[R] influence measures for multivariate linear models

[Michael Friendly]

Barrett & Ling, JASA, 1992, v.87(417), pp184-191 define general classes 
of influence measures for multivariate
regression models, including analogs of Cook's D, Andrews & Pregibon 
COVRATIO, etc.  As in univariate
response models, these are based on leverage and residuals based on 
omitting one (or more) observations at
a time and refitting, although, in the univariate case, the computations 
can be optimized, as they are in
stats::influence() and related methods.

I'm interested in exploring the multivariate extension in R.  I tried 
the following, and was surprised to find that
R returned a result rather than an error -- presumably because mlm 
objects are not trapped before they
get to lm.influence()

 > # multivariate model
 > data(Rohwer, package="heplots")
 > rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ n + s + ns + na + ss, 
data=Rohwer)

 > names(influence(rohwer.mod))
[1] "hat"          "coefficients" "sigma"        "wt.res"     
 > head(influence(rohwer.mod)$coefficients, 2)
        [,1]       [,2]      [,3]     [,4]      [,5]      [,6]
[1,] 2.25039  0.0254739 -0.025252 -0.06297 -0.121507  0.094355
[2,] 0.84649 -0.0062656 -0.077430  0.08345 -0.022579 -0.059480
 >

Of course, the correct calculations would result from refitting, 
omitting each observation in turn, though doing this
directly would be horribly inefficient.
e.g, calculating B(i), deleting case i:

 > coef(update(rohwer.mod, subset=1:69 !=1, data=Rohwer))
                  SAT     PPVT     Raven
(Intercept) -2.466079 35.68664 11.510068
n            1.888286  0.60949  0.075931
s           -0.034524 -0.53040  0.160328
ns          -2.739834 -0.67355  0.066392
na           2.219340  1.20481 -0.037272
ss           1.072300  0.99033  0.058509
 > coef(update(rohwer.mod, subset=1:69 !=2, data=Rohwer))
                  SAT     PPVT      Raven
(Intercept) -1.062178 33.88199 10.8988006
n            1.920026  0.59735  0.0713976
s            0.017654 -0.47464  0.1774135
ns          -2.886254 -0.67905  0.0673686
na           2.120411  1.29016 -0.0077484
ss           1.226135  0.96430  0.0471764

Is there anything existing for this case that I've missed, or does 
anyone have an interest in pursuing this topic?

-Michael

-- 
Michael Friendly     Email: friendly AT yorku DOT ca 
Professor, Psychology Dept.
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA