Projecting enrollment with enrollcast

library(enrollcast)

The grade progression ratio method

The cohort survival / grade progression ratio method projects enrollment by asking: of the students in grade g this year, how many appear in grade g+1 next year? That ratio captures net retention, migration, and repetition. enrollcast estimates these ratios from history and applies them forward with a matrix projection.

A small district

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)
)
history
#>   year grade enrollment
#> 1 2021     K        100
#> 2 2021     1         90
#> 3 2021     2         80
#> 4 2022     K        110
#> 5 2022     1         95
#> 6 2022     2         88
#> 7 2023     K        120
#> 8 2023     1         99
#> 9 2023     2         91

Step 1: progression ratios

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

The ratios sit on the sub-diagonal of the projection matrix; the entry-grade row is zero because entry is supplied exogenously.

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

Step 2: project forward

The entry grade (kindergarten here) has no feeder grade, so you supply its future values — for example from a birth-cohort or housing model.

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

Stitching history and projection

project_enrollment() returns projected years only. Combine with history for plotting:

observed <- data.frame(
  year = history$year,
  grade = as.character(history$grade),
  enrollment = history$enrollment
)
combined <- rbind(observed, projection)
head(combined)
#>   year grade enrollment
#> 1 2021     K        100
#> 2 2021     1         90
#> 3 2021     2         80
#> 4 2022     K        110
#> 5 2022     1         95
#> 6 2022     2         88

Modeling a school modernization swing

A school temporarily relocated during modernization typically sees depressed enrollment that recovers after it returns. swing_schedule() builds a per-year projection schedule: enrollment is held flat during the swing, scaled by recovery multipliers for a few years, then projected normally.

depressed <- c(K = 80, `1` = 66, `2` = 60)
schedule <- swing_schedule(ratios,
  horizon = 6, swing_years = 2,
  recovery = c(1.10, 1.10, 1.05), entry = 130
)
project_enrollment(depressed, schedule = schedule, start_year = 2023)
#>    year grade enrollment
#> 1  2024     K   80.00000
#> 2  2024     1   66.00000
#> 3  2024     2   60.00000
#> 4  2025     K   80.00000
#> 5  2025     1   66.00000
#> 6  2025     2   60.00000
#> 7  2026     K   88.00000
#> 8  2026     1   72.60000
#> 9  2026     2   66.00000
#> 10 2027     K   96.80000
#> 11 2027     1   79.86000
#> 12 2027     2   72.60000
#> 13 2028     K  101.64000
#> 14 2028     1   83.85300
#> 15 2028     2   76.23000
#> 16 2029     K  130.00000
#> 17 2029     1   94.01700
#> 18 2029     2   81.15597