rms (version 8.2-1)

gIndex: Calculate Total and Partial g-indexes for an rms Fit

Description

gIndex computes the total \(g\)-index for a model based on the vector of linear predictors, and the partial \(g\)-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 \(b_{1}, b_{2}, b_{3}\) will have the \(g\)-index for age computed from Gini's mean difference on the product of age \(\times (b_{1} + b_{3}w)\) where \(w\) 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 \(g\)-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 gIndex
print(x, digits=4, abbrev=FALSE,
 vnames=c("names","labels"), ...)
# S3 method for gIndex
plot(x, what=c('pre', 'post'),
 xlab=NULL, pch=16, rm.totals=FALSE,
sort=c('descending', 'ascending', 'none'), ...)

Value

gIndex returns a matrix of class "gIndex" with auxiliary information stored as attributes, such as variable labels.

GiniMd returns a scalar.

Details

For stratification factors in a Cox proportional hazards model, there is no contribution of variation towards computing a partial \(g\) except from terms that interact with the stratification variable.

References

David HA (1968): Gini's mean difference rediscovered. Biometrika 55:573--575.

See Also

predict.rms,GiniMd

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, reltol=1e-5)

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))

if (FALSE) {
# 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)
}

options(datadist=NULL)