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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.
Given:
households[uss,usdt,th] population[uss,th]
Want to get:
peoplePerHousehold[uss,usdt,th]
constraints:
population[uss,th] = sum (households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th]; dim=usdt)
makeup a relative propensity:
relPopPersPerHH[usdt] = where each value is related to one of the entries
Finally the math to calculate peoplePerHousehold[uss,usdt,th] is:
!Equation A: 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]
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]