gIndex {rms} | R Documentation

## 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 b1, b2, b3 will have the g-index for age computed from Gini's mean difference on the product of age times (b1 + b3*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 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 `rms` fitting function
`partials` | set to `FALSE` to suppress computation of partial gs

`type`

defaults to `'ccterms'` which causes partial discrimination indexes to be computed after maximally combining all related main effects and interactions. The is usually the only way that makes sense when considering partial linear predictors. Specify `type='cterms'` to only combine a main effect with interactions containing it, not also with other main effects connected through interactions. Use `type='terms'` to separate interactions into their own effects.

`lplabel` | a replacement for default values such as `"X*Beta"` or `"log odds"`/
`fun` | an optional function to transform the linear predictors before computing the total (only) g. When this is present, a new component `gtrans` is added to the attributes of the object resulting from `gIndex`.
`funlabel` | a character string label for `fun`, otherwise taken from the function name itself
`postfun` | a function to transform g such as `exp` (anti-log), which is the default for certain models such as the logistic and Cox models
`postlabel` | a label for `postfun`
`...` | For `gIndex`, passed to `predict.rms`. Ignored for `print`. Passed to `dotchart2` for `plot`.
`x` | an object created by `gIndex` (for `print` or `plot`)
`digits` | causes rounding to the `digits` decimal place
`abbrev` | set to `TRUE` to abbreviate labels if `vname="labels"`
`vnames` | set to `"labels"` to print predictor labels instead of names
`what` | set to `"post"` to plot the transformed g-index if there is one (e.g., ratio scale)
`xlab` | x-axis label; constructed by default
`pch` | plotting character for point
`rm.totals` | set to `TRUE` to remove the total g-index when plotting
`sort` | specifies how to sort predictors by g-index; default is in descending order going down the dot chart

### 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.

### 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
f.harrell@vanderbilt.edu

### 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)
    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)

[Package rms version 5.1-2 Index]