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Posterior expectations of derivatives from an estimated model


derivative_samples(object, ...)

# Default S3 method
derivative_samples(object, ...)

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

# S3 method for class 'gam'
  focal = NULL,
  data = NULL,
  order = 1L,
  type = c("forward", "backward", "central"),
  scale = c("response", "linear_predictor"),
  method = c("gaussian", "mh", "inla", "user"),
  n = 100,
  eps = 1e-07,
  n_sim = 10000,
  level = lifecycle::deprecated(),
  seed = NULL,
  envir = environment(formula(object)),
  draws = NULL,
  mvn_method = c("mvnfast", "mgcv"),



an R object to compute derivatives for


arguments passed to other methods and on to fitted_samples()


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


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.


numeric; the order of derivative.


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


character; should the derivative be estimated on the response or the linear predictor (link) scale? One of "response" (the default), or "linear predictor".


character; which method should be used to draw samples from the posterior distribution. "gaussian" uses a Gaussian (Laplace) approximation to the posterior. "mh" uses a Metropolis Hastings sample that alternates t proposals with proposals based on a shrunken version of the posterior covariance matrix. "inla" uses a variant of Integrated Nested Laplace Approximation due to Wood (2019), (currently not implemented). "user" allows for user-supplied posterior draws (currently not implemented).


numeric; the number of points to evaluate the derivative at (if data is not supplied).


numeric; the finite difference.


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




numeric; a random seed for the simulations.


the environment within which to recreate the data used to fit object.


matrix; user supplied posterior draws to be used when method = "user".


character; one of "mvnfast" or "mgcv". The default is uses mvnfast::rmvn(), which can be considerably faster at generate large numbers of MVN random values than mgcv::rmvn(), but which might not work for some marginal fits, such as those where the covariance matrix is close to singular.


A tibble, currently with the following variables:

  • .derivative: the estimated partial derivative,

  • additional columns containing the covariate values at which the derivative was evaluated.


Gavin L. Simpson


df <- data_sim("eg1", dist = "negbin", scale = 0.25, seed = 42)

# fit the GAM (note: for execution time reasons using bam())
m <- bam(y ~ s(x0) + s(x1) + s(x2) + s(x3),
  data = df, family = nb(), method = "fREML")

# data slice through data along x2 - all other covariates will be set to
# typical values (value closest to median)
ds <- data_slice(m, x2 = evenly(x2, n = 200))

# samples from posterior of derivatives
fd_samp <- derivative_samples(m,
  data = ds, type = "central",
  focal = "x2", eps = 0.01, seed = 21, n_sim = 100

# plot the first 20 posterior draws
if (requireNamespace("ggplot2") && requireNamespace("dplyr")) {
  fd_samp |>
    dplyr::filter(.draw <= 20) |>
    ggplot(aes(x = x2, y = .derivative, group = .draw)) +
    geom_line(alpha = 0.5)