# 3-D Plots Showing Effects of Two Continuous Predictors in a Regression Model Fit Uses lattice graphics and the output from `Predict` to plot image, contour, or perspective plots showing the simultaneous effects of two continuous predictor variables. Unless `formula` is provided, 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. ```r bplot(x, formula, lfun=lattice::levelplot, xlab, ylab, zlab, adj.subtitle=!info$ref.zero, cex.adj=.75, cex.lab=1, perim, showperim=FALSE, zlim=range(yhat, na.rm=TRUE), scales=list(arrows=FALSE), xlabrot, ylabrot, zlabrot=90, ...) perimeter(x, y, xinc=diff(range(x))/10, n=10, lowess.=TRUE) ``` ## Arguments - `x`: for `bplot`, an object created by `Predict` for which two or more numeric predictors varied. For `perim` is the first variable of a pair of predictors forming a 3-d plot. - `formula`: a formula of the form `f(yhat) ~ x*y` optionally followed by |a*b*c which are 1-3 paneling variables that were specified to `Predict`. `f` can represent any R function of a vector that produces a vector. If the left hand side of the formula is omitted, `yhat` will be inserted. If `formula` is omitted, it will be inferred from the first two variables that varied in the call to `Predict`. - `lfun`: a high-level lattice plotting function that takes formulas of the form `z ~ x*y`. The default is an image plot (`levelplot`). Other common choices are `wireframe` for perspective plot or `contourplot` for a contour plot. - `xlab`: Character string label for $x$-axis. Default is given by `Predict`. - `ylab`: Character string abel for $y$-axis - `zlab`: Character string $z$-axis label for perspective (wireframe) plots. Default comes from `Predict`. `zlab` will often be specified if `fun` was specified to `Predict`. - `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 and `ref.zero` was not used. - `cex.adj`: `cex` parameter for size of adjustment settings in subtitles. Default is 0.75 - `cex.lab`: `cex` parameter for axis labels. Default is 1. - `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 omitted, 3-d plotting will use the marginal distributions of the two predictors to determine the plotting region, when the grid is not specified explicitly in `variables`. When instead a series of curves is being plotted, `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. - `showperim`: set to `TRUE` if `perim` is specified and you want to show the actual perimeter used. - `zlim`: Controls the range for plotting in the $z$-axis if there is one. Computed by default. - `scales`: see `wireframe` - `xlabrot`: rotation angle for the x-axis. Default is 30 for `wireframe` and 0 otherwise. - `ylabrot`: rotation angle for the y-axis. Default is -40 for `wireframe`, 90 for `contourplot` or `levelplot`, and 0 otherwise. - `zlabrot`: rotation angle for z-axis rotation for `wireframe` plots - ``...``: other arguments to pass to the lattice function - `y`: second variable of the pair for `perim`. 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` - `n`: 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` interval, no `y` ranges are used for that interval. - `lowess.`: set to `FALSE` to not have `lowess` smooth the data perimeters ## Returns `perimeter` returns a matrix of class `perimeter`. This outline can be conveniently plotted by `lines.perimeter`. ## 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 `x`s 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`. ## Author(s) Frank Harrell Department of Biostatistics, Vanderbilt University fh@fharrell.com ## See Also `datadist`, `Predict`, `rms`, `rmsMisc`, `levelplot`, `contourplot`, `wireframe` ## Examples ```r 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, sex, np=50) # vary sex last require(lattice) bplot(p) # image plot for age, cholesterol with color # coming from yhat; use default ranges for # both continuous predictors; two panels (for sex) bplot(p, lfun=wireframe) # same as bplot(p,,wireframe) # View from different angle, change y label orientation accordingly # Default is z=40, x=-60 bplot(p,, wireframe, screen=list(z=40, x=-75), ylabrot=-25) bplot(p,, contourplot) # contour plot bounds <- perimeter(age, cholesterol, lowess=TRUE) plot(age, cholesterol) # show bivariate data density and perimeter lines(bounds[,c('x','ymin')]); lines(bounds[,c('x','ymax')]) p <- Predict(fit, age, cholesterol) # use only one sex bplot(p, perim=bounds) # draws image() plot # don't show estimates where data are sparse # doesn't make sense here since vars don't interact bplot(p, plogis(yhat) ~ age*cholesterol) # Probability scale options(datadist=NULL) ```

bplot function