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howtos:toolcoding:using_a_relative_propensity [2010/11/12 20:58] shona.weldon created |
howtos:toolcoding:using_a_relative_propensity [2010/11/12 21:06] shona.weldon |
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When you have an equation with more unknowns that constraints and you want to add some assumptions to solve it you may add a relative propensity calculation. Best served by an example. | When you have an equation with more unknowns that constraints and you want to add some assumptions to solve it you may add a relative propensity calculation. Best served by an example. | ||
+ | ===== Example ===== | ||
Given: | Given: | ||
- | households[uss,usdt,th] | + | households[uss,usdt,th] |
- | population[uss,th] | + | population[uss,th] |
Want to get: | Want to get: | ||
- | peoplePerHousehold[uss,usdt,th] | + | peoplePerHousehold[uss,usdt,th] |
constraints: | constraints: | ||
- | population[uss,th] = sum (households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th]; dim=usdt) | + | population[uss,th] = sum (households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th]; dim=usdt) |
makeup a relative propensity: | makeup a relative propensity: | ||
- | relPopPersPerHH[usdt] = where each value is related to one of the entries | + | relPopPersPerHH[usdt] = where each value is related to one of the entries |
Finally the math to calculate peoplePerHousehold[uss,usdt,th] is: | Finally the math to calculate peoplePerHousehold[uss,usdt,th] is: | ||
+ | !Equation A: | ||
local peoplePerHouseholdEst[uss,usdt,th] = households[uss,usdt,th] * peoplePerHousehold[usdt] | local peoplePerHouseholdEst[uss,usdt,th] = households[uss,usdt,th] * peoplePerHousehold[usdt] | ||
+ | !Equation B: | ||
peoplePerHousehold[uss,usdt,th] = population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] * relPopPersPerHH[usdt] | peoplePerHousehold[uss,usdt,th] = population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] * relPopPersPerHH[usdt] | ||
+ | ===== Check your above equation through symbol substitution algebra ===== | ||
+ | You know your identity : | ||
+ | population[uss,th] = households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th] | ||
+ | substituting from your final math Equation B for personPerHousehold: | ||
+ | population[uss,th] = households[uss,usdt,th] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] * relPopPersPerHH[usdt] | ||
+ | reordering: | ||
+ | population[uss,th] = households[uss,usdt,th] * relPopPersPerHH[usdt] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] | ||
+ | Then notice the substitution can be done for Equation A from the final math above: | ||
+ | population[uss,th] = peoplePerHouseholdEst[uss,usdt,th] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] | ||
+ | And the estimates cancel so you have an identity and you are comfortable your math worked | ||
+ | population[uss,th] = population[uss,th] | ||