R: Plot Effects of Variables Estimated by a Regression Model Fit

plot.Predict {rms} | R Documentation

## Plot Effects of Variables Estimated by a Regression Model Fit

### Description

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 x-axis variable. If there is a `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 x-axes, and multiple panels are drawn, you can use `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.

### Usage

    ## S3 method for class '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)

### Arguments

`x` | a data frame created by `Predict`, or for `pantext` the x-coordinate for text
`formula` | 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`.
`groups` | 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.
`cond` | 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.
`varypred` | 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.
`subset` | 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.
`xlim` | 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.
`ylim` | Range for plotting on response variable axis. Computed by default.
`xlab` | Label for `x`-axis. Default is one given to `asis, rcs`, etc., which may have been the `"label"` attribute of the variable.
`ylab` | 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.
`data` | a data frame containing the original raw data on which the regression model were based, or at least containing the x-axis and grouping variable. If `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`.
`subdata` | 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()]`.
`anova` | 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.
`pval` | specify `pval=TRUE` for `anova` to include not only the test statistic but also the P-value
`cex.anova` | character size for the test statistic printed on the panel
`col.fill` | a vector of colors used to fill confidence bands for successive superposed groups. Default is inceasingly dark gray scale.
`adj.subtitle` | Set to `FALSE` to suppress subtitling the graph with the list of settings of non-graphed adjustment values.
`cex.adj` | `cex` parameter for size of adjustment settings in subtitles. Default is 0.75 times `par("cex")`.
`cex.axis` | `cex` parameter for x-axis tick labels
`perim` | `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.
`digits` | Controls how numeric variables used for panel labels are formatted. The default is 4 significant digits.
`nlevels` | 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.
`nlines` | 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.
`addpanel` | an additional panel function to call along with panel functions used for `xYplot` and `Dotplot` displays
`scat1d.opts` | 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.
`type` | a value (`"l","p","b"`) to override default choices related to showing or connecting points. Especially useful for discrete x coordinate variables.
`yscale` | 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
`scaletrans` | 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))`.
`object` | an object having a `print` method
`y` | y-coordinate for placing text in a `lattice` panel or on a base graphics plot
`cex` | character expansion size for `pantext`
`adj` | text justification. Default is left justified.
`fontfamily` | font family for `pantext`. Default is `"Courier"` which will line up columns of a table.
`lattice` | set to `FALSE` to use `text` instead of `ltext` in the function generated by `pantext`, to use base graphics

### Details

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.

### Value

a `lattice` object ready to `print` for rendering.

### Note

If plotting the effects of all predictors you can reorder the panels using for example `p <- Predict(fit); p$.predictor. <- factor(p$.predictor., v)` where `v` is a vector of predictor names specified in the desired order.

### Author(s)

Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu

### References

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.

### See Also

`Predict`, `ggplot.Predict`, `link{plotp.Predict}`, `rbind.Predict`, `datadist`, `predictrms`, `anova.rms`, `contrast.rms`, `summary.rms`, `rms`, `rmsMisc`, `labcurve`, `scat1d`, `xYplot`, `Overview`

### Examples

    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)

    ## Not run:
    # 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'))

    ## End(Not run)

    # Plots for a parametric survival model
    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)

    ## Not run:
    # 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)

    ## End(Not run)

[Package rms version 5.1-1 Index]