Recency transform of inter-event time gaps

Maps non-negative time gaps \(\delta\) to bounded recency weights via $$ w(\delta) \;=\; \exp\!\Bigl(-\frac{\delta}{2\,m}\Bigr), $$ where \(m\) is the median of the supplied (or reference) gaps. Large gaps map toward 0; gaps near 0 map toward 1. The half-life of the kernel is \(2 m \log 2\), so the median gap itself is mapped to approximately \(e^{-1/2} \approx 0.607\).

Usage

transform_recency(delta, half_life = NULL, reference = NULL)

Arguments

delta

Numeric vector of non-negative time gaps. NAs propagate.

half_life

Optional positive scalar. If supplied, used directly as the kernel scale \(2 m\), bypassing the median rule.

reference

Optional numeric vector. If supplied, the median is computed on reference instead of delta. Useful when transforming new data using a scale fitted on training data.

Value

Numeric vector the same length as delta, with values in (0, 1]. NAs in delta are preserved.

Details

This is the data-driven recency parametrisation used as a preprocessing step for global and exogenous covariates in Lembo, Juozaitiene, Vinciotti & Wit (2025) and matches the "recency" axis of endogenous_features().

References

Lembo M, Juozaitiene R, Vinciotti V, Wit EC (2025). Relational Event Models with Global Covariates. JRSS-C.

Examples

set.seed(1)
gaps <- rexp(20, rate = 0.5)
transform_recency(gaps)
#>  [1] 0.64441165 0.50280024 0.91871222 0.92187776 0.77589724 0.18553812
#>  [7] 0.48897442 0.73050063 0.57315574 0.91799657 0.44520214 0.64184900
#> [13] 0.48669180 0.07621828 0.54139459 0.54750852 0.33567618 0.68319337
#> [19] 0.82196996 0.71005091
transform_recency(gaps, half_life = 1)
#>  [1] 0.2208296551 0.0941105091 0.7472066790 0.7560932803 0.4180571006
#>  [6] 0.0030581746 0.0855098156 0.3398110062 0.1476168834 0.7452079433
#> [11] 0.0619473618 0.2178257798 0.0841455618 0.0001436877 0.1213487880
#> [16] 0.1261242317 0.0234691064 0.2699568158 0.5097336458 0.3082144590