Calculate cycling uptake for UK 'Government Target' scenario

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)

Arguments

distance	Vector distance numeric values of routes.
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	document!
i2	document!

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)])

Examples

l = routes_fast_leeds
pcycle_scenario = uptake_pct_govtarget(l$length, l$av_incline)
#> Distance assumed in m, switching to km
plot(l$length, pcycle_scenario)