xxIRT (version 2.0.3)

cat_sim: Computerized Adaptive Testing (CAT) Simulation

Description

cat_sim simulates CAT with user-defined algorithms

cat_estimate_default is a maximum likelihood estimator of the theta parameter

cat_estimate_mle_step is a maximum likelihood estimator of the theta parameter, with a fixed incremental/decremental change for all 1s or 0s responses

cat_estimate_eap is an expected a posteriori estimator of the theta parameter

cat_estimate_hybrid is a hybrid estimator of the theta parameter: EAP for all 1s or 0s responses, and MLE otherwise

cat_stop_default is a trifold stopping rule: it is the minimum standard error rule when stop_se is set in options, the minimum information rule when stop_mi is set in options, and the 95

cat_select_default selects the item with maximum information or the item set with maximum averaged information for the current theta estimate.

cat_select_ccat implements the constrained CAT selection algorithm. The 'ccat_perc' argument defines the percentage targets, and the 'ccat_var' argument defines the constrained variable.

cat_select_shadow implements the shadow-test CAT selection algorithm. The 'shadow_constraints' argument defines the constraints.

Usage

cat_sim(true, pool, ...)
cat_estimate_default(len, theta, stats, admin, pool, opts)
cat_estimate_mle_step(len, theta, stats, admin, pool, opts)
cat_estimate_eap(len, theta, stats, admin, pool, opts)
cat_estimate_hybrid(len, theta, stats, admin, pool, opts)
cat_stop_default(len, theta, stats, admin, pool, opts)
cat_select_default(len, theta, stats, admin, pool, opts)
cat_select_ccat(len, theta, stats, admin, pool, opts)
cat_select_shadow(len, theta, stats, admin, pool, opts)
# S3 method for cat
print(x, ...)
# S3 method for cat
plot(x, ...)

Arguments

true

the true theta

pool

the item pool (data.frame)

...

additional option parameters. See details.

len

the current test length

theta

the current theta estimate

stats

a matrix of responses and statistics

admin

a data frame of administered item pool

opts

a list of options passed in cat_sim

x

a cat object

Value

cat_sim returns a cat object. See details.

the estimate rule should return a numeric value

the stopping rule should return a boolean with TRUE to stop the CAT

the selection rule should return a list of the selected item and the updated pool

Details

... takes additional option/control parameters from users. min and max are mandatory in order to control the minimum and maximum test length. The selection, estimation, and stopping rules takes the same set of arguments: fucntion(len, theta, stats, admin, pool, opts), which are the current test length, the current theta estimate, the matrix of statistics, the data.frame of administered items, the item pool, and the options. To override default rules, first write new rules using the same function signature and pass the new rule and its required parameters to cat_sim() options. The returned cat object contains the remaining item pool, the administration history, the true and estimated thetas.

Examples

# NOT RUN {
## generate item pool
pool <- model_3pl()$gendata(1, 100)$items
pool$set_id <- sample(1:30, 100, replace=TRUE)
pool$content <- sample(1:3, 100, replace=TRUE)
pool$time <- round(rlnorm(100, mean=4.1, sd=.2))
## randomesque to control exposure in selection
cat_sim(1.0, pool, min=10, max=20, randomesque=5)
## use user-defined ID variable to select item sets
cat_sim(1.0, pool, min=10, max=20, selct_id="set")
## use the mle_step estimation rule
cat_sim(1.0, pool, min=10, max=20, mle_step=.5, 
    estimate_rule=cat_estimate_mle_step)
## use the hybrid estimation rule
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_hybrid)
## use the standard error stopping rule
cat_sim(1.0, pool, min=10, max=20, stop_rule=cat_stop_default, stop_se=.25)
## use the 95% confidence interval classification stopping rule
cat_sim(1.0, pool, min=10, max=20, stop_rule=cat_stop_default, stop_cut=0)
## use the constrained CAT item selection
cat_sim(1.0, pool, min=10, max=20, select_rule=cat_select_ccat, 
    ccat_var='content', ccat_perc=c('1'=.2, '2'=.3, '3'=.5))
## use the constrained CAT item selection with initial randomness
cat_sim(1.0, pool, min=10, max=20, select_rule=cat_select_ccat, 
    ccat_var='content', ccat_perc=c('1'=.2, '2'=.3, '3'=.5), ccat_init_rand=5)
## use the shadow-test CAT 
cons <- data.frame(var='content', level=1:3, min=3, max=5)
cons <- rbind(cons, data.frame(var='time', level=NA, min=55*10, max=65*10))
cat_sim(1.0, pool, min=10, max=10, shadow_constraints=cons, select_id="set_id")
# }