irt (version 0.2.9)

cusum_single: CUSUM based statistics for one examinee

Description

CUSUM based statistics for one examinee

Usage

cusum_single(ip, resp, theta = NULL, method = "T1", initial_theta_est = NULL)

Value

The function will return a data frame consist of two columns:

Cp column for \(C^+\) values and Cn column for \(C^-\)

values.

Arguments

ip

An Itempool-class object

resp

a response vector, where the order of items represent the administration order.

theta

A vector or length 1 or length equal to the number of items administered.

method

Method of calculating the CUSUM statistic. Choices are: "T1", "T2", "T3", "T4", "T5", "T6", "T7" and "T8". "T1" through "T4" uses the ability estimate each stage of the test. "T5" through "T8" uses the final ability estimate and needs only one theta estimate.

initial_theta_est

For CAT, the initial theta estimate of an examinee. For CAT, if theta = NULL, this initial theta estimate will be used to calculate \(T_1\), \(C^-_1\) and \(C^+_1\). For CAT, this value should be provided. By this way for the calculation of \(T_1\), \(C^-_1\) and \(C^+_1\), \(\hat \theta_{n-1}\) will be used.

If it's value is NULL and theta = NULL, then for the calculation of \(T_1\), \(C^-_1\) and \(C^+_1\), \(\hat \theta_{n}\) will be used.

The default value is NULL

Author

Emre Gonulates

References

van Krimpen-Stoop, E. M. L. A., & Meijer, R. R. (2000). Detecting person-misfit in adaptive testing using statistical process control techniques. In W. J. van der Linden & C. A. W. Glas (Eds.), Computerized adaptive testing: Theory and practice (pp. 210–219). Kluwer.

Xiaofeng Yu & Ying Cheng (2020): A Comprehensive Review and Comparison of CUSUM and Change-Point-Analysis Methods to Detect Test Speededness, Multivariate Behavioral Research, <doi:10.1080/00273171.2020.1809981>

Examples

# Example from Table 1 (p.4) of Yu and Cheng (2020):
ip <- itempool(a = c(0.976, 0.973, 0.871, 0.768, 0.94, 1.109, 1.063, 0.888,
                     0.648, 0.733, 0.8, 0.823, 0.611, 0.965, 1.052, 0.937,
                     0.894, 0.72, 0.686, 0.608),
               b = c(-0.693, 0.6, -0.607, -0.637, -1.095, -0.202, -0.679,
                     0.058, -0.822, -0.768, -0.737, -1.158, -0.294, -0.856,
                     -0.833, -0.613, -0.151, -0.614, -0.07, -0.806),
               c = c(0.371, 0.224, 0.159, 0.377, 0.159, 0.146, 0.181, 0.251,
                     0.179, 0.214, 0.312, 0.224, 0.246, 0.225, 0.155, 0.166,
                     0.456, 0.327, 0.112, 0.169),
               D = 1.7)
resp <- c(0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1)
theta <- -0.06

cusum_single(ip, resp, theta, method = "T5")