bplot: 3-D Plots Showing Effects of Two Continuous Predictors in a Regression Model Fit

Description

Uses base graphics and the output from Predict to plot image, contour, or perspective plots showing the simultaneous effects of two continuous predictor variables. The $x$-axis is constructed from the first variable listed in the call to Predict and the $y$-axis variable comes from the second.

The perimeter function is used to generate the boundary of data to plot when a 3-d plot is made. It finds the area where there are sufficient data to generate believable interaction fits.

iLegend is function for adding legends to an existing graph produced with bplot using method="image".

Usage

bplot(x, xlab, ylab, zlab,
      adj.subtitle=TRUE, cex.adj, perim,
      method=c("image", "persp", "contour"),
      zlim=range(yhat, na.rm=TRUE), ...)
perimeter(x, y, xinc=diff(range(x))/10, n=10, lowess.=TRUE)
## S3 method for class 'perimeter':
lines(x, \dots)
iLegend(object, x, y, size=c(1,1), horizontal=TRUE,
       nint=50, fun.=NULL, at=NULL, zlab, zlim, ...)

Arguments

for bplot, an object created by Predict for which exactly two numeric predictors varied. For iLegend, is either a vector of 1 or 2 $x$-coordinates or a list with elements x and y each

xlab

Label for $x$-axis. Default is given by Predict.

ylab

Label for $y$-axis

zlab

$z$-axis label for perspective plots or for iLegend. Default comes from Predict. zlab will often be specified if fun was specified to Predict or iLegend.

adj.subtitle

Set to FALSE to suppress subtitling the graph with the list of settings of non-graphed adjustment values. Default is TRUE if there are non-plotted adjustment variables.

cex.adj

cex parameter for size of adjustment settings in subtitles. Default is 0.75 times par("cex").

perim

names a matrix created by perimeter when used for 3-d plots of two continuous predictors. When the combination of variables is outside the range in perim, that section of the plot is suppressed. If perim is omitte

method

Use method="persp" for perspective plots (persp()), method="contour" to use contour(), or method="image" to use image() (the default).

zlim

If 'type="persp"' controls the range for plotting in the $z$-axis. Computed by default. Also used by iLegend.

...

optional arguments to pass to persp, image, or contour. Specify a vector to assign different colors to different curves or to components of 3-d plots, e.g. col=rainbow(30) when method='imag

second variable of the pair for perim, or $y$-coordinates for iLegend. If omitted, x is assumed to be a list with both x and y components.

xinc

increment in x over which to examine the density of y in perimeter

within intervals of x for perimeter, takes the informative range of y to be the $n$th smallest to the $n$th largest values of y. If there aren't at least 2$n$ y values in the x

lowess.

set to FALSE to not have lowess smooth the data perimeters

object

object created by Predict

size

size of legend in inches; omitted with 2 points are given in x and y

horizontal

set to FALSE to make the labeled legend axis vertical

nint

number of intervals of predicted values to use in legend

fun.

For iLegend, fun is a function for transforming tick mark labels for color or gray scale legends for method="image". For example, if bplot is used to make an image plot of log odds ratios, specif

If fun is specified to iLegend, at may be given. at is a vector of values at which to evaluate fun for drawing tick marks in the color legend. For example, if you want to show the median s

Value

perimeter returns a matrix of class perimeter. This outline can be conveniently plotted by lines.perimeter. iLegend invisibly returns the position of the legend.

Details

perimeter is a kind of generalization of datadist for 2 continuous variables. First, the n smallest and largest x values are determined. These form the lowest and highest possible xs to display. Then x is grouped into intervals bounded by these two numbers, with the interval widths defined by xinc. Within each interval, y is sorted and the $n$th smallest and largest y are taken as the interval containing sufficient data density to plot interaction surfaces. The interval is ignored when there are insufficient y values. When the data are being readied for persp, bplot uses the approx function to do linear interpolation of the y-boundaries as a function of the x values actually used in forming the grid (the values of the first variable specified to Predict). To make the perimeter smooth, specify lowess.=TRUE to perimeter.

Examples

Run this code

n <- 1000    # define sample size
set.seed(17) # so can reproduce the results
age            <- rnorm(n, 50, 10)
blood.pressure <- rnorm(n, 120, 15)
cholesterol    <- rnorm(n, 200, 25)
sex            <- factor(sample(c('female','male'), n,TRUE))
label(age)            <- 'Age'      # label is in Hmisc
label(cholesterol)    <- 'Total Cholesterol'
label(blood.pressure) <- 'Systolic Blood Pressure'
label(sex)            <- 'Sex'
units(cholesterol)    <- 'mg/dl'   # uses units.default in Hmisc
units(blood.pressure) <- 'mmHg'

# Specify population model for log odds that Y=1
L <- .4*(sex=='male') + .045*(age-50) +
  (log(cholesterol - 10)-5.2)*(-2*(sex=='female') + 2*(sex=='male'))
# Simulate binary y to have Prob(y=1) = 1/[1+exp(-L)]
y <- ifelse(runif(n) < plogis(L), 1, 0)

ddist <- datadist(age, blood.pressure, cholesterol, sex)
options(datadist='ddist')

fit <- lrm(y ~ blood.pressure + sex * (age + rcs(cholesterol,4)),
               x=TRUE, y=TRUE)
p <- Predict(fit, age=., cholesterol=., np=100)
bplot(p)                 # image plot for age, cholesterol with color
                         # coming from yhat; use default ranges for
                         # both continuous predictors
bplot(p, method='persp', theta=30, ticktype='detailed')
                         # 3-d perspective plot
bplot(p, method='contour')       # contour plot
boundaries <- perimeter(age, cholesterol, lowess=TRUE)
plot(age, cholesterol)   # show bivariate data density
lines(boundaries)        # and perimeter that will be used for 3-D plot
p <- Predict(fit, age=., cholesterol=.)
par(mgp=c(1.7, .35, 0))
bplot(p, perim=boundaries)
                         # draws image() plot
                         # don't show estimates where data are sparse
                         # doesn't make sense here since vars don't interact
iLegend(p, x=c(30,40), y=c(230, 245))   # original logit scale
iLegend(p, x=c(65,75), y=c(230, 245), fun=plogis,
        at=qlogis(c(.1,.25,.5,.75,.9)),
        zlab='Probability')             # probability scale
options(datadist=NULL)

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