Funny behaviour of coef() and vcov() if X is singular
coef() and vcov() have different dimensions if a model contains alised parameters as the following example illustrates. A search on "alised" gave noting as far as I could see. Is this a known bug? Bendix C ---------------------- Bendix Carstensen Senior Statistician Steno Diabetes Center Niels Steensens Vej 2 DK-2820 Gentofte Denmark tel: +45 44 43 87 38 mob: +45 30 75 87 38 fax: +45 44 43 07 06 bxc at steno.dk www.biostat.ku.dk/~bxc ----------------------
x <- rnorm(100) y <- rnorm(100) z <- rnorm(100) summary( mu <- lm( y ~x + I(x-z)+z ) )
Call:
lm(formula = y ~ x + I(x - z) + z)
Residuals:
Min 1Q Median 3Q Max
-1.917325 -0.633091 -0.003363 0.561464 2.473183
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.07806 0.09118 0.856 0.3940
x -0.27373 0.11415 -2.398 0.0184
I(x - z) 0.08617 0.08524 1.011 0.3146
z NA NA NA NA
Residual standard error: 0.9061 on 97 degrees of freedom
Multiple R-Squared: 0.05813, Adjusted R-squared: 0.03871
F-statistic: 2.993 on 2 and 97 DF, p-value: 0.05476
coef( mu )
(Intercept) x I(x - z) z 0.07805884 -0.27373500 0.08617152 NA
vcov( mu )
(Intercept) x I(x - z) (Intercept) 8.313341e-03 -5.702109e-05 0.0007248947 x -5.702109e-05 1.303028e-02 -0.0057006507 I(x - z) 7.248947e-04 -5.700651e-03 0.0072657814
length( coef( mu ) )
[1] 4
dim( vcov( mu ) )
[1] 3 3
version
_ platform i386-pc-mingw32 arch i386 os mingw32 system i386, mingw32 status major 1 minor 9.1 year 2004 month 06 day 21 language R