Partial Dependence Functions

Compute partial dependence functions (i.e., marginal effects) for various model fitting objects.

partial(object, ...)

# S3 method for default
partial(object, pred.var, pred.grid, pred.fun = NULL,
  grid.resolution = NULL, ice = FALSE, center = FALSE,
  quantiles = FALSE, probs = 1:9/10, trim.outliers = FALSE,
  type = c("auto", "regression", "classification"), inv.link = NULL,
  which.class = 1L, prob = FALSE, recursive = TRUE, plot = FALSE,
  plot.engine = c("lattice", "ggplot2"), smooth = FALSE, rug = FALSE,
  chull = FALSE, levelplot = TRUE, contour = FALSE,
  contour.color = "white", palette = c("viridis", "magma", "inferno",
  "plasma", "cividis"), alpha = 1, train, cats = NULL,
  check.class = TRUE, progress = "none", parallel = FALSE,
  paropts = NULL, ...)

Arguments

object	A fitted model object of appropriate class (e.g., "gbm", "lm", "randomForest", "train", etc.).
...	Additional optional arguments to be passed onto predict.
pred.var	Character string giving the names of the predictor variables of interest. For reasons of computation/interpretation, this should include no more than three variables.
pred.grid	Data frame containing the joint values of interest for the variables listed in pred.var.
pred.fun	Optional prediction function that requires two arguments: object and newdata. If specified, then the function must return a single prediction or a vector of predictions (i.e., not a matrix or data frame). Default is NULL.
grid.resolution	Integer giving the number of equally spaced points to use for the continuous variables listed in pred.var when pred.grid is not supplied. If left NULL, it will default to the minimum between 51 and the number of unique data points for each of the continuous independent variables listed in pred.var.
ice	Logical indicating whether or not to compute individual conditional expectation (ICE) curves. Default is FALSE. See Goldstein et al. (2014) for details.
center	Logical indicating whether or not to produce centered ICE curves (c-ICE curves). Only used when ice = TRUE. Default is FALSE. See Goldstein et al. (2014) for details.
quantiles	Logical indicating whether or not to use the sample quantiles of the continuous predictors listed in pred.var. If quantiles = TRUE and grid.resolution = NULL the sample quantiles will be used to generate the grid of joint values for which the partial dependence is computed.
probs	Numeric vector of probabilities with values in [0,1]. (Values up to 2e-14 outside that range are accepted and moved to the nearby endpoint.) Default is 1:9/10 which corresponds to the deciles of the predictor variables. These specify which quantiles to use for the continuous predictors listed in pred.var when quantiles = TRUE.
trim.outliers	Logical indicating whether or not to trim off outliers from the continuous predictors listed in pred.var (using the simple boxplot method) before generating the grid of joint values for which the partial dependence is computed. Default is FALSE.
type	Character string specifying the type of supervised learning. Current options are "auto", "regression" or "classification". If type = "auto" then partial will try to extract the necessary information from object.
inv.link	Function specifying the transformation to be applied to the predictions before the partial dependence function is computed (experimental). Default is NULL (i.e., no transformation). This option is intended to be used for models that allow for non-Gaussian response variables (e.g., counts). For these models, predictions are not typically returned on the original response scale by default. For example, Poisson GBMs typically return predictions on the log scale. In this case setting inv.link = exp will return the partial dependence function on the response (i.e., raw count) scale.
which.class	Integer specifying which column of the matrix of predicted probabilities to use as the "focus" class. Default is to use the first class. Only used for classification problems (i.e., when type = "classification").
prob	Logical indicating whether or not partial dependence for classification problems should be returned on the probability scale, rather than the centered logit. If FALSE, the partial dependence function is on a scale similar to the logit. Default is FALSE.
recursive	Logical indicating whether or not to use the weighted tree traversal method described in Friedman (2001). This only applies to objects that inherit from class "gbm". Default is TRUE which is much faster than the exact brute force approach used for all other models. (Based on the C++ code behind plot.gbm.)
plot	Logical indicating whether to return a data frame containing the partial dependence values (FALSE) or plot the partial dependence function directly (TRUE). Default is FALSE. See plotPartial for plotting details.
plot.engine	Character string specifying which plotting engine to use whenever plot = TRUE. Options include "lattice" (default) or "ggplot2".
smooth	Logical indicating whether or not to overlay a LOESS smooth. Default is FALSE.
rug	Logical indicating whether or not to include a rug display on the predictor axes. The tick marks indicate the min/max and deciles of the predictor distributions. This helps reduce the risk of interpreting the partial dependence plot outside the region of the data (i.e., extrapolating). Only used when plot = TRUE. Default is FALSE.
chull	Logical indicating whether or not to restrict the values of the first two variables in pred.var to lie within the convex hull of their training values; this affects pred.grid. This helps reduce the risk of interpreting the partial dependence plot outside the region of the data (i.e., extrapolating).Default is FALSE.
levelplot	Logical indicating whether or not to use a false color level plot (TRUE) or a 3-D surface (FALSE). Default is TRUE.
contour	Logical indicating whether or not to add contour lines to the level plot. Only used when levelplot = TRUE. Default is FALSE.
contour.color	Character string specifying the color to use for the contour lines when contour = TRUE. Default is "white".
palette	Character string indicating the colormap option to use. Five options are available: "viridis" (the default), "magma", "inferno", "plasma", and "cividis".
alpha	Numeric value in [0, 1] specifying the opacity alpha ( most useful when plotting ICE/c-ICE curves). Default is 1 (i.e., no transparency). In fact, this option only affects ICE/c-ICE curves and level plots.
train	An optional data frame, matrix, or sparse matrix containing the original training data. This may be required depending on the class of object. For objects that do not store a copy of the original training data, this argument is required. For reasons discussed below, it is good practice to always specify this argument.
cats	Character string indicating which columns of train should be treated as categorical variables. Only used when train inherits from class "matrix" or "dgCMatrix".
check.class	Logical indicating whether or not to make sure each column in pred.grid has the correct class, levels, etc. Default is TRUE.
progress	Character string giving the name of the progress bar to use while constructing the partial dependence function. See create_progress_bar for details. Default is "none".
parallel	Logical indicating whether or not to run partial in parallel using a backend provided by the foreach package. Default is FALSE.
paropts	List containing additional options to be passed onto foreach when parallel = TRUE.

Value

By default, partial returns an object of class c("data.frame", "partial"). If ice = TRUE and center = FALSE then an object of class c("data.frame", "ice") is returned. If ice = TRUE and center = TRUE then an object of class c("data.frame", "cice") is returned. These three classes determine the behavior of the plotPartial function which is automatically called whenever plot = TRUE. Specifically, when plot = TRUE, a "trellis" object is returned (see lattice for details); the "trellis" object will also include an additional attribute, "partial.data", containing the data displayed in the plot.

Note

In some cases it is difficult for partial to extract the original training data from object. In these cases an error message is displayed requesting the user to supply the training data via the train argument in the call to partial. In most cases where partial can extract the required training data from object, it is taken from the same environment in which partial is called. Therefore, it is important to not change the training data used to construct object before calling partial. This problem is completely avoided when the training data are passed to the train argument in the call to partial.

It is recommended to call partial with plot = FALSE and store the results. This allows for more flexible plotting, and the user will not have to waste time calling partial again if the default plot is not sufficient.

It is possible to retrieve the last printed "trellis" object, such as those produced by plotPartial, using trellis.last.object().

If ice = TRUE or the prediction function given to pred.fun returns a prediction for each observation in newdata, then the result will be a curve for each observation. These are called individual conditional expectation (ICE) curves; see Goldstein et al. (2015) and ice for details.

References

J. H. Friedman. Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29: 1189-1232, 2001.

Goldstein, A., Kapelner, A., Bleich, J., and Pitkin, E., Peeking Inside the Black Box: Visualizing Statistical Learning With Plots of Individual Conditional Expectation. (2014) Journal of Computational and Graphical Statistics, 24(1): 44-65, 2015.

Examples

if (FALSE) {
#
# Regression example (requires randomForest package to run)
#

# Fit a random forest to the boston housing data
library(randomForest)
data (boston)  # load the boston housing data
set.seed(101)  # for reproducibility
boston.rf <- randomForest(cmedv ~ ., data = boston)

# Using randomForest's partialPlot function
partialPlot(boston.rf, pred.data = boston, x.var = "lstat")

# Using pdp's partial function
head(partial(boston.rf, pred.var = "lstat"))  # returns a data frame
partial(boston.rf, pred.var = "lstat", plot = TRUE, rug = TRUE)

# The partial function allows for multiple predictors
partial(boston.rf, pred.var = c("lstat", "rm"), grid.resolution = 40,
        plot = TRUE, chull = TRUE, progress = "text")

# The plotPartial function offers more flexible plotting
pd <- partial(boston.rf, pred.var = c("lstat", "rm"), grid.resolution = 40)
plotPartial(pd, levelplot = FALSE, zlab = "cmedv", drape = TRUE,
            colorkey = FALSE, screen = list(z = -20, x = -60))

# The autplot function can be used to produce graphics based on ggplot2
library(ggplot2)
autoplot(pd, contour = TRUE, legend.title = "Partial\ndependence")

#
# Individual conditional expectation (ICE) curves
#

# Use partial to obtain ICE/c-ICE curves
rm.ice <- partial(boston.rf, pred.var = "rm", ice = TRUE)
plotPartial(rm.ice, rug = TRUE, train = boston, alpha = 0.2)
autoplot(rm.ice, center = TRUE, alpha = 0.2, rug = TRUE, train = boston)

#
# Classification example (requires randomForest package to run)
#

# Fit a random forest to the Pima Indians diabetes data
data (pima)  # load the boston housing data
set.seed(102)  # for reproducibility
pima.rf <- randomForest(diabetes ~ ., data = pima, na.action = na.omit)

# Partial dependence of positive test result on glucose (default logit scale)
partial(pima.rf, pred.var = "glucose", plot = TRUE, chull = TRUE,
        progress = "text")

# Partial dependence of positive test result on glucose (probability scale)
partial(pima.rf, pred.var = "glucose", prob = TRUE, plot = TRUE,
        chull = TRUE, progress = "text")
}