Skip to contents

Stock and flow across the OTIS strata

Source: R/mrm_stockflow.R
mrm_otis_stock_flow.Rd

MRM (Multilevel Reconciliation Methodology) applied to person-days: the same confinement appears at three strata in the OTIS release and they do not automatically agree.

Usage

mrm_otis_stock_flow(
  person_days,
  placements = NULL,
  totals = NULL,
  year_col = "EndFiscalYear",
  id_col = "UniqueIndividual_ID",
  days_col = "TotalAggregatedDays_Segregation",
  consecutive_col = "NumberConsecutiveDays_Segregation",
  placement_col = "Number_Of_Placements",
  totals_col = "NumberIndividuals_Segregation",
  t = 365,
  exposure = NULL,
  per = 1e+05
)

Arguments

person_days

Data frame at the PERSON stratum: one row per individual per period, with a period column, an identifier column and a column of days served.

placements

Optional data frame at the PLACEMENT stratum, used only for reconciliation: rows per individual per spell, with the consecutive-days and placement-count columns.

totals

Optional data frame at the AGGREGATE stratum, one or more rows per period carrying a stated total of individuals.

year_col

Period column name, present in every stratum given.

id_col

Identifier column in person_days and placements.

days_col

Days column in person_days.

consecutive_col

Consecutive-days column in placements.

placement_col

Placement-count column in placements.

totals_col

Stated-total column in totals.

t

Length of each period in days. Default 365.

exposure

Optional population to express rates against, one value or one per period.

per

Rate denominator when exposure is given. Default 100000.

Value

A list with:

  • stock_flow: the measures per period, from rmoriebricklayer::stock_flow().

  • reconciliation: one row per period comparing the strata – people at the person and placement strata, the stated aggregate total, whether they agree, and the ratio of summed consecutive days to person-days.

  • strata_agree: TRUE when every stratum given agrees on the number of people in every period.

  • decomposition_exact: TRUE when the change in days is recovered by the changes in people and stay.

Details

  • PERSON stratum (b02): one row per individual per year, carrying the days that person served across the year. This is the additive quantity, and the one Lakner's measures need.

  • PLACEMENT stratum (b01): several rows per individual, carrying the consecutive days of a spell and the count of placements. Spell lengths are NOT an additive share of the year.

  • AGGREGATE stratum (c01): the yearly totals stated directly.

Reconciling them is the point. Summing the placement stratum's consecutive days as though they were person-days understates the total by about a third on the published release, and the two strata can disagree about how many people there even were. Both are reported rather than assumed away.

The measures themselves come from rmoriebricklayer: the average daily population is days per day, the average length of stay is days per person, and a change in days decomposes exactly into a change in people and a change in stay. After Lakner, A Manual of Statistical Sampling Methods for Corrections Planners (University of Illinois at Urbana-Champaign, 1976), p.15-18.

References

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

Examples

# needs rmoriebricklayer (>= 0.4.8) for adp()/alos()/stock_flow()
if (utils::packageVersion("rmoriebricklayer") >= "0.4.8") {
person <- data.frame(
  EndFiscalYear = c(rep(2023, 3), rep(2025, 2)),
  UniqueIndividual_ID = c("a", "b", "c", "a", "d"),
  TotalAggregatedDays_Segregation = c(10, 20, 30, 40, 50))
mrm_otis_stock_flow(person)$stock_flow
}
#> ── Stock and flow over 2 periods ───────────────────────────────── 
#>  period people days alos       adp
#>    2023      3   60   20 0.1643836
#>    2025      2   90   45 0.2465753
#> 
#>   2023 to 2025: people -33.3%, stay +125.0%, days +50.0%
#> ──────────────────────────────────────────────────────────────────