Weibull adstock

Adstock with a Weibull kernel, which can place its peak after the period of spend. See adstock_weights_weibull() for the two parameterisations.

Usage

adstock_weibull(
  x,
  shape,
  scale,
  max_lag,
  type = c("cdf", "pdf"),
  normalise = TRUE,
  state = 0,
  by = NULL,
  na_action = c("error", "zero", "keep")
)

Arguments

x

Numeric vector of media spend (or impressions, or GRPs) in time order. x must already be sorted by time and evenly spaced; the function has no index argument and cannot check this for you. Use step_adstock() if you want the time index validated.

shape, scale

Weibull shape and scale, both positive. scale is in periods.

max_lag

Number of periods the kernel spans. Required and finite: the Weibull kernel has no recursive form.

type

Either "cdf" (monotone decay) or "pdf" (permits a delayed peak).

normalise

Should the kernel sum to 1? Defaults to TRUE. See the Normalisation section.

state

The preceding max_lag - 1 values of x, oldest first, or 0 for a cold start. When by is supplied, a named list with one entry per group. adstock_state() produces one of the right shape when called with the same max_lag; for a finite kernel the state is simply the tail of x, so utils::tail(x, max_lag - 1) works too.

by

Optional grouping vector, or data frame of grouping vectors, the same length as x. Adstock is applied independently within each group, which is what geo-level and panel models need. Never rely on dplyr::group_by() for this: grouping metadata does not reliably survive into every context where this function is called.

na_action

What to do about missing values in x. "error" (the default) refuses to guess. "zero" treats missing media as no media, which is usually right for spend but is a substantive assumption. "keep" lets NA propagate through the filter, which for the recursive form poisons every subsequent value.

Value

A numeric vector the same length as x, in the same order.

See also

adstock_geometric(), adstock_weights_weibull()

Examples

spend <- c(100, 0, 0, 0, 0, 0, 0, 0)

# Delayed peak: the response builds before it decays
round(adstock_weibull(spend, shape = 2, scale = 3, max_lag = 8,
                      type = "pdf"), 2)
#> [1] 20.27 29.05 25.00 15.31  7.04  2.49  0.69  0.15

# Monotone form
round(adstock_weibull(spend, shape = 2, scale = 3, max_lag = 8,
                      type = "cdf"), 2)
#> [1] 36.80 32.93 21.11  7.77  1.31  0.08  0.00  0.00