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Simulate a through-year system with known true growth

Source: R/simulate.R
ty_simulate.Rd

Students grow linearly, `theta(t) = theta0 + g * t`, and take interims at `times` (reported on their own scale, `scale[1] + scale[2] * theta`, with error from a Rasch form of `interim_items` items) and the summative at t = 1. Late enrollers miss the first `late_missing` interims. "Fast growers" gain an extra `fast_extra` logits after the last interim (e.g. a spring intervention), which interims cannot reveal. They are the hardest case for prior-informed scoring.

Usage

ty_simulate(
  n_calibration = 3000,
  n_operational = 3000,
  times = c(0.2, 0.5, 0.8),
  theta0_mean = -0.6,
  theta0_sd = 1,
  growth_mean = 0.6,
  growth_sd = 0.25,
  p_fast = 0.1,
  fast_extra = 0.6,
  p_late = 0.1,
  late_missing = 2,
  scale = c(200, 10),
  interim_items = 30,
  summative_se = 0.3,
  seed = NULL
)

Arguments

n_calibration, n_operational

Cohort sizes.

times

Interim occasions as fractions of the year.

theta0_mean, theta0_sd, growth_mean, growth_sd

True-score model.

p_fast, fast_extra

Share of fast growers and their extra growth.

p_late, late_missing

Share of late enrollers and interims they miss.

scale

Interim reporting scale: intercept and slope.

interim_items

Items per interim form (sets measurement error).

summative_se

SE of the calibration cohort's summative scores.

seed

Optional seed.

Value

A `ty_sim` data frame, one row per student.

Details

Two cohorts: `calibration` (last year: summative observed, used to link) and `operational` (this year: summative not yet taken). A second, independent set of interim scores (`*_r2`) supports decision-consistency analyses.

Examples

sim <- ty_simulate(n_calibration = 300, n_operational = 300, seed = 1)
head(sim[c("id", "cohort", "late", "fast", "I1", "I2", "I3", "S")])
#>       id      cohort  late  fast       I1       I2       I3          S
#> 1 S00001 calibration FALSE  TRUE 184.5541 196.4382 189.2712 -0.2992317
#> 2 S00002 calibration FALSE  TRUE 195.1590 193.7398 205.8098  1.3310255
#> 3 S00003 calibration FALSE FALSE 180.0460 191.0278 194.9717 -0.7313841
#> 4 S00004 calibration FALSE FALSE 217.2454 213.8085 217.6036  2.0792275
#> 5 S00005 calibration FALSE  TRUE 196.0563 199.6011 192.8997  0.7238655
#> 6 S00006 calibration FALSE FALSE 192.0438 187.3062 187.3337 -1.9784995