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Inverse penetration rate weights

Source: R/adjust_inverse_penetration.R
adjust_inverse_penetration.Rd

Adjusts MPD-derived OD flows using inverse penetration weights derived from coverage information on population and active users at origins and/or destinations.

Usage

adjust_inverse_penetration(
  mpd_od_df,
  coverage_df,
  flow_col = "flow",
  weight_by = c("origin", "destination", "both")
)

Arguments

mpd_od_df

Data frame of MPD flows with at least: origin, destination, and a flow column (default "flow"). If present, mpd_source is used to match coverage by source.

coverage_df

Data frame with at least:

  • origin, population, user_count

and optionally mpd_source.

flow_col

Name of the MPD flow column in mpd_od_df. Default "flow".

weight_by

One of "origin", "destination", "both".

Value

A tibble with:

  • origin, destination (and mpd_source if present),

  • flow: original MPD flow,

  • flow_adj: adjusted flow,

  • weight_origin: origin-side inverse-penetration weight (if applicable),

  • weight_destination: destination-side weight (if applicable),

  • weight_both: geometric mean of the two (if weight_by = "both").

Details

Notation used throughout:

  • \(P_i^{(O)}, P_j^{(D)}\): population at origin \(i\) and destination \(j\)

  • \(U_i^{(O)}, U_j^{(D)}\): active users at origin \(i\) and destination \(j\)

  • \(F_{ij}^{mpd}\): observed MPD flow from \(i\) to \(j\)

  • \(F_{ij}^{adj}\): adjusted flow

The coverage data frame is expected to contain, at minimum:

  • origin, population, user_count

possibly with a mpd_source column for source-specific coverage.

Penetration at origins is defined as

$$p^{(O)}_i = \frac{U^{(O)}_i}{P^{(O)}_i}$$

and the inverse-penetration weight is \(w^{(O)}_i = P^{(O)}_i / U^{(O)}_i\). Analogously for destinations.

For weight_by = "origin", adjusted flows are:

$$F^{adj}_{ij} = w^{(O)}_i F^{mpd}_{ij}.$$

For weight_by = "destination":

$$F^{adj}_{ij} = w^{(D)}_j F^{mpd}_{ij}.$$

For weight_by = "both", we use the geometric mean of the two:

$$w^{(B)}_{ij} = \sqrt{w^{(O)}_i w^{(D)}_j}, \quad F^{adj}_{ij} = w^{(B)}_{ij} F^{mpd}_{ij}.$$