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coefficient of partial determination...partial r square [ redux]

2 messages · Liaw, Andy, Andy Bunn

Liaw, Andy
# 
If I'm not mistaken, partial R-squared is the R^2 of the quantities plotted
in a partial residual plot, so you can base the computation on that.  Prof.
Fox's `car' package on CRAN has a function for creating those plots, but you
need to figure out the way to extract the quantities being plotted.

[In any case, the basic tools for doing such computations are all in R, and
it shouldn't be hard at all to cook up such a thing, starting from the
formula.  Writing a function that works on any conceivable models that can
be fitted with lm() would be a bit more challenging, but I doubt you need
that.]

HTH,
Andy
Andy Bunn
# 
Dr. C:

I implemented this example of partial r square from Neter et al.'s big blue
book. It's easily extendable to a three variable model (or more). I might
write it to work with class lm or glm if there is interest.

HTH, Andy


Applied Linear Statistical Models by John Neter, Michael H Kutner, William
Wasserman, Christopher J. Nachtsheim

Section 7.4 in my copy page 274:


# body fat example from Neter et al.
bf.dat <- read.csv("body.fat.data.csv", header = T)
#R > bf.dat
#     x1   x2   x3    y
#1  19.5 43.1 29.1 11.9
#2  24.7 49.8 28.2 22.8
#3  30.7 51.9 37.0 18.7
#4  29.8 54.3 31.1 20.1
#5  19.1 42.2 30.9 12.9
#6  25.6 53.9 23.7 21.7
#7  31.4 58.5 27.6 27.1
#8  27.9 52.1 30.6 25.4
#9  22.1 49.9 23.2 21.3
#10 25.5 53.5 24.8 19.3
#11 31.1 56.6 30.0 25.4
#12 30.4 56.7 28.3 27.2
#13 18.7 46.5 23.0 11.7
#14 19.7 44.2 28.6 17.8
#15 14.6 42.7 21.3 12.8
#16 29.5 54.4 30.1 23.9
#17 27.7 55.3 25.7 22.6
#18 30.2 58.6 24.6 25.4
#19 22.7 48.2 27.1 14.8
#20 25.2 51.0 27.5 21.1
#R >
# Not run:
#names(bf.dat) <- c('Triceps Skinfold Thickness', x2 = 'Thigh
Circumference', x3 = 'Midarm Circumference', y = 'Body Fat')
summary(bf.dat)
lm.x1 <- lm(y ~ x1, data = bf.dat)
lm.x2 <- lm(y ~ x2, data = bf.dat)
lm.x1.x2 <- lm(y ~ x1 + x2, data = bf.dat)

# SSR(x2|x1) = SSR(x1,x2) - SSR(x1)
ssr.x1.x2 <- sum(anova(lm.x1.x2)$"Sum Sq"[1:2])
ssr.x1    <- anova(lm.x1)$"Sum Sq"[1]
ssr.x2    <- anova(lm.x2)$"Sum Sq"[1]
ssr.x1.x2 - ssr.x1
# also
sse.x1    <- anova(lm.x1)$"Sum Sq"[2] # eq sum(lm.x1$resid^2)
sse.x2    <- anova(lm.x2)$"Sum Sq"[2] # eq sum(lm.x2$resid^2)

# The partial r2 of x1 while controlling for x2 is 0.031
# pr2_1.2 = SSR(x1|x2) / SSE(x2)
(ssr.x1.x2 - ssr.x2) / sse.x2
# The partial r2 of x2 while controlling for x1 is 0.232
# pr2_2.1 = SSR(x2|x1) / SSE(x1)
(ssr.x1.x2 - ssr.x1) / sse.x1