Estimate Std. Error t value Pr(>|t|)
x1 1.00000 0.05774 17.32 6.52e-05 ***
x2 2.00000 0.05774 34.64 4.14e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1 on 4 degrees of freedom
Multiple R-Squared: 0.9973, Adjusted R-squared: 0.996
F-statistic: 750 on 2 and 4 DF, p-value: 7.073e-06
> m2nc=lm(y~x-1)
> m2wc=lm(y~x)
> resid(m2nc)
1 2 3 4 5
6
1.000000e-01 5.026734e-16 -1.000000e-01 4.404571e-20 1.000000e-01
-1.000000e-01
> resid(m2wc)
1 2 3 4 5
6
1.000000e-01 -4.980012e-16 -1.000000e-01 8.538092e-18 1.000000e-01
-1.000000e-01
> model.matrix(m2nc)
x1 x2
1 1 0
2 1 0
3 1 0
4 0 1
5 0 1
6 0 1
attr(,"assign")
[1] 1 1
attr(,"contrasts")
attr(,"contrasts")$x
[1] "contr.treatment"
> model.matrix(m2wc)
(Intercept) x2
1 1 0
2 1 0
3 1 0
4 1 1
5 1 1
6 1 1
attr(,"assign")
[1] 0 1
attr(,"contrasts")
attr(,"contrasts")$x
[1] "contr.treatment"
Brian McGill
Dept of Biology
McGill University
Stewart Biology Bldg
1205 ave Docteur Penfield
Montreal, QC H3A 1B1
CANADA
(514) 398-6417
http://www.brianmcgill.org
[EMAIL PROTECTED]
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