---
title: "Introduction to pdp"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to pdp}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6,
  fig.height = 4.5,
  fig.align = "center",
  message = FALSE,
  warning = FALSE
)
```

Complex machine learning models (e.g., random forests and gradient boosted
trees) often predict well but are hard to interpret. *Partial dependence plots*
(PDPs) help visualize the relationship between a subset of the features
(typically 1--3) and the response while accounting for the average effect of
the other predictors in the model. The **pdp** package provides
`partial()`, a general function for computing partial dependence from a wide
variety of fitted model objects, along with simple plotting methods.

## Installation

**pdp** is hosted on [r-universe](https://bgreenwell.r-universe.dev/pdp):

```{r install, eval=FALSE}
# Install from r-universe (recommended):
install.packages("pdp", repos = c("https://bgreenwell.r-universe.dev",
                                  "https://cloud.r-project.org"))

# Install the latest development version from GitHub:
pak::pak("bgreenwell/pdp")
```

## A first example

We'll use the Boston housing data (included with **pdp**) and a random forest.
The `partial()` function needs (at minimum) a fitted model and the name of the
predictor of interest. It's good practice to also supply the original training
data via the `train` argument.

```{r boston-rf}
library(pdp)
library(randomForest)

data(boston)  # load the (corrected) Boston housing data
set.seed(101)  # for reproducibility
boston.rf <- randomForest(cmedv ~ ., data = boston, ntree = 250)

# Partial dependence of cmedv on lstat
pd <- partial(boston.rf, pred.var = "lstat", train = boston)
head(pd)
```

By default `partial()` returns a data frame, which makes it easy to plot with
whatever graphics package you prefer. **pdp** ships with a `plot()` method
that draws lightweight base R graphics via
[tinyplot](https://grantmcdermott.com/tinyplot/) by default, or
[lattice](https://cran.r-project.org/package=lattice) graphics whenever
`lattice = TRUE`:

```{r boston-plot}
# tinyplot-based display; rug marks show the min/max and deciles of lstat to
# help avoid interpreting the plot where there's little data
plot(pd, rug = TRUE, train = boston)
```

```{r boston-plot-lattice}
# lattice-based equivalent
plot(pd, rug = TRUE, train = boston, lattice = TRUE)
```

You can also let `partial()` plot directly by setting `plot = TRUE` and
choosing a `plot.engine` (`"tinyplot"`, the default, or `"lattice"`).

## Two predictors

Partial dependence extends naturally to pairs of predictors (the plot becomes
a false color level plot, i.e., heatmap):

```{r boston-two}
pd2 <- partial(boston.rf, pred.var = c("lstat", "rm"), chull = TRUE,
               train = boston)
plot(pd2, contour = TRUE)
```

Here `chull = TRUE` restricts the grid to the convex hull of the training
values of `lstat` and `rm`, which reduces the risk of extrapolating outside
the region of the data. Factor predictors are handled automatically and result
in faceted displays.

## 3-D surfaces and three predictors (lattice)

The lattice engine (`lattice = TRUE`) additionally supports 3-D surfaces and
paneled three-predictor displays, like the figures in the [R Journal
paper](https://journal.r-project.org/articles/RJ-2017-016/):

```{r boston-wireframe}
# 3-D surface instead of a false color level plot
plot(pd2, lattice = TRUE, levelplot = FALSE, zlab = "cmedv", drape = TRUE,
     colorkey = FALSE, screen = list(z = -20, x = -60))
```

```{r boston-three, fig.width=7}
# Three predictors: the third is binned into overlapping intervals and used
# to panel the display (see the `number` and `overlap` arguments)
pd3 <- partial(boston.rf, pred.var = c("lstat", "rm", "age"),
               grid.resolution = 10, chull = TRUE, batch.size = 1e6,
               train = boston)
plot(pd3, lattice = TRUE)
```

## Classification

For classification models, partial dependence is computed for the predicted
probability of the "focus" class (the first class, by default; use
`which.class` to change it) on the centered logit scale. Set `prob = TRUE` to
use the probability scale instead:

```{r pima-rf}
data(pima)  # load the Pima Indians diabetes data
pima2 <- na.omit(pima)
set.seed(102)
pima.rf <- randomForest(diabetes ~ ., data = pima2, ntree = 250)

# Partial dependence of the probability of testing positive on glucose
partial(pima.rf, pred.var = "glucose", prob = TRUE, which.class = "pos",
        plot = TRUE, rug = TRUE, train = pima2)
```

## Models with non-Gaussian responses

Some models make predictions on a transformed scale (e.g., Poisson models
often predict on the log scale). Use `inv.link` to transform the predictions
back to the response scale *before* the partial dependence function is
computed:

```{r inv-link}
fit <- glm(carb ~ ., data = mtcars, family = poisson)

# Partial dependence of the number of carburetors on mpg (response scale)
partial(fit, pred.var = "mpg", inv.link = exp, plot = TRUE, train = mtcars)
```

## Controlling the grid

By default, `partial()` evaluates continuous predictors over an equally spaced
grid of (at most) 51 values spanning their range. This can be controlled via:

* `grid.resolution` --- the number of equally spaced grid points;
* `quantiles = TRUE` --- use sample quantiles (see `probs`) instead, which
  keeps the grid inside the bulk of the data;
* `trim.outliers = TRUE` --- trim outliers before constructing the grid;
* `pred.grid` --- supply the exact grid of values yourself.

```{r grid}
partial(boston.rf, pred.var = "lstat", quantiles = TRUE, probs = 1:19/20,
        plot = TRUE, train = boston)
```

## Learn more

* `vignette("ice-curves", package = "pdp")` covers *individual conditional
  expectation* (ICE) curves and user-supplied prediction functions.
* `vignette("faster-pdp", package = "pdp")` covers options for speeding up
  the computations (e.g., batched predictions and parallel processing).
* The R Journal article ["pdp: An R Package for Constructing Partial
  Dependence Plots"](https://journal.r-project.org/articles/RJ-2017-016/)
  provides a detailed introduction.