Simulation Example
(Note: the following simulations build one upon the other, but are otherwise
very simple. They apply only one factor for each simulation. There
are cases when it is appropriate to apply thousands of factors in a single
simulation, and our tools excel at handling those more complex cases.)
A heating oil dealer wants to analyze a particular area (we are using PUMA 3200 in Pennsylvania) to estimate the amount of money that will be spent on heating oil. His problem is that we have 1990 PUMS data (which reflects 1989 usage) and this year is 2002. He brings us the following numbers indicating changes since 1989:
- 8% of the existing homes that had electric heat in 1989 have converted from electric heat to oil.
- There has been an 18% increase in housing, due to new construction, and 50% of the 18% (9%) heat with oil. He doesn't care what fuel the other 9% use.
- There has been, since 1989, a 35% increase in heating oil prices.
(Note: all of the above percentages are fabricated, and do not really apply to Pennsylvania
puma 3200. Other than the fabricated percentages, the analyses and simulations are real.)
The oil dealer's ultimate question is this: "How much money will be spent on heating oil this year, sliced-and-diced by number of bedrooms and value of home?"
We will approach his problem in this manner:
1. First, we want to account for the electric-to-oil conversions. Assume that the homes converted from electric to oil are typical - some are older,
well ventilated homes, some are newer, thoroughly sealed, insulated, and caulked. So we will find out (via slicing-and-dicing) how many homes use electric heat, and how many homes use oil heat. Then, using simple algebra, we figure out how many homes 8% of the electric homes are, and what percentage we need to "bump up" the oil heated homes by. Note that we do not simply want to recode 8% of the electric homes to oil, because that would misrepresent the costs. We find
from the analysis below that we must increase the oil households by 5.5%. (Note that if we were analyzing all energy usage, we would apply the appropriate simulation
factor to electric homes to decrease their numbers.)
Fuelheat Puma Houswgt
3200 83969
Electricity 3200 23438
Fuel oil kerosene etc. 3200 34346
Fuelheat Puma PHouseholds
Electricity 3200 23438
Fuel oil kerosene etc. 3200 34346
The above analysis, like all our analyses, has a household level section (above)
and a person level section (below). Because it is such a simple analysis,
the two sections are nearly identical.
There are 23,438 households with electric heat. 8% of that figure is
1,875. So we need to find some number to multiply 34,346 (the number of
oil heated homes) by to get 36,221 (34,346 + 1,875). 34,346 * 1.055
is 36,221. So our simulation factor for the first simulation is
105.5%, which raises the number of oil heated households by 5.5%.
2. Next, we want to account for the 9% increase due to new construction. Because they are new homes, they will be energy efficient (unlike the electric to oil conversions, which were a mixed bag for efficiency). We need to know:
a. What is 9% of the total households?
b. What factor must we apply, via a simulation, to the new oil heated households in order to increase the
total household count by 9%? We are only considering new oil heated households (those houses no more than 5 years old) in order to reflect the usage of new, energy efficient oil heated homes.
To answer these questions, we run an analysis to slice-and-dice based on "oil heat" or "other", and "home built '85-'90" or "other"
Fuelheat Yrbuilt Puma Houswgt
Other Other 3200 76146
Other 1985 to 1990 3200 31261
Fuel oil kerosene etc. Other 3200 30852
Fuel oil kerosene etc. 1985 to 1990 3200 3494
Fuelheat Yrbuilt Puma PHouseholds
Other Other 3200 35195
Other 1985 to 1990 3200 12013
Fuel oil kerosene etc. Other 3200 30852
Fuel oil kerosene etc. 1985 to 1990 3200 3494
We find, by adding up the weighted household counts, that there are
3,494 oil-heated new houses, and 141,753 total houses.
9% of 141,753 is 12,758. We are going to apply our second simulation to
the results of our first simulation, so we don't really want to bump up the
3,494 oil heated new homes, but we want to bump up the (3,494 * 1.055 sim
factor) new homes. There are a simulated 3,686 new oil heated homes
after applying the first simulation. A little algebra shows us that our
simulation factor for the second simulation is 4.46, or 446%.
3. We apply a 35% across the board increase in oil prices, via a third simulation.
To summarize, we will create 3 simulations. The first will increase the housing weights for all oil heated homes by 5.5%. The second will increase the housing weights for all new oil heated homes by
446%. The third will increase all oil expenses by 35%.
To test our simulations, we apply all three in a single analysis and slice-and-dice by age of home and heating fuel. We display the following
volumes:
- Houswgt (weighted housing count)
- simdemo3.1 (First simulation, which bumps up all oil-heated household weights by 5.5%, to account for electric to oil conversions)
- simdemo3.2 (Second simulation, which bumps up all new oil-heated household weights by
446%, to account for new construction. It uses the results of simdemo3.1.)
- Fuelcost (Unweighted cost of heating fuel, as recorded by the Census Bureau)
- simdemo3.3 (Bumps up the Fuelcost, for oil heated households only, by 35%)
- simdemo3.3 * simdemo3.2 (Multiplies the simulated oil cost by the adjusted [simulated] housing weight)
- Households (Unweighted household count, for sanity checking)
- PHouseholds (Weighted person level household count, for sanity checking)
We then place the results of that analysis in a spreadsheet, and calculate the percentage differences between the appropriate columns to insure that the simulations were applied properly. We see that they were applied properly.
In "Test 1", simdemo3.1 is identical to Houswgt (100%) for non-oil heated households, and 105.5% of Houswgt for oil heated houses.
(Scroll to the right to see the "Test" columns.)
In "Test 2", simdemo3.2 is identical to simdemo3.1 for all but new oil heated houses.
For the new oil heated houses, "Test 2" is 446%, just as it should
be.
In "Test 3", we see that all heating oil prices were increased by 35%, and other heating prices were not changed.
(Puma was included as a dimension in the first two analyses as an extra
check. It really isn't necessary, because the file we were analyzing had
only puma 3200 data in it, so we've removed it from the remaining analyses to
reduce clutter.)
Fuelheat Yrbuilt Houswgt simdemo3.1 Test 1 simdemo3.2 Test 2 Fuelcost simdemo3.3 Test 3 simdemo3.3*simdemo3.2 Households
Other Other 76146 76146 100 76146 100 511165 511165 100 7900752 6281
Other 1985 to 1990 31261 31261 100 31261 100 79857 79857 100 1240612 2398
Fuel oil kerosene etc. Other 30852 32549 105.5004538 32549 100 1664388 2246924 135.000012 38168775 1934
Fuel oil kerosene etc. 1985 to 1990 3494 3686 105.4951345 16440 446.0119371 172201 232471 134.9997967 16411529 241
Fuelheat Yrbuilt PHouseholds
Other Other 35195
Other 1985 to 1990 12013
Fuel oil kerosene etc. Other 30852
Fuel oil kerosene etc. 1985 to 1990 3494
The final step is to run an analysis with the simulations in place (but only the simulated housing count, and the product of the second and third simulations are displayed, as requested by the customer), sliced-and-diced by the type of heat, number of bedrooms and the value of homes.
The analysis is restricted to oil heat only (the other fuels would reflect 1989
usage, because no simulations were applied to them).
Before we get to the final product, there is something about this analysis that
is troubling. Click here for a brief digression
on that topic.
It's worth noting that all simulations are conducted on individual records at either the household or person level. It is not possible to come anywhere close to doing something like this with aggregate (summarized) data.
The final analysis follows. We've left this one just as it would be delivered to the customer, as a comma delimited ASCII file.
simdemo3.2 represents the simulated number of households, and simdemo3.3*simdemo3.2 represents the simulated amount spent on oil. There is no "person level section" in this analysis, because all dimensions and volumes were
at the household level. Fuelheat,Value,Bedrooms,simdemo3.2,simdemo3.3*simdemo3.2
Fuel oil kerosene etc.,N/A (GQ/rental unit/vacant not for sale only),No bedrooms, 205, 1863
Fuel oil kerosene etc.,N/A (GQ/rental unit/vacant not for sale only),1 Bedroom, 1253, 324231
Fuel oil kerosene etc.,N/A (GQ/rental unit/vacant not for sale only),2 Bedrooms, 3357, 2323302
Fuel oil kerosene etc.,N/A (GQ/rental unit/vacant not for sale only),3 Bedrooms, 3297, 3593818
Fuel oil kerosene etc.,N/A (GQ/rental unit/vacant not for sale only),4 Bedrooms, 470, 509309
Fuel oil kerosene etc.,N/A (GQ/rental unit/vacant not for sale only),5 or more bedrooms, 556, 1131494
Fuel oil kerosene etc.,Less than $ 10000,1 Bedroom, 54, 33427
Fuel oil kerosene etc.,Less than $ 10000,2 Bedrooms, 595, 501306
Fuel oil kerosene etc.,Less than $ 10000,3 Bedrooms, 232, 218014
Fuel oil kerosene etc.,$ 10000 - $ 14999,1 Bedroom, 44, 9765
Fuel oil kerosene etc.,$ 10000 - $ 14999,2 Bedrooms, 657, 409593
Fuel oil kerosene etc.,$ 10000 - $ 14999,3 Bedrooms, 293, 261917
Fuel oil kerosene etc.,$ 10000 - $ 14999,4 Bedrooms, 50, 52737
Fuel oil kerosene etc.,$ 15000 - $ 19999,1 Bedroom, 8, 6836
Fuel oil kerosene etc.,$ 15000 - $ 19999,2 Bedrooms, 159, 144137
Fuel oil kerosene etc.,$ 15000 - $ 19999,3 Bedrooms, 442, 436939
Fuel oil kerosene etc.,$ 15000 - $ 19999,4 Bedrooms, 84, 103822
Fuel oil kerosene etc.,$ 20000 - $ 24999,2 Bedrooms, 348, 282073
Fuel oil kerosene etc.,$ 20000 - $ 24999,3 Bedrooms, 505, 815427
Fuel oil kerosene etc.,$ 20000 - $ 24999,4 Bedrooms, 73, 90867
Fuel oil kerosene etc.,$ 20000 - $ 24999,5 or more bedrooms, 7, 5483
Fuel oil kerosene etc.,$ 25000 - $ 29999,1 Bedroom, 12, 3917
Fuel oil kerosene etc.,$ 25000 - $ 29999,2 Bedrooms, 301, 237155
Fuel oil kerosene etc.,$ 25000 - $ 29999,3 Bedrooms, 380, 440230
Fuel oil kerosene etc.,$ 25000 - $ 29999,4 Bedrooms, 41, 63863
Fuel oil kerosene etc.,$ 30000 - $ 34999,1 Bedroom, 254, 114531
Fuel oil kerosene etc.,$ 30000 - $ 34999,2 Bedrooms, 471, 506479
Fuel oil kerosene etc.,$ 30000 - $ 34999,3 Bedrooms, 510, 401603
Fuel oil kerosene etc.,$ 30000 - $ 34999,4 Bedrooms, 92, 154679
Fuel oil kerosene etc.,$ 30000 - $ 34999,5 or more bedrooms, 38, 69076
Fuel oil kerosene etc.,$ 35000 - $ 39999,1 Bedroom, 16, 17162
Fuel oil kerosene etc.,$ 35000 - $ 39999,2 Bedrooms, 497, 426735
Fuel oil kerosene etc.,$ 35000 - $ 39999,3 Bedrooms, 442, 506398
Fuel oil kerosene etc.,$ 35000 - $ 39999,4 Bedrooms, 105, 143399
Fuel oil kerosene etc.,$ 40000 - $ 44999,2 Bedrooms, 443, 426116
Fuel oil kerosene etc.,$ 40000 - $ 44999,3 Bedrooms, 780, 873557
Fuel oil kerosene etc.,$ 40000 - $ 44999,4 Bedrooms, 116, 95037
Fuel oil kerosene etc.,$ 40000 - $ 44999,5 or more bedrooms, 38, 61528
Fuel oil kerosene etc.,$ 45000 - $ 49999,1 Bedroom, 19, 21865
Fuel oil kerosene etc.,$ 45000 - $ 49999,2 Bedrooms, 468, 441846
Fuel oil kerosene etc.,$ 45000 - $ 49999,3 Bedrooms, 734, 778456
Fuel oil kerosene etc.,$ 45000 - $ 49999,4 Bedrooms, 141, 136785
Fuel oil kerosene etc.,$ 50000 - $ 54999,2 Bedrooms, 605, 512042
Fuel oil kerosene etc.,$ 50000 - $ 54999,3 Bedrooms, 849, 1109718
Fuel oil kerosene etc.,$ 50000 - $ 54999,4 Bedrooms, 136, 255838
Fuel oil kerosene etc.,$ 50000 - $ 54999,5 or more bedrooms, 50, 102950
Fuel oil kerosene etc.,$ 55000 - $ 59999,2 Bedrooms, 138, 120492
Fuel oil kerosene etc.,$ 55000 - $ 59999,3 Bedrooms, 425, 524912
Fuel oil kerosene etc.,$ 55000 - $ 59999,4 Bedrooms, 12, 18800
Fuel oil kerosene etc.,$ 55000 - $ 59999,5 or more bedrooms, 30, 45861
Fuel oil kerosene etc.,$ 60000 - $ 64999,2 Bedrooms, 430, 532231
Fuel oil kerosene etc.,$ 60000 - $ 64999,3 Bedrooms, 760, 1023042
Fuel oil kerosene etc.,$ 60000 - $ 64999,4 Bedrooms, 255, 605759
Fuel oil kerosene etc.,$ 60000 - $ 64999,5 or more bedrooms, 15, 17946
Fuel oil kerosene etc.,$ 65000 - $ 69999,1 Bedroom, 23, 18800
Fuel oil kerosene etc.,$ 65000 - $ 69999,2 Bedrooms, 527, 537805
Fuel oil kerosene etc.,$ 65000 - $ 69999,3 Bedrooms, 497, 577489
Fuel oil kerosene etc.,$ 65000 - $ 69999,4 Bedrooms, 222, 276450
Fuel oil kerosene etc.,$ 70000 - $ 74999,2 Bedrooms, 356, 313064
Fuel oil kerosene etc.,$ 70000 - $ 74999,3 Bedrooms, 702, 866495
Fuel oil kerosene etc.,$ 70000 - $ 74999,4 Bedrooms, 207, 239744
Fuel oil kerosene etc.,$ 70000 - $ 74999,5 or more bedrooms, 19, 30913
Fuel oil kerosene etc.,$ 75000 - $ 79999,1 Bedroom, 15, 19163
Fuel oil kerosene etc.,$ 75000 - $ 79999,2 Bedrooms, 320, 356283
Fuel oil kerosene etc.,$ 75000 - $ 79999,3 Bedrooms, 822, 973911
Fuel oil kerosene etc.,$ 75000 - $ 79999,4 Bedrooms, 37, 49849
Fuel oil kerosene etc.,$ 75000 - $ 79999,5 or more bedrooms, 64, 132356
Fuel oil kerosene etc.,$ 80000 - $ 89999,1 Bedroom, 41, 42977
Fuel oil kerosene etc.,$ 80000 - $ 89999,2 Bedrooms, 445, 540632
Fuel oil kerosene etc.,$ 80000 - $ 89999,3 Bedrooms, 1739, 1709190
Fuel oil kerosene etc.,$ 80000 - $ 89999,4 Bedrooms, 292, 441140
Fuel oil kerosene etc.,$ 80000 - $ 89999,5 or more bedrooms, 71, 95980
Fuel oil kerosene etc.,$ 90000 - $ 99999,1 Bedroom, 34, 35749
Fuel oil kerosene etc.,$ 90000 - $ 99999,2 Bedrooms, 711, 712172
Fuel oil kerosene etc.,$ 90000 - $ 99999,3 Bedrooms, 1317, 1521205
Fuel oil kerosene etc.,$ 90000 - $ 99999,4 Bedrooms, 223, 214005
Fuel oil kerosene etc.,$ 90000 - $ 99999,5 or more bedrooms, 12, 21933
Fuel oil kerosene etc.,$100000 - $124999,No bedrooms, 19, 15382
Fuel oil kerosene etc.,$100000 - $124999,2 Bedrooms, 571, 598334
Fuel oil kerosene etc.,$100000 - $124999,3 Bedrooms, 2748, 3213460
Fuel oil kerosene etc.,$100000 - $124999,4 Bedrooms, 734, 1051187
Fuel oil kerosene etc.,$100000 - $124999,5 or more bedrooms, 96, 125115
Fuel oil kerosene etc.,$125000 - $149999,1 Bedroom, 19, 56144
Fuel oil kerosene etc.,$125000 - $149999,2 Bedrooms, 431, 616021
Fuel oil kerosene etc.,$125000 - $149999,3 Bedrooms, 2017, 2461849
Fuel oil kerosene etc.,$125000 - $149999,4 Bedrooms, 724, 817653
Fuel oil kerosene etc.,$125000 - $149999,5 or more bedrooms, 261, 381114
Fuel oil kerosene etc.,$150000 - $174999,2 Bedrooms, 514, 644617
Fuel oil kerosene etc.,$150000 - $174999,3 Bedrooms, 2352, 2733813
Fuel oil kerosene etc.,$150000 - $174999,4 Bedrooms, 745, 1064993
Fuel oil kerosene etc.,$150000 - $174999,5 or more bedrooms, 294, 417171
Fuel oil kerosene etc.,$175000 - $199999,1 Bedroom, 7, 6480
Fuel oil kerosene etc.,$175000 - $199999,2 Bedrooms, 65, 102147
Fuel oil kerosene etc.,$175000 - $199999,3 Bedrooms, 704, 866907
Fuel oil kerosene etc.,$175000 - $199999,4 Bedrooms, 538, 709945
Fuel oil kerosene etc.,$175000 - $199999,5 or more bedrooms, 148, 237618
Fuel oil kerosene etc.,$200000 - $249999,1 Bedroom, 34, 32473
Fuel oil kerosene etc.,$200000 - $249999,2 Bedrooms, 231, 289160
Fuel oil kerosene etc.,$200000 - $249999,3 Bedrooms, 977, 1321037
Fuel oil kerosene etc.,$200000 - $249999,4 Bedrooms, 583, 875769
Fuel oil kerosene etc.,$200000 - $249999,5 or more bedrooms, 231, 141654
Fuel oil kerosene etc.,$250000 - $299999,2 Bedrooms, 15, 19939
Fuel oil kerosene etc.,$250000 - $299999,3 Bedrooms, 634, 880830
Fuel oil kerosene etc.,$250000 - $299999,4 Bedrooms, 638, 656559
Fuel oil kerosene etc.,$250000 - $299999,5 or more bedrooms, 262, 301340
Fuel oil kerosene etc.,$300000 - $399999,1 Bedroom, 23, 68620
Fuel oil kerosene etc.,$300000 - $399999,2 Bedrooms, 74, 142995
Fuel oil kerosene etc.,$300000 - $399999,3 Bedrooms, 232, 249463
Fuel oil kerosene etc.,$300000 - $399999,4 Bedrooms, 487, 747730
Fuel oil kerosene etc.,$300000 - $399999,5 or more bedrooms, 103, 123454
Fuel oil kerosene etc.,$400000 or more,2 Bedrooms, 26, 24924
Fuel oil kerosene etc.,$400000 or more,3 Bedrooms, 96, 100489
Fuel oil kerosene etc.,$400000 or more,4 Bedrooms, 212, 332279
Fuel oil kerosene etc.,$400000 or more,5 or more bedrooms, 154, 377960
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