Derivatives of estimated smooths via finite differences

## Usage

derivatives(object, ...)

# S3 method for default
derivatives(object, ...)

# S3 method for gamm
derivatives(object, ...)

# S3 method for gam
derivatives(
object,
select = NULL,
term = deprecated(),
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,
...,
newdata = NULL
)

## Arguments

object

an R object to compute derivatives for.

...

arguments passed to other methods.

select

character; select which smooth's posterior to draw from. The default (NULL) means the posteriors of all smooths in model wil be sampled from. If supplied, a character vector of requested terms. Can be a partial match to a smooth term; see argument partial_match below.

term

Use select instead.

data

a data frame containing the values of the model covariates at which to evaluate the first derivatives of the smooths.

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.

newdata

Deprecated: use data instead.

## Value

A tibble, currently with the following variables:

• smooth: the smooth each row refers to,

• var: the name of the variable involved in the smooth,

• data: values of var at which the derivative was evaluated,

• derivative: the estimated derivative,

• se: the standard error of the estimated 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: the lower bound of the confidence or simultaneous interval,

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

## Note

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

Gavin L. Simpson

## Examples


# \dontshow{
op <- options(pillar.sigfig = 3, cli.unicode = FALSE)
# }
dat <- data_sim("eg1", n = 400, dist = "normal", scale = 2, seed = 42)
mod <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data = dat, method = "REML")

## first derivatives of all smooths using central finite differences
derivatives(mod, type = "central")
#> # A tibble: 400 x 12
#>    .smooth .by   .fs   .derivative   .se .crit .lower_ci .upper_ci      x0    x1
#>    <chr>   <chr> <chr>       <dbl> <dbl> <dbl>     <dbl>     <dbl>   <dbl> <dbl>
#>  1 s(x0)   NA    NA           7.41  3.33  1.96     0.874      13.9 2.39e-4    NA
#>  2 s(x0)   NA    NA           7.40  3.33  1.96     0.884      13.9 1.03e-2    NA
#>  3 s(x0)   NA    NA           7.39  3.30  1.96     0.929      13.8 2.04e-2    NA
#>  4 s(x0)   NA    NA           7.36  3.24  1.96     1.01       13.7 3.04e-2    NA
#>  5 s(x0)   NA    NA           7.32  3.15  1.96     1.14       13.5 4.05e-2    NA
#>  6 s(x0)   NA    NA           7.26  3.04  1.96     1.30       13.2 5.06e-2    NA
#>  7 s(x0)   NA    NA           7.18  2.90  1.96     1.49       12.9 6.06e-2    NA
#>  8 s(x0)   NA    NA           7.09  2.76  1.96     1.69       12.5 7.07e-2    NA
#>  9 s(x0)   NA    NA           6.99  2.61  1.96     1.87       12.1 8.07e-2    NA
#> 10 s(x0)   NA    NA           6.87  2.47  1.96     2.03       11.7 9.08e-2    NA
#> # i 390 more rows
#> # i 2 more variables: x2 <dbl>, x3 <dbl>

## derivatives for a selected smooth
derivatives(mod, type = "central", select = "s(x1)")
#> # A tibble: 100 x 9
#>    .smooth .by   .fs   .derivative   .se .crit .lower_ci .upper_ci       x1
#>    <chr>   <chr> <chr>       <dbl> <dbl> <dbl>     <dbl>     <dbl>    <dbl>
#>  1 s(x1)   NA    NA         -0.907  3.12  1.96     -7.02      5.20 0.000405
#>  2 s(x1)   NA    NA         -0.906  3.11  1.96     -7.01      5.20 0.0105
#>  3 s(x1)   NA    NA         -0.898  3.10  1.96     -6.97      5.17 0.0205
#>  4 s(x1)   NA    NA         -0.880  3.06  1.96     -6.88      5.12 0.0306
#>  5 s(x1)   NA    NA         -0.849  3.00  1.96     -6.73      5.03 0.0406
#>  6 s(x1)   NA    NA         -0.803  2.92  1.96     -6.52      4.92 0.0507
#>  7 s(x1)   NA    NA         -0.740  2.81  1.96     -6.25      4.77 0.0607
#>  8 s(x1)   NA    NA         -0.659  2.69  1.96     -5.93      4.61 0.0708
#>  9 s(x1)   NA    NA         -0.557  2.56  1.96     -5.57      4.46 0.0809
#> 10 s(x1)   NA    NA         -0.436  2.42  1.96     -5.19      4.32 0.0909
#> # i 90 more rows
## or via a partial match
derivatives(mod, type = "central", select = "x1", partial_match = TRUE)
#> # A tibble: 100 x 9
#>    .smooth .by   .fs   .derivative   .se .crit .lower_ci .upper_ci       x1
#>    <chr>   <chr> <chr>       <dbl> <dbl> <dbl>     <dbl>     <dbl>    <dbl>
#>  1 s(x1)   NA    NA         -0.907  3.12  1.96     -7.02      5.20 0.000405
#>  2 s(x1)   NA    NA         -0.906  3.11  1.96     -7.01      5.20 0.0105
#>  3 s(x1)   NA    NA         -0.898  3.10  1.96     -6.97      5.17 0.0205
#>  4 s(x1)   NA    NA         -0.880  3.06  1.96     -6.88      5.12 0.0306
#>  5 s(x1)   NA    NA         -0.849  3.00  1.96     -6.73      5.03 0.0406
#>  6 s(x1)   NA    NA         -0.803  2.92  1.96     -6.52      4.92 0.0507
#>  7 s(x1)   NA    NA         -0.740  2.81  1.96     -6.25      4.77 0.0607
#>  8 s(x1)   NA    NA         -0.659  2.69  1.96     -5.93      4.61 0.0708
#>  9 s(x1)   NA    NA         -0.557  2.56  1.96     -5.57      4.46 0.0809
#> 10 s(x1)   NA    NA         -0.436  2.42  1.96     -5.19      4.32 0.0909
#> # i 90 more rows
# \dontshow{
options(op)
# }