aberrance (version 0.3.0)

detect_cp: Detect change point

Description

Detect a single change point.

Usage

detect_cp(
  method,
  cpi,
  psi,
  xi = NULL,
  xi_c = NULL,
  xi_s = NULL,
  x = NULL,
  y = NULL,
  interval = c(-4, 4)
)

Value

A list is returned with the following elements:

stat

A matrix of change point analysis statistics.

cp

A matrix of estimated change points.

Arguments

method

The change point analysis statistic(s) to compute. Options for score-based statistics are:

• "L_S_*" for the likelihood ratio test-based statistic (Shao et al., 2016; Sinharay, 2016; Tu et al., 2023).

• "S_S_*" for the score test-based statistic (Sinharay, 2016; Tu et al., 2023).

• "W_S_*" for the Wald test-based statistic (Sinharay, 2016; Tu et al., 2023).

Options for response time-based statistics are:

• "L_T_*" for the likelihood ratio test-based statistic (Cheng & Shao, 2022).

• "W_T_*" for the Wald test-based statistic (Cheng & Shao, 2022).

Statistics ending in "*" can be computed in different ways. Options are:

• "*" for all possible ways.

• "MAX2" for the maximum of all two-sided statistics in the change point interval.

• "MAX1" for the maximum of all one-sided statistics in the change point interval.

• "MIN1" for the minimum of all one-sided statistics in the change point interval.

cpi

The interval to search for the change point. The lower endpoint must be greater than or equal to 1 and the upper endpoint must be less than the number of items in the test.

psi

A matrix of item parameters. Rows correspond to items and columns to parameters.

xi

A matrix of person parameters. Rows correspond to persons and columns to parameters. If NULL (default), person parameters are estimated using maximum likelihood estimation.

xi_c, xi_s

Arrays of person parameters. The first dimension corresponds to persons, the second dimension to parameters, and the third dimension to change point locations. xi_c is based on the items before or at the change point and xi_s is based on the items after the change point. If NULL (default), person parameters are estimated using maximum likelihood estimation.

x, y

Matrices of raw data. Rows correspond to persons and columns to items. x is for the item scores and y the item log response times.

interval

The interval to search for the person parameters. Default is c(-4, 4).

References

Cheng, Y., & Shao, C. (2022). Application of change point analysis of response time data to detect test speededness. Educational and Psychological Measurement, 82(5), 1031--1062.

Shao, C., Li, J., & Cheng, Y. (2016). Detection of test speededness using change-point analysis. Psychometrika, 81(4), 1118--1141.

Sinharay, S. (2016). Person fit analysis in computerized adaptive testing using tests for a change point. Journal of Educational and Behavioral Statistics, 41(5), 521--549.

Tu, D., Li, Y., & Cai, Y. (2023). A new perspective on detecting performance decline: A change-point analysis based on Jensen-Shannon divergence. Behavior Research Methods, 55(3), 963--980.

Examples

# Setup for Example ---------------------------------------------------------

# Settings
set.seed(0)     # seed for reproducibility
N <- 50         # number of persons
n <- 40         # number of items

# Randomly select 10% speeded examinees
cv <- sample(1:N, size = N * 0.10)

# Assign change point corresponding to 10% speeded items
cp <- n * 0.90
ci <- (cp + 1):n

# Create vector of indicators (1 = speeded, 0 = non-speeded)
ind <- ifelse(1:N %in% cv, 1, 0)

# Example: Item Scores and Response Times -----------------------------------

# Generate person parameters for the 3PL model and lognormal model
xi <- MASS::mvrnorm(
  N,
  mu = c(theta = 0.00, tau = 0.00),
  Sigma = matrix(c(1.00, 0.25, 0.25, 0.25), ncol = 2)
)

# Generate item parameters for the 3PL model and lognormal model
psi <- cbind(
  a = rlnorm(n, meanlog = 0.00, sdlog = 0.25),
  b = NA,
  c = runif(n, min = 0.05, max = 0.30),
  alpha = runif(n, min = 1.50, max = 2.50),
  beta = NA
)

# Generate positively correlated difficulty and time intensity parameters
psi[, c("b", "beta")] <- MASS::mvrnorm(
  n,
  mu = c(b = 0.00, beta = 3.50),
  Sigma = matrix(c(1.00, 0.20, 0.20, 0.15), ncol = 2)
)

# Simulate uncontaminated data
dat <- sim(psi, xi)
x <- dat$x
y <- dat$y

# Modify contaminated data by changing the item scores and response times
x[cv, ci] <- rbinom(length(cv) * length(ci), size = 1, prob = 0.25)
y[cv, ci] <- runif(length(cv) * length(ci), min = log(1), max = log(10))

# Detect change point
out <- detect_cp(
  method = c("L_S_MAX1", "L_T_MIN1"),
  cpi = c(1, n - 1),
  psi = psi,
  x = x,
  y = y
)