gIndex {rms} | R Documentation |
Calculate Total and Partial g-indexes for an rms Fit
Description
gIndex
computes the total -index for a model based on
the vector of linear predictors, and the partial
-index for
each predictor in a model. The latter is computed by summing all the
terms involving each variable, weighted by their regression
coefficients, then computing Gini's mean difference on this sum. For
example, a regression model having age and sex and age*sex on the
right hand side, with corresponding regression coefficients
will have the
-index for age
computed from Gini's mean
difference on the product of age
where
is an indicator set to one for observations with sex not equal
to the reference value. When there are nonlinear terms associated
with a predictor, these terms will also be combined.
A print
method is defined, and there is a plot
method for displaying
-indexes using a dot chart.
These functions use Hmisc::GiniMd
.
Usage
gIndex(object, partials=TRUE, type=c('ccterms', 'cterms', 'terms'),
lplabel=if(length(object$scale) && is.character(object$scale))
object$scale[1] else 'X*Beta',
fun, funlabel=if(missing(fun)) character(0) else
deparse(substitute(fun)),
postfun=if(length(object$scale)==2) exp else NULL,
postlabel=if(length(postfun))
ifelse(missing(postfun),
if((length(object$scale) > 1) &&
is.character(object$scale)) object$scale[2] else
'Anti-log',
deparse(substitute(postfun))) else character(0),
...)
## S3 method for class 'gIndex'
print(x, digits=4, abbrev=FALSE,
vnames=c("names","labels"), ...)
## S3 method for class 'gIndex'
plot(x, what=c('pre', 'post'),
xlab=NULL, pch=16, rm.totals=FALSE,
sort=c('descending', 'ascending', 'none'), ...)
Arguments
object |
result of an |
partials |
set to |
type |
defaults to |
lplabel |
a replacement for default values such as
|
fun |
an optional function to transform the linear predictors
before computing the total (only) |
funlabel |
a character string label for |
postfun |
a function to transform |
postlabel |
a label for |
... |
For |
x |
an object created by |
digits |
causes rounding to the |
abbrev |
set to |
vnames |
set to |
what |
set to |
xlab |
|
pch |
plotting character for point |
rm.totals |
set to |
sort |
specifies how to sort predictors by |
Details
For stratification factors in a Cox proportional hazards model, there is
no contribution of variation towards computing a partial
except from terms that interact with the stratification variable.
Value
gIndex
returns a matrix of class "gIndex"
with auxiliary
information stored as attributes, such as variable labels.
GiniMd
returns a scalar.
Author(s)
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
References
David HA (1968): Gini's mean difference rediscovered. Biometrika 55:573–575.
See Also
Examples
set.seed(1)
n <- 40
x <- 1:n
w <- factor(sample(c('a','b'), n, TRUE))
u <- factor(sample(c('A','B'), n, TRUE))
y <- .01*x + .2*(w=='b') + .3*(u=='B') + .2*(w=='b' & u=='B') + rnorm(n)/5
dd <- datadist(x,w,u); options(datadist='dd')
f <- ols(y ~ x*w*u, x=TRUE, y=TRUE)
f
anova(f)
z <- list()
for(type in c('terms','cterms','ccterms'))
{
zc <- predict(f, type=type)
cat('type:', type, '\n')
print(zc)
z[[type]] <- zc
}
zc <- z$cterms
GiniMd(zc[, 1])
GiniMd(zc[, 2])
GiniMd(zc[, 3])
GiniMd(f$linear.predictors)
g <- gIndex(f)
g
g['Total',]
gIndex(f, partials=FALSE)
gIndex(f, type='cterms')
gIndex(f, type='terms')
y <- y > .8
f <- lrm(y ~ x * w * u, x=TRUE, y=TRUE)
gIndex(f, fun=plogis, funlabel='Prob[y=1]')
# Manual calculation of combined main effect + interaction effort of
# sex in a 2x2 design with treatments A B, sexes F M,
# model -.1 + .3*(treat=='B') + .5*(sex=='M') + .4*(treat=='B' & sex=='M')
set.seed(1)
X <- expand.grid(treat=c('A','B'), sex=c('F', 'M'))
a <- 3; b <- 7; c <- 13; d <- 5
X <- rbind(X[rep(1, a),], X[rep(2, b),], X[rep(3, c),], X[rep(4, d),])
y <- with(X, -.1 + .3*(treat=='B') + .5*(sex=='M') + .4*(treat=='B' & sex=='M'))
f <- ols(y ~ treat*sex, data=X, x=TRUE)
gIndex(f, type='cterms')
k <- coef(f)
b1 <- k[2]; b2 <- k[3]; b3 <- k[4]
n <- nrow(X)
( (a+b)*c*abs(b2) + (a+b)*d*abs(b2+b3) + c*d*abs(b3))/(n*(n-1)/2 )
# Manual calculation for combined age effect in a model with sex,
# age, and age*sex interaction
a <- 13; b <- 7
sex <- c(rep('female',a), rep('male',b))
agef <- round(runif(a, 20, 30))
agem <- round(runif(b, 20, 40))
age <- c(agef, agem)
y <- (sex=='male') + age/10 - (sex=='male')*age/20
f <- ols(y ~ sex*age, x=TRUE)
f
gIndex(f, type='cterms')
k <- coef(f)
b1 <- k[2]; b2 <- k[3]; b3 <- k[4]
n <- a + b
sp <- function(w, z=w) sum(outer(w, z, function(u, v) abs(u-v)))
( abs(b2)*sp(agef) + abs(b2+b3)*sp(agem) + 2*sp(b2*agef, (b2+b3)*agem) ) / (n*(n-1))
( abs(b2)*GiniMd(agef)*a*(a-1) + abs(b2+b3)*GiniMd(agem)*b*(b-1) +
2*sp(b2*agef, (b2+b3)*agem) ) / (n*(n-1))
## Not run:
# Compare partial and total g-indexes over many random fits
plot(NA, NA, xlim=c(0,3), ylim=c(0,3), xlab='Global',
ylab='x1 (black) x2 (red) x3 (green) x4 (blue)')
abline(a=0, b=1, col=gray(.9))
big <- integer(3)
n <- 50 # try with n=7 - see lots of exceptions esp. for interacting var
for(i in 1:100) {
x1 <- runif(n)
x2 <- runif(n)
x3 <- runif(n)
x4 <- runif(n)
y <- x1 + x2 + x3 + x4 + 2*runif(n)
f <- ols(y ~ x1*x2+x3+x4, x=TRUE)
# f <- ols(y ~ x1+x2+x3+x4, x=TRUE) # also try this
w <- gIndex(f)[,1]
gt <- w['Total']
points(gt, w['x1, x2'])
points(gt, w['x3'], col='green')
points(gt, w['x4'], col='blue')
big[1] <- big[1] + (w['x1, x2'] > gt)
big[2] <- big[2] + (w['x3'] > gt)
big[3] <- big[3] + (w['x4'] > gt)
}
print(big)
## End(Not run)
options(datadist=NULL)