irt (version 0.2.9)

score_info: Calculate Score Information Function

Description

This function calculates the score information function of a given CAT test. Ideally, a large number of simulees (say 1,000) will be simulated at each theta level equally spaced along a large theta range (like [-4, 4]). The score information function at each theta will be calculated using the formulas 11-2 and 11-3 presented in Sands, Waters and McBride (1997, pages 127-128). Also see Lord (1980), Eqn. 10-7.

For example if 1000 examinees simulated at each of the following theta values (-3, -2, -1, 0, 1, 2, 3), the function will not calculate score information values at theta = -3 and theta = 3. Score information values at second values to the edges (i.e. theta = -2 and theta = 2) will be calculated using Equation 11-2 of Sands et.al. (1997). The rest of the score information values (at theta = -1, 0, 1) will be calculated using equation 11-3 (page 128).

Usage

score_info(true_theta, est_theta, bins = NULL)

Value

A data frame of true theta values and score information value at each theta value will be returned.

Arguments

true_theta

A vector of true theta values.

est_theta

A vector of estimated theta values.

bins

The number of bins true theta values should be grouped into. Ideally, this value is NULL and equal number of simulees are already in bins, and within each bin true_theta values are equal to each other. If these conditions are not satisfied, a bin value can be supplied.

Author

Emre Gonulates

References

Lord, F. M. (1980). Applications of item response theory to practical testing problems. Routledge.

Sands, W. A., Waters, B. K., & McBride, J. R. (1997). Computerized adaptive testing: From inquiry to operation. American Psychological Association.

Examples

ip <- generate_ip(n = 30)
cd <- create_cat_design(ip = ip, next_item_rule = 'mfi',
                        termination_rule = 'max_item',
                        termination_par = list(max_item = 10))
# The following true_theta example is not ideal. For more informative score
# score information functions you can use more bins and more simulees like:
# rep(seq(-4, 4, .1), each = 1000)
true_theta <- rep(seq(-3, 3, 1), each = 10)
cat_data <- cat_sim(true_ability = true_theta, cd = cd)
dtf <- summary(cat_data)

s_info <- score_info(true_theta = dtf$true_ability,
                     est_theta = dtf$est_ability)
s_info