[R] Funny behaviour of coef() and vcov() if X is singular

[Prof Brian Ripley]

Yes, and that's intentional.  You don't want non-information on
unestimated parameters, do you?  (What would you do with it?)

BTW, you forgot the very important caveat `the "lm" methods of coef() and
vcov()'.

On Mon, 27 Sep 2004, BXC (Bendix Carstensen) wrote:

> 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
> 
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> 
> 

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595