Project School Enrollment with Grade Progression Ratios

Projects school enrollment using the cohort survival / grade progression ratio method described in Webster (1970) , implemented as a matrix projection. Works at any level of aggregation and any number of grades. Provides functions to compute progression ratios from historical grade-level enrollment and to project future enrollment forward an arbitrary horizon.

enrollcast

enrollcast projects school enrollment with the cohort survival / grade progression ratio method, implemented as a matrix projection. It works on one grade-by-year enrollment series at a time, so you can use it at any level (school, district, local education agency, or city) and with any number of grades.

Awesome hex logo provided by Adam Higerd.

Installation

install.packages("enrollcast")

Install the development version from GitHub:

# install.packages("pak")
pak::pak("localopen/enrollcast")

Usage

library(enrollcast)

# Historical grade-level enrollment (long format).
history <- data.frame(
  year = rep(2021:2023, each = 3),
  grade = factor(rep(c("K", "1", "2"), 3), levels = c("K", "1", "2")),
  enrollment = c(100, 90, 80, 110, 95, 88, 120, 99, 91)
)

# 1. Calculate progression ratios.
ratios <- progression_ratios(history, method = "mean")
ratios
#>   grade_from grade_to     ratio
#> 1          K        1 0.9250000
#> 2          1        2 0.9678363

# 2. Project forward. The entry grade (K) is supplied exogenously.
base <- history[history$year == 2023, c("grade", "enrollment")]
projection <- project_enrollment(
  base = base,
  ratios = ratios,
  horizon = 3,
  entry = c(125, 130, 128),
  start_year = 2023
)
projection
#>   year grade enrollment
#> 1 2024     K  125.00000
#> 2 2024     1  111.00000
#> 3 2024     2   95.81579
#> 4 2025     K  130.00000
#> 5 2025     1  115.62500
#> 6 2025     2  107.42982
#> 7 2026     K  128.00000
#> 8 2026     1  120.25000
#> 9 2026     2  111.90607

Inspect the underlying projection matrix at any time:

progression_matrix(ratios)
#>       K         1 2
#> K 0.000 0.0000000 0
#> 1 0.925 0.0000000 0
#> 2 0.000 0.9678363 0

Multiple aggregation units

enrollcast projects one series per call. To project several schools or local education agencies, split the data and map over the pieces:

# fmt: skip
school_history <- data.frame(
  school = rep(c("North", "South"), each = 9),
  year = rep(2021:2023, each = 3, times = 2),
  grade = factor(rep(c("K", "1", "2"), times = 6), levels = c("K", "1", "2")),
  enrollment = c(100, 90, 80, 110, 95, 88, 120, 99, 91, 120, 
                 110, 100, 130, 115, 108, 140, 119, 111)
)

projections <- lapply(
  split(school_history, school_history$school),
  function(df) {
    ratios <- progression_ratios(df)
    base <- df[df$year == max(df$year), c("year", "grade", "enrollment")]
    project_enrollment(base, ratios, horizon = 3, entry = rep(100, 3))
  }
)

projections$North
#>   year grade enrollment
#> 1 2024     K  100.00000
#> 2 2024     1  111.00000
#> 3 2024     2   95.81579
#> 4 2025     K  100.00000
#> 5 2025     1   92.50000
#> 6 2025     2  107.42982
#> 7 2026     K  100.00000
#> 8 2026     1   92.50000
#> 9 2026     2   89.52485