Maximum-information item selection with an exposure-rate cap.

A maximum Fisher information selector with a simple exposure control. Each item's share of all administrations so far (the diagonal of adj_mat, normalized to sum to one) is treated as an exposure rate, and items whose rate has reached r_max are withheld. The most informative permitted item is then administered to each respondent. If a respondent has no permitted unadministered item, they receive no item that iteration; when this occurs for every remaining respondent at once, the simulation administers nothing new and stops, so this selector also acts as an implicit stopping rule.

Usage

select_restrict_rate(pers, item, R, admin, adj_mat = NULL, r_max = 0.025)

Arguments

pers: A data frame of current respondent ability estimates.
item: A data frame of current item parameter estimates.
R: A respondent-by-item matrix of potential responses.
admin: An integer administration matrix; 0 indicates an item has not been administered to a respondent. See meow() for details.
adj_mat: An item-item adjacency matrix. See construct_adj_mat().
r_max: The maximum permitted exposure rate (an item's share of all administrations) before that item is withheld. Defaults to 0.025.

Value

An updated administration matrix with the most informative permitted item marked for each respondent who still has one.

Details

Because the exposure rate is each item's share of all administrations, its average across items is 1 / N_items. Values of r_max above 1 / N_items rarely bind, values near it bind only transiently, and values below it induce early stopping.

Examples

sim <- meow(select_restrict_rate, update_theta_mle, data_simple_1pl,
            data_args = list(N_persons = 10, N_items = 10), fix = "item",
            select_args = list(r_max = 0.2))
nrow(sim$results)
#> [1] 6