Stock and flow side by side, with the decomposition

Reports the same person-days as a stock and as a flow, and says how much of any change in the stock came from the number of people and how much from how long they stayed.

Usage

stock_flow(
  days,
  people,
  period = NULL,
  t = 365,
  exposure = NULL,
  per = 1e+05,
  baseline = c("first", "previous")
)

Arguments

days: Person-days, one element per period.
people: Number of people, one element per period.
period: Optional labels for the periods.
t: Length of each period in days, one value or one per period. Default 365. period_days() turns dates into this.
exposure: Optional population to express rates against, one per period; for example provincial residents.
per: Rate denominator when exposure is given. Default 100000.
baseline: What the change columns compare against: "first" (the default) measures every period against the first, which is what a report on a whole window wants; "previous" measures each period against the one before it, which is what a series wants.

Value

A data frame of class rmbl_stock_flow, one row per period: people, days, alos, adp, and when exposure is supplied flow_rate and stock_rate. Change columns compare each period with the first.

Details

The decomposition is exact, because days are people times length of stay: a change in days is \((1+p)(1+l) - 1\) for proportional changes \(p\) in people and \(l\) in stay. The two rates can therefore carry OPPOSITE signs, and the point of putting them in one table is that neither can then be quoted alone.

References

Lakner, E. (1976) A Manual of Statistical Sampling Methods for Corrections Planners. University of Illinois at Urbana-Champaign.

Examples

# Fewer people, held longer: the flow falls while the stock rises.
stock_flow(days = c(115674, 126121), people = c(12647, 9608),
           period = c("2023", "2025"),
           exposure = c(15495050, 16256538))
#> ── Stock and flow over 2 periods ───────────────────────────────── 
#>  period people   days      alos      adp flow_rate stock_rate
#>    2023  12647 115674  9.146359 316.9151  81.61961   2.045267
#>    2025   9608 126121 13.126665 345.5370  59.10237   2.125526
#> 
#>   2023 to 2025: people -24.0%, stay +43.5%, days +9.0%
#>   flow rate -27.6%, stock rate +3.9%  <- opposite signs: quote both
#> ──────────────────────────────────────────────────────────────────