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
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