1Demonstration 1 of 4
A gap held open is the growth
How much of the list's growth does a steady gap between arrivals and departures explain?
A stock changes by the net flow times the time it runs. The record's average gap, taken from its own start and end, times 44 months rebuilds the growth, and a shorter or scaled gap shows how far a straight line sits from the month by month record.
The list is incomplete pathways. The gap is arrivals minus all departures, in pathways per month. Months is how long the gap is held open, counted from April 2016.
Predict first. If the record's gap is held open for 44 months, does the straight line end on the December 2019 count?
Choose an example
Constructed example on the committed public record: the gap is computed from the record, and the scale factor is a constructed value.
Calculated values
- Gap per month in the record
- 18,439 pathways
- Gap used in this state
- 18,439 pathways (x 1.0)
- Months the gap is held open
- 44
- Change in the list
- 811,305
- List after those months (constructed)
- 4,414,911
- List in the record at that month
- 4,414,911
- Constructed minus record
- 0
- Referrals, first year to third (percent)
- 7.5
- Completions, first year to third (percent)
- 5.6
The record's list moves from 3,603,606 to 4,414,911 in 44 months, so the average gap is (4,414,911 - 3,603,606) / 44 = 18438.75 pathways a month. This state uses 1.0 x 18438.75 = 18438.75. Held open for 44 months that is 18438.75 x 44 = 811,305, so the list reads 3,603,606 + 811,305 = 4,414,911. The record at that month reads 4,414,911. The straight line lands on the record's December 2019 count because the gap is defined by it.
Use the idea
Before arguing about referrals or activity, multiply the net gap by the months it has run.
Where the conclusion applies
One average gap for the whole window and no other flow. It fails when the gap changes sign inside the window, as it does in the record around 2020.
Check your understanding: If the gap were half the record's, what would the list read after 44 months?
Chapter 36 source: section "The list did not grow because referrals grew". Demonstration C36-D01.
2Demonstration 2 of 4
A fit that passes and a holdout that fails
Does a small error on 2016 to 2019 say anything about 2021 to 2026?
The fit scores only the 45 fit months. The holdout months sit outside that window, so the same model can pass one and miss the other by a large factor.
The model is the chapter's three stock structure started in April 2016. The validation rate is the share of the list removed each month without a recorded treatment. System growth is the shared monthly growth of capacity and referrals.
Predict first. At the fitted values, will the error over the holdout months be closer to 4 percent or to 36 percent?
Choose an example
Constructed example on the committed public record: the fitted values are inferred from it, and the neighbouring settings are constructed.
Calculated values
- Validation rate (per month)
- 0.06
- System growth (per month)
- 0.004
- Fit window error (percent)
- 3.63
- Against the 5 percent tolerance
- inside
- Holdout error (percent)
- 35.57
- Model, December 2019
- 4,206,670
- Model, June 2026
- 4,676,007
Error at one month is |model - record| / record. December 2019: |4,206,670 - 4,414,911| / 4,414,911 = 4.7 percent. June 2026: |4,676,007 - 7,147,562| / 7,147,562 = 34.6 percent. The mean of that ratio over the 45 fit months is 3.63 percent, inside the 5 percent tolerance set before the search, and over the holdout months it is 35.57 percent. These values are read off a grid of constructed settings around the fitted ones, not refitted.
Use the idea
Report the holdout error beside the fit error every time, even when it fails.
Where the conclusion applies
The tail steepness is held at its fitted value of 4.5, the top of its searched range. The comparison fails if definitions in the record change between windows.
Check your understanding: If the model reads 5,000,000 where the record reads 4,000,000, what is that month's error?
Chapter 36 source: section "The record, month by month". Demonstration C36-D02.
3Demonstration 3 of 4
Which parameter decides the long-wait stock
Which assumed or fitted parameter moves the over 52 week stock most, and does that depend on where the rest are held?
The swing is the gap between two runs that differ in one parameter. How big it is depends on how much of the stock the run still holds, which depends on the other settings.
Long waiters are pathways over 52 weeks, counted in the stock of that name. Each parameter is swung across a range somebody would defend, with the others held at the stated place, and read at month 20.
Predict first. With the others at their midpoints, which of long_share and tail_steepness moves the stock more?
Choose an example
Constructed example on the committed public record: ranges are the chapter's chosen ranges, and the fitted-values hold is a constructed variant of the midpoint hold.
Calculated values
- Parameter swung
- long_share
- Range swung
- 0.020 to 0.150
- Others held at
- midpoints of their ranges
- Long waiters at month 20, low end
- 142,700
- Long waiters at month 20, high end
- 16,339
- Swing (pathways)
- 126,362
Swing = |high end - low end| = |16,339 - 142,700| = 126,362 pathways at month 20. This is a one-at-a-time swing with the others held where stated, so it ranks parameters for this setting only. It is a chosen range, not a confidence interval.
Use the idea
Treat a ranking as a statement about where to measure first, under stated settings.
Where the conclusion applies
One parameter moves at a time and the ranges are chosen, not estimated. The ranking changes with the hold setting, so it does not rank the parameters in general.
Check your understanding: If the high end reads 130,000 and the low end 4,000, what is the swing?
Chapter 36 source: section "Which parameter decides it". Demonstration C36-D03.
4Demonstration 4 of 4
A recovery date, or the honest None
When does the modelled list first reach a threshold, and when does it never?
The function scans the run from the start and returns the first month at or under the threshold. If no month qualifies it returns None rather than a date.
The list is total incomplete pathways. A threshold is a count. recovery_date returns the first month the list is at or under the threshold, counted from June 2022, or None.
Predict first. Under the unchanged model, does the list reach 4 million within 48 months?
Choose an example
Constructed example on the committed public record: policies and thresholds are the chapter's constructed values, run on the fitted structure.
Calculated values
- Policy
- baseline
- Threshold
- 6,000,000
- First month at or under it
- 2023-04
- List at month 0
- 6,760,060
- Lowest list in 48 months
- 5,340,226
The first step at or under the threshold is model month 9.5: 5,983,210 - 6,000,000 = (-16790), while the step before reads 6,016,644 - 6,000,000 = 16644. Adding 10 months to June 2022 gives 2023-04. This is a property of the fitted structure, which failed its holdout, so it is not a forecast.
Use the idea
Ask for the None branch whenever a tool hands out a date.
Where the conclusion applies
The fitted structure, reset to June 2022, which failed its holdout. A date here is a property of that structure and is not a forecast of the record.
Check your understanding: If a run starts at 6,760,060 and its lowest count is 5,430,712, does it reach 6,000,000, and does it reach 4,000,000?
Chapter 36 source: section "The exported artifact: recovery_date". Demonstration C36-D04.