Update person ability via maximum likelihood estimation.

This update function treats item parameters as fixed and known and updates person ability estimates after each iteration with a maximum likelihood estimate based on a 2PL item response function.

Usage

update_theta_mle(pers, item, R, admin)

Arguments

pers: A data frame of current respondent parameter estimates.
item: A data frame of item parameter values.
R: A respondent-by-item matrix of potential responses.
admin: An integer administration matrix; non-zero entries indicate administered items. See meow() for details.

Value

A list with two entries: pers, a data frame with updated respondent ability estimates, and item, the unchanged data frame of item parameters.

Examples

data <- data_simple_1pl(N_persons = 10, N_items = 10)
admin <- matrix(0L, 10, 10)
admin[, 1:5] <- 1L
R <- matrix(data$resp$resp, nrow = 10, byrow = TRUE)
upd <- update_theta_mle(data$pers_tru, data$item_tru, R, admin)
head(upd$pers)
#>   id      theta
#> 1  1  0.3489388
#> 2  2 -1.6450743
#> 3  3  1.4305338
#> 4  4 -4.0000000
#> 5  5  1.4305196
#> 6  6 -1.6450809