Calculate cycling uptake for UK 'Government Target' scenario

Source: R/uptake.R

Uptake model that takes distance and hilliness and returns a percentage of people likely to cycle along a desire line. Source: appendix of pct paper, hosted at: www.jtlu.org which states that:

uptake_pct_govtarget(
  distance,
  gradient,
  alpha = -3.959,
  d1 = -0.5963,
  d2 = 1.866,
  d3 = 0.00805,
  h1 = -0.271,
  i1 = 0.009394,
  i2 = -0.05135,
  verbose = FALSE
)

uptake_pct_govtarget_2020(
  distance,
  gradient,
  alpha = -4.018,
  d1 = -0.6369,
  d2 = 1.988,
  d3 = 0.008775,
  h1 = -0.2555,
  h2 = -0.78,
  i1 = 0.02006,
  i2 = -0.1234,
  verbose = FALSE
)

uptake_pct_godutch_2020(
  distance,
  gradient,
  alpha = -4.018 + 2.55,
  d1 = -0.6369 - 0.08036,
  d2 = 1.988,
  d3 = 0.008775,
  h1 = -0.2555,
  h2 = -0.78,
  i1 = 0.02006,
  i2 = -0.1234,
  verbose = FALSE
)

uptake_pct_govtarget_school2(
  distance,
  gradient,
  alpha = -7.178,
  d1 = -1.87,
  d2 = 5.961,
  h1 = -0.529,
  h2 = -0.63,
  verbose = FALSE
)

uptake_pct_godutch_school2(
  distance,
  gradient,
  alpha = -7.178 + 3.574,
  d1 = -1.87 + 0.3438,
  d2 = 5.961,
  h1 = -0.529,
  h2 = -0.63,
  verbose = FALSE
)

Arguments

distance

Vector distance numeric values of routes in km (switches to km if more than 100).
gradient

Vector gradient numeric values of routes.
alpha

The intercept
d1

Distance term 1
d2

Distance term 2
d3

Distance term 3
h1

Hilliness term 1
i1

Distance-hilliness interaction term 1
i2

Distance-hilliness interaction term 2
verbose

Print messages? FALSE by default.
h2

Hilliness term 2

Details

logit (pcycle) = -3.959 +   # alpha
  (-0.5963 * distance) +    # d1
  (1.866 * distancesqrt) +  # d2
  (0.008050 * distancesq) + # d3
  (-0.2710 * gradient) +    # h1
  (0.009394 * distance * gradient) +  # i1
  (-0.05135 * distancesqrt *gradient) # i2

pcycle = exp ([logit (pcycle)]) / (1 + (exp([logit(pcycle)])

uptake_pct_govtarget_2020() and uptake_pct_godutch_2020() approximate the uptake models used in the updated 2020 release of the PCT results.

If the distance parameter is greater than 100, it is assumed that it is in m. If for some reason you want to model cycling uptake associated with trips with distances of less than 100 m, convert the distances to km first.

Examples

distance = 15
gradient = 2
logit_pcycle = -3.959 + # alpha
  (-0.5963 * distance) + # d1
  (1.866 * sqrt(distance)) + # d2
  (0.008050 * distance^2) + # d3
  (-0.2710 * gradient) + # h1
  (0.009394 * distance * gradient) + # i1
  (-0.05135 * sqrt(distance) * gradient) # i2
boot::inv.logit(logit_pcycle)

#> [1] 0.0107377
uptake_pct_govtarget(15, 2)

#> [1] 0.0107377
l = routes_fast_leeds
pcycle_scenario = uptake_pct_govtarget(l$length, l$av_incline)
pcycle_scenario_2020 = uptake_pct_govtarget_2020(l$length, l$av_incline)
plot(l$length, pcycle_scenario, ylim = c(0, 0.2))

points(l$length, pcycle_scenario_2020, col = "blue")


# compare with published PCT data:
l_pct_2020 = get_pct_lines(region = "isle-of-wight")
# test for another region:
# l_pct_2020 = get_pct_lines(region = "west-yorkshire")
l_pct_2020$rf_avslope_perc[1:5]

#> [1] 0.52 0.30 0.32 0.46 0.49
l_pct_2020$rf_dist_km[1:5]

#> [1] 14.6 11.7 11.3 11.7 12.1
govtarget_slc = uptake_pct_govtarget(
  distance = l_pct_2020$rf_dist_km,
  gradient = l_pct_2020$rf_avslope_perc
) * l_pct_2020$all + l_pct_2020$bicycle
govtarget_slc_2020 = uptake_pct_govtarget_2020(
  distance = l_pct_2020$rf_dist_km,
  gradient = l_pct_2020$rf_avslope_perc
) * l_pct_2020$all + l_pct_2020$bicycle
mean(l_pct_2020$govtarget_slc)

#> [1] 1.233474
mean(govtarget_slc)

#> [1] 1.171526
mean(govtarget_slc_2020)

#> [1] 1.233669
godutch_slc = uptake_pct_godutch(
  distance = l_pct_2020$rf_dist_km,
  gradient = l_pct_2020$rf_avslope_perc
) * l_pct_2020$all + l_pct_2020$bicycle
godutch_slc_2020 = uptake_pct_godutch_2020(
  distance = l_pct_2020$rf_dist_km,
  gradient = l_pct_2020$rf_avslope_perc
) * l_pct_2020$all + l_pct_2020$bicycle
mean(l_pct_2020$dutch_slc)

#> [1] 3.574052
mean(godutch_slc)

#> [1] 3.828446
mean(godutch_slc_2020)

#> [1] 4.191658
# Take an origin destination (OD) pair between an LSOA centroid and a
# secondary school. In this OD pair, 30 secondary school children travel, of
# whom 3 currently cycle. The fastest route distance is 3.51 km and the
# gradient is 1.11%. The
# gradient as centred on Dutch hilliness levels is 1.11 – 0.63 = 0.48%.
# The observed number of cyclists is 2. ... Modelled baseline= 30 * .0558 = 1.8.
uptake_pct_govtarget_school2(3.51, 1.11)

#> [1] 0.05584607
# pcycle = exp ([logit (pcycle)])/(1 + (exp([logit(pcycle)]))).
# pcycle = exp(1.953)/(1 + exp(1.953)) = .8758, or 87.58%.
uptake_pct_godutch_school2(3.51, 1.11)

#> [1] 0.8757786