Plan pretest sample sizes for a target precision

Uses the normal approximation `posterior precision = 1 / prior_sd^2 + n * I(b)`, where `I(b)` is the average information of one response about the item's difficulty in the pretest population, evaluated at the predicted difficulty. Compares the responses needed with the predicted prior against the conventional (no-prior) requirement `1 / (target_sd^2 * I(b))`.

Usage

cs_plan(prior, target_sd = 0.2, theta_mean = 0, theta_sd = 1)

Arguments

prior

Output of `predict()` on a `cs_predictor`.

target_sd

Desired posterior SD of each difficulty.

theta_mean, theta_sd

Pretest population.

Value

Data frame: `item`, `prior_sd`, `info`, `n_with_prior`, `n_without_prior`, `saved`.

Examples

sim <- cs_simulate(n_train = 200, n_new = 60, seed = 1)
it <- sim$items; tr <- it$set == "train"
pr <- cs_predictor(it$b_legacy[tr], sim$features[tr, ], it$family[tr], seed = 1)
pred <- predict(pr, sim$features[!tr, ], it$family[!tr])
plan <- cs_plan(pred, target_sd = 0.3)
summary(plan[c("n_with_prior", "n_without_prior")])
#>   n_with_prior   n_without_prior
#>  Min.   :42.00   Min.   :54.00  
#>  1st Qu.:42.00   1st Qu.:55.00  
#>  Median :43.00   Median :56.00  
#>  Mean   :45.55   Mean   :59.03  
#>  3rd Qu.:45.50   3rd Qu.:58.25  
#>  Max.   :70.00   Max.   :86.00