ref_derivative

Usage

ref_derivative(
  reference,
  newdata,
  with_respect_to,
  centiles = c(0.05, 0.25, 0.5, 0.75, 0.95),
  h = 0.01,
  outcomes = NULL
)

Estimates $\partial Q_t(p)/\partial t$ of the modeled quantile curves by central finite differences, with a delta-method standard error from the fitted coefficient covariance (Vp) applied to the finite-difference of the linear-predictor matrix. This is a population-chart derivative, not an individual longitudinal estimate.

Arguments

Argument	Description
reference	A ref_fit.
newdata	Grid of covariate values.
with_respect_to	The time covariate, as a bare column name or a string.
centiles	Probability levels.
h	Finite-difference step.
outcomes	Optional subset of outcomes (default: all).

Details

chart_velocity_se is the sampling error of the fitted coefficients. It does not cover the bias of the spline itself, which is the larger error whenever the basis of the with_respect_to smooth is too small to represent the trajectory. That case is detectable – the smooth’s effective degrees of freedom saturate its basis – so it is warned about; refit with a larger k and compare.

Value

A ref_derivative tibble with columns .outcome, time, centile, chart_velocity, and chart_velocity_se (NA when the engine does not expose a coefficient covariance).

Examples

ref <- ref_simulate(150, seed = 1)
fit <- ref_fit(ref_spec(ref_gaussian(), ~ s(age, k = 5) + sex), ref, "y")
grid <- data.frame(age = c(30, 50, 70), sex = factor("F", levels = c("F", "M")))
ref_derivative(fit, grid, with_respect_to = age, centiles = c(0.1, 0.5, 0.9))

# A tibble: 9 × 5
  .outcome  time centile chart_velocity chart_velocity_se
* <chr>    <dbl>   <dbl>          <dbl>             <dbl>
1 y           30     0.1         0.134             0.0259
2 y           50     0.1         0.0686            0.0151
3 y           70     0.1         0.0156            0.0239
4 y           30     0.5         0.134             0.0259
5 y           50     0.5         0.0686            0.0151
6 y           70     0.5         0.0156            0.0239
7 y           30     0.9         0.134             0.0259
8 y           50     0.9         0.0686            0.0151
9 y           70     0.9         0.0156            0.0239