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Uses lattice graphics to plot the effect of one or two predictors
on the linear predictor or X beta scale, or on some transformation of
that scale. The first argument specifies the result of the
Predict function. The predictor is always plotted in its
original coding. plot.Predict uses the
xYplot function unless formula is omitted and the x-axis
variable is a factor, in which case it reverses the x- and y-axes and
uses the Dotplot function.
If data is given, a rug plot is drawn showing
the location/density of data values for the groups (superposition) variable that generated separate
curves, the data density specific to each class of points is shown.
This assumes that the second variable was a factor variable. The rug plots
are drawn by scat1d. When the same predictor is used on all
subdata to specify an expression to subset according to other
criteria in addition.
To plot effects instead of estimates (e.g., treatment differences as a
function of interacting factors) see contrast.rms and
summary.rms.
pantext creates a lattice panel function for including
text such as that produced by print.anova.rms inside a panel or
in a base graphic.
# S3 method for Predict
plot(x, formula, groups=NULL,
cond=NULL, varypred=FALSE, subset,
xlim, ylim, xlab, ylab,
data=NULL, subdata, anova=NULL, pval=FALSE, cex.anova=.85,
col.fill=gray(seq(.825, .55, length=5)),
adj.subtitle, cex.adj, cex.axis, perim=NULL, digits=4, nlevels=3,
nlines=FALSE, addpanel, scat1d.opts=list(frac=0.025, lwd=0.3),
type=NULL, yscale=NULL, scaletrans=function(z) z, ...)pantext(object, x, y, cex=.5, adj=0, fontfamily="Courier", lattice=TRUE)
a lattice object ready to print for rendering.
a data frame created by Predict, or for pantext
the x-coordinate for text
the right hand side of a lattice formula reference variables in
data frame x. You may not specify formula if you varied
multiple predictors separately when calling Predict.
Otherwise, when formula is not given, plot.Predict
constructs one from information in x.
an optional name of one of the variables in x that
is to be used as a grouping (superpositioning) variable. Note that
groups does not contain the groups data as is customary in
lattice; it is only a single character string specifying the
name of the grouping variable.
when plotting effects of different predictors, cond
is a character string that specifies a single variable name in
x that can be used to form panels. Only applies if using
rbind to combine several Predict results.
set to TRUE if x is the result of
passing multiple Predict results, that represent different
predictors, to rbind.Predict. This will cause the .set.
variable created by rbind to be copied to the
.predictor. variable.
a subsetting expression for restricting the rows of
x that are used in plotting. For example, predictions may have
been requested for males and females but one wants to plot only females.
This parameter is seldom used, as limits are usually controlled with
Predict. One reason to use xlim is to plot a
factor variable on the x-axis that was created with the cut2 function
with the levels.mean option, with val.lev=TRUE specified to plot.Predict.
In this case you may want the axis to
have the range of the original variable values given to cut2 rather
than the range of the means within quantile groups.
Range for plotting on response variable axis. Computed by default.
Label for x-axis. Default is one given to asis, rcs, etc.,
which may have been the "label" attribute of the variable.
Label for y-axis. If fun is not given,
default is "log Odds" for
lrm, "log Relative Hazard" for cph, name of the response
variable for ols, TRUE or log(TRUE) for psm, or "X * Beta" otherwise.
a data frame containing the original raw data on which the
regression model were based, or at least containing the data is present and contains the
needed variables, the original data are added to the graph in the form
of a rug plot using scat1d.
if data is specified, an expression to be
evaluated in the data environment that evaluates to a logical
vector specifying which observations in data to keep. This
will be intersected with the criterion for the groups
variable. Example: if conditioning on two paneling variables using
|a*b you can specify
subdata=b==levels(b)[which.packet()[2]], where the 2
comes from the fact that b was listed second after the
vertical bar (this assumes b is a factor in
data. Another example:
subdata=sex==c('male','female')[current.row()].
an object returned by anova.rms. If
anova is specified, the overall test of association for
predictor plotted is added as text to each panel, located at the spot
at which the panel is most empty unless there is significant empty
space at the top or bottom of the panel; these areas are given preference.
specify pval=TRUE for anova to include not
only the test statistic but also the P-value
character size for the test statistic printed on the panel
a vector of colors used to fill confidence bands for successive superposed groups. Default is inceasingly dark gray scale.
Set to FALSE to suppress subtitling the graph with the list of
settings of non-graphed adjustment values.
cex parameter for size of adjustment settings in subtitles. Default is
0.75 times par("cex").
cex parameter for x-axis tick labels
perim specifies a function having two
arguments. The first is the vector of values of the first variable that
is about to be plotted on the x-axis. The second argument is the single
value of the variable representing different curves, for the current
curve being plotted. The function's returned value must be a logical
vector whose length is the same as that of the first argument, with
values TRUE if the corresponding point should be plotted for the
current curve, FALSE otherwise. See one of the latter examples.
If a predictor is not specified to plot, NULL is passed as
the second argument to perim, although it makes little sense to
use perim when the same perim is used for multiple predictors.
Controls how numeric variables used for panel labels are formatted. The default is 4 significant digits.
when groups and formula are not specified, if any panel
variable has nlevels or fewer values, that variable is
converted to a groups (superpositioning) variable. Set
nlevels=0 to prevent this behavior. For other situations, a
numeric x-axis variable with nlevels or fewer unique values
will cause a dot plot to be drawn instead of an x-y plot.
If formula is given, you can set nlines to
TRUE to convert the x-axis variable to a factor and then to an
integer. Points are plotted at integer values on the x-axis but
labeled with category levels. Points are connected by lines.
an additional panel function to call along with panel
functions used for xYplot and Dotplot displays
a list containing named elements that specifies
parameters to scat1d when data is given. The
col parameter is usually derived from other plotting
information and not specified by the user.
a value ("l","p","b") to override default choices
related to showing or connecting points. Especially useful for
discrete x coordinate variables.
a lattice scale list for the y-axis
to be added to what is automatically generated for the x-axis.
Example:
yscale=list(at=c(.005,.01,.05),labels=format(c(.005,.01,.05))).
See xyplot
a function that operates on the scale object
created by plot.Predict to produce a modified scale
object that is passed to the lattice graphics function. This is
useful for adding other scales options or for changing the
x-axis limits for one predictor.
extra arguments to pass to xYplot or Dotplot. Some
useful ones are label.curves and abline.
Set label.curves to FALSE to suppress labeling of
separate curves. Default is TRUE, which
causes labcurve to be invoked to place labels at positions where the
curves are most separated, labeling each curve with the full curve label.
Set label.curves to a list to specify options to
labcurve, e.g., label.curves= list(method="arrow",
cex=.8).
These option names may be abbreviated in the usual way arguments
are abbreviated. Use for example label.curves=list(keys=letters[1:5])
to draw single lower case letters on 5 curves where they are most
separated, and automatically position a legend
in the most empty part of the plot. The col, lty, and
lwd parameters are passed automatically to labcurve
although they may be overridden here.
It is also useful to use ... to pass lattice graphics parameters, e.g.
par.settings=list(axis.text=list(cex=1.2), par.ylab.text=list(col='blue',cex=.9),par.xlab.text=list(cex=1)).
an object having a print method
y-coordinate for placing text in a lattice panel
or on a base graphics plot
character expansion size for pantext
text justification. Default is left justified.
font family for pantext. Default is "Courier" which
will line up columns of a table.
set to FALSE to use text instead of
ltext in the function generated by pantext, to use base
graphics
Frank Harrell
Department of Biostatistics, Vanderbilt University
fh@fharrell.com
When a groups (superpositioning) variable was used, you can issue
the command Key(...) after printing the result of
plot.Predict, to draw a key for the groups.
Fox J, Hong J (2009): Effect displays in R for multinomial and proportional-odds logit models: Extensions to the effects package. J Stat Software 32 No. 1.
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)
an <- anova(fit)
# Plot effects of all 4 predictors with test statistics from anova, and P
plot(Predict(fit), anova=an, pval=TRUE)
plot(Predict(fit), data=llist(blood.pressure,age))
# rug plot for two of the predictors
p <- Predict(fit, name=c('age','cholesterol')) # Make 2 plots
plot(p)
p <- Predict(fit, age=seq(20,80,length=100), sex, conf.int=FALSE)
# Plot relationship between age and log
# odds, separate curve for each sex,
plot(p, subset=sex=='female' | age > 30)
# No confidence interval, suppress estimates for males <= 30
p <- Predict(fit, age, sex)
plot(p, label.curves=FALSE, data=llist(age,sex))
# use label.curves=list(keys=c('a','b'))'
# to use 1-letter abbreviations
# data= allows rug plots (1-dimensional scatterplots)
# on each sex's curve, with sex-
# specific density of age
# If data were in data frame could have used that
p <- Predict(fit, age=seq(20,80,length=100), sex='male', fun=plogis)
# works if datadist not used
plot(p, ylab=expression(hat(P)))
# plot predicted probability in place of log odds
per <- function(x, y) x >= 30
plot(p, perim=per) # suppress output for age < 30 but leave scale alone
# Take charge of the plot setup by specifying a lattice formula
p <- Predict(fit, age, blood.pressure=c(120,140,160),
cholesterol=c(180,200,215), sex)
plot(p, ~ age | blood.pressure*cholesterol, subset=sex=='male')
# plot(p, ~ age | cholesterol*blood.pressure, subset=sex=='female')
# plot(p, ~ blood.pressure|cholesterol*round(age,-1), subset=sex=='male')
plot(p)
# Plot the age effect as an odds ratio
# comparing the age shown on the x-axis to age=30 years
ddist$limits$age[2] <- 30 # make 30 the reference value for age
# Could also do: ddist$limits["Adjust to","age"] <- 30
fit <- update(fit) # make new reference value take effect
p <- Predict(fit, age, ref.zero=TRUE, fun=exp)
plot(p, ylab='Age=x:Age=30 Odds Ratio',
abline=list(list(h=1, lty=2, col=2), list(v=30, lty=2, col=2)))
# Compute predictions for three predictors, with superpositioning or
# conditioning on sex, combined into one graph
p1 <- Predict(fit, age, sex)
p2 <- Predict(fit, cholesterol, sex)
p3 <- Predict(fit, blood.pressure, sex)
p <- rbind(age=p1, cholesterol=p2, blood.pressure=p3)
plot(p, groups='sex', varypred=TRUE, adj.subtitle=FALSE)
plot(p, cond='sex', varypred=TRUE, adj.subtitle=FALSE)
if (FALSE) {
# For males at the median blood pressure and cholesterol, plot 3 types
# of confidence intervals for the probability on one plot, for varying age
ages <- seq(20, 80, length=100)
p1 <- Predict(fit, age=ages, sex='male', fun=plogis) # standard pointwise
p2 <- Predict(fit, age=ages, sex='male', fun=plogis,
conf.type='simultaneous') # simultaneous
p3 <- Predict(fit, age=c(60,65,70), sex='male', fun=plogis,
conf.type='simultaneous') # simultaneous 3 pts
# The previous only adjusts for a multiplicity of 3 points instead of 100
f <- update(fit, x=TRUE, y=TRUE)
g <- bootcov(f, B=500, coef.reps=TRUE)
p4 <- Predict(g, age=ages, sex='male', fun=plogis) # bootstrap percentile
p <- rbind(Pointwise=p1, 'Simultaneous 100 ages'=p2,
'Simultaneous 3 ages'=p3, 'Bootstrap nonparametric'=p4)
xYplot(Cbind(yhat, lower, upper) ~ age, groups=.set.,
data=p, type='l', method='bands', label.curve=list(keys='lines'))
}
# Plots for a parametric survival model
require(survival)
n <- 1000
set.seed(731)
age <- 50 + 12*rnorm(n)
label(age) <- "Age"
sex <- factor(sample(c('Male','Female'), n,
rep=TRUE, prob=c(.6, .4)))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
t <- -log(runif(n))/h
label(t) <- 'Follow-up Time'
e <- ifelse(t<=cens,1,0)
t <- pmin(t, cens)
units(t) <- "Year"
ddist <- datadist(age, sex)
Srv <- Surv(t,e)
# Fit log-normal survival model and plot median survival time vs. age
f <- psm(Srv ~ rcs(age), dist='lognormal')
med <- Quantile(f) # Creates function to compute quantiles
# (median by default)
p <- Predict(f, age, fun=function(x) med(lp=x))
plot(p, ylab="Median Survival Time")
# Note: confidence intervals from this method are approximate since
# they don't take into account estimation of scale parameter
# Fit an ols model to log(y) and plot the relationship between x1
# and the predicted mean(y) on the original scale without assuming
# normality of residuals; use the smearing estimator
# See help file for rbind.Predict for a method of showing two
# types of confidence intervals simultaneously.
set.seed(1)
x1 <- runif(300)
x2 <- runif(300)
ddist <- datadist(x1,x2)
y <- exp(x1+x2-1+rnorm(300))
f <- ols(log(y) ~ pol(x1,2)+x2)
r <- resid(f)
smean <- function(yhat)smearingEst(yhat, exp, res, statistic='mean')
formals(smean) <- list(yhat=numeric(0), res=r[!is.na(r)])
#smean$res <- r[!is.na(r)] # define default res argument to function
plot(Predict(f, x1, fun=smean), ylab='Predicted Mean on y-scale')
# Make an 'interaction plot', forcing the x-axis variable to be
# plotted at integer values but labeled with category levels
n <- 100
set.seed(1)
gender <- c(rep('male', n), rep('female',n))
m <- sample(c('a','b'), 2*n, TRUE)
d <- datadist(gender, m); options(datadist='d')
anxiety <- runif(2*n) + .2*(gender=='female') + .4*(gender=='female' & m=='b')
tapply(anxiety, llist(gender,m), mean)
f <- ols(anxiety ~ gender*m)
p <- Predict(f, gender, m)
plot(p) # horizontal dot chart; usually preferred for categorical predictors
Key(.5, .5)
plot(p, ~gender, groups='m', nlines=TRUE)
plot(p, ~m, groups='gender', nlines=TRUE)
plot(p, ~gender|m, nlines=TRUE)
options(datadist=NULL)
if (FALSE) {
# Example in which separate curves are shown for 4 income values
# For each curve the estimated percentage of voters voting for
# the democratic party is plotted against the percent of voters
# who graduated from college. Data are county-level percents.
incomes <- seq(22900, 32800, length=4)
# equally spaced to outer quintiles
p <- Predict(f, college, income=incomes, conf.int=FALSE)
plot(p, xlim=c(0,35), ylim=c(30,55))
# Erase end portions of each curve where there are fewer than 10 counties having
# percent of college graduates to the left of the x-coordinate being plotted,
# for the subset of counties having median family income with 1650
# of the target income for the curve
show.pts <- function(college.pts, income.pt) {
s <- abs(income - income.pt) < 1650 #assumes income known to top frame
x <- college[s]
x <- sort(x[!is.na(x)])
n <- length(x)
low <- x[10]; high <- x[n-9]
college.pts >= low & college.pts <= high
}
plot(p, xlim=c(0,35), ylim=c(30,55), perim=show.pts)
# Rename variables for better plotting of a long list of predictors
f <- ...
p <- Predict(f)
re <- c(trt='treatment', diabet='diabetes', sbp='systolic blood pressure')
for(n in names(re)) {
names(p)[names(p)==n] <- re[n]
p$.predictor.[p$.predictor.==n] <- re[n]
}
plot(p)
}
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