partial_derivatives {gratia}

Partial derivatives of estimated multivariate smooths via finite differences

Description

Partial derivatives of estimated multivariate smooths via finite differences

Usage

partial_derivatives(object, ...)

## Default S3 method:
partial_derivatives(object, ...)

## S3 method for class 'gamm'
partial_derivatives(object, ...)

## S3 method for class 'gam'
partial_derivatives(
  object,
  select = NULL,
  term = deprecated(),
  focal = NULL,
  data = newdata,
  order = 1L,
  type = c("forward", "backward", "central"),
  n = 100,
  eps = 1e-07,
  interval = c("confidence", "simultaneous"),
  n_sim = 10000,
  level = 0.95,
  unconditional = FALSE,
  frequentist = FALSE,
  offset = NULL,
  ncores = 1,
  partial_match = FALSE,
  seed = NULL,
  ...,
  newdata = NULL
)

Arguments

object

an R object to compute derivatives for.

...

arguments passed to other methods.

select

character; vector of one or more smooth terms for which derivatives are required. If missing, derivatives for all smooth terms will be returned. Can be a partial match to a smooth term; see argument partial_match below.

term

Use select instead.

focal

character; name of the focal variable. The partial derivative of the estimated smooth with respect to this variable will be returned. All other variables involved in the smooth will be held at constant. This can be missing if supplying data, in which case, the focal variable will be identified as the one variable that is not constant.

data

a data frame containing the values of the model covariates at which to evaluate the first derivatives of the smooths. If supplied, all but one variable must be held at a constant value.

order

numeric; the order of derivative.

type

character; the type of finite difference used. One of "forward", "backward", or "central".

n

numeric; the number of points to evaluate the derivative at.

eps

numeric; the finite difference.

interval

character; the type of interval to compute. One of "confidence" for point-wise intervals, or "simultaneous" for simultaneous intervals.

n_sim

integer; the number of simulations used in computing the simultaneous intervals.

level

numeric; ⁠0 < level < 1⁠; the confidence level of the point-wise or simultaneous interval. The default is 0.95 for a 95% interval.

unconditional

logical; use smoothness selection-corrected Bayesian covariance matrix?

frequentist

logical; use the frequentist covariance matrix?

offset

numeric; a value to use for any offset term

ncores

number of cores for generating random variables from a multivariate normal distribution. Passed to mvnfast::rmvn(). Parallelization will take place only if OpenMP is supported (but appears to work on Windows with current R).

partial_match

logical; should smooths be selected by partial matches with term? If TRUE, term can only be a single string to match against.

seed

numeric; RNG seed to use.

newdata

Deprecated: use data instead.

Value

A tibble, currently with the following variables:

• .smooth: the smooth each row refers to,

• .partial_deriv: the estimated partial derivative,

• .se: the standard error of the estimated partial derivative,

• .crit: the critical value such that derivative ± (crit * se) gives the upper and lower bounds of the requested confidence or simultaneous interval (given level),

• .lower_ci: the lower bound of the confidence or simultaneous interval,

• .upper_ci: the upper bound of the confidence or simultaneous interval.

Note

partial_derivatives() will ignore any random effect smooths it encounters in object.

Author(s)

Gavin L. Simpson

Examples

library("ggplot2")
library("patchwork")
load_mgcv()

df <- data_sim("eg2", n = 2000, dist = "normal", scale = 0.5, seed = 42)

# fit the GAM (note: for execution time reasons, k is set articifially low)
m <- gam(y ~ te(x, z, k = c(5, 5)), data = df, method = "REML")

# data slice through te(x,z) holding z == 0.4
ds <- data_slice(m, x = evenly(x, n = 100), z = 0.4)

# evaluate te(x,z) at values of x & z
sm <- smooth_estimates(m, select = "te(x,z)", data = ds) |>
  add_confint()

# partial derivatives
pd_x <- partial_derivatives(m, data = ds, type = "central", focal = "x")

# draw te(x,z)
p1 <- draw(m, rug = FALSE) &
  geom_hline(yintercept = 0.4, linewidth = 1)
p1

# draw te(x,z) along slice
cap <- expression(z == 0.4)
p2 <- sm |>
  ggplot(aes(x = x, y = .estimate)) +
  geom_ribbon(aes(ymin = .lower_ci, ymax = .upper_ci), alpha = 0.2) +
  geom_line() +
  labs(
    x = "x", y = "Partial effect", title = "te(x,z)",
    caption = cap
  )
p2

# draw partial derivs
p3 <- pd_x |>
  draw() +
  labs(caption = cap)
p3

# draw all three panels
p1 + p2 + p3 + plot_layout(ncol = 3)