detect_ac {aberrance}

Detect answer copying

Description

Detect answer copying for all possible source-copier pairs.

Usage

detect_ac(
  method,
  psi,
  xi = NULL,
  x = NULL,
  d = NULL,
  r = NULL,
  interval = c(-4, 4),
  alpha = 0.05
)

Arguments

method

The answer copying statistic(s) to compute. Options for score-based statistics are:

• "OMG_S" for the conditional \omega statistic (Wollack, 1997).

• "GBT_S" for the conditional GBT statistic (van der Linden & Sotaridona, 2006).

Options for score and distractor-based statistics are:

• "OMG_SD" for the conditional \omega statistic (Wollack, 1997).

• "GBT_SD" for the conditional GBT statistic (van der Linden & Sotaridona, 2006).

Options for response-based statistics are:

• "OMG_R" for the conditional \omega statistic (Wollack, 1997).

• "GBT_R" for the conditional GBT statistic (van der Linden & Sotaridona, 2006).

psi

A matrix of item parameters.

xi

A matrix of person parameters. If NULL (default), person parameters are estimated using maximum likelihood estimation.

x, d, r

Matrices of raw data. x is for the item scores, d the item distractors, and r the item responses.

interval

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

alpha

Value(s) between 0 and 1 indicating the significance level(s) used for flagging. Default is 0.05.

Value

A list is returned with the following elements:

stat

A matrix of answer copying statistics.

pval

A matrix of p-values.

flag

An array of flagging results. The first dimension corresponds to source-copier pairs, the second dimension to methods, and the third dimension to significance levels.

References

van der Linden, W. J., & Sotaridona, L. (2006). Detecting answer copying when the regular response process follows a known response model. Journal of Educational and Behavioral Statistics, 31(3), 283–304.

Wollack, J. A. (1997). A nominal response model approach for detecting answer copying. Applied Psychological Measurement, 21(4), 307–320.

See Also

detect_as() to detect answer similarity.

Examples

# Setup for Examples 1 to 3 -------------------------------------------------

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

# Randomly select 10% sources and 10% copiers
s <- sample(1:N, size = N * 0.10)
c <- sample(setdiff(1:N, s), size = N * 0.10)

# Create vector of indicators (1 = copying pair, 0 = non-copying pair)
pair <- t(combn(N, 2))
pair <- rbind(pair, pair[, 2:1])
ind <- ifelse(1:nrow(pair) %in% apply(
  rbind(cbind(s, c), cbind(c, s)), 1, function(p)
  which(pair[, 1] == p[1] & pair[, 2] == p[2])), 1, 0)
names(ind) <- paste(pair[, 1], pair[, 2], sep = "-")

# Example 1: Item Scores ----------------------------------------------------

# Generate person parameters for the 3PL model
xi <- cbind(theta = rnorm(N, mean = 0.00, sd = 1.00))

# Generate item parameters for the 3PL model
psi <- cbind(
  a = rlnorm(n, meanlog = 0.00, sdlog = 0.25),
  b = rnorm(n, mean = 0.00, sd = 1.00),
  c = runif(n, min = 0.05, max = 0.30)
)

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

# Modify contaminated data by replacing 40% of the copier scores with source
# scores
for (v in 1:length(c)) {
  ci <- sample(1:n, size = n * 0.40)
  x[c[v], ci] <- x[s[v], ci]
}

# Detect answer copying
out <- detect_ac(
  method = c("OMG_S", "GBT_S"),
  psi = psi,
  x = x
)

# Example 2: Item Scores and Distractors ------------------------------------

# Generate person parameters for the nested logit model
xi <- MASS::mvrnorm(
  N,
  mu = c(theta = 0.00, eta = 0.00),
  Sigma = matrix(c(1.00, 0.80, 0.80, 1.00), ncol = 2)
)

# Generate item parameters for the nested logit model
psi <- cbind(
  a = rlnorm(n, meanlog = 0.00, sdlog = 0.25),
  b = rnorm(n, mean = 0.00, sd = 1.00),
  c = runif(n, min = 0.05, max = 0.30),
  lambda1 = rnorm(n, mean = 0.00, sd = 1.00),
  lambda2 = rnorm(n, mean = 0.00, sd = 1.00),
  lambda3 = rnorm(n, mean = 0.00, sd = 1.00),
  zeta1 = rnorm(n, mean = 0.00, sd = 1.00),
  zeta2 = rnorm(n, mean = 0.00, sd = 1.00),
  zeta3 = rnorm(n, mean = 0.00, sd = 1.00)
)

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

# Modify contaminated data by replacing 40% of the copier scores and
# distractors with source scores and distractors
for (v in 1:length(c)) {
  ci <- sample(1:n, size = n * 0.40)
  x[c[v], ci] <- x[s[v], ci]
  d[c[v], ci] <- d[s[v], ci]
}

# Detect answer copying
out <- detect_ac(
  method = c("OMG_S", "GBT_S", "OMG_SD", "GBT_SD"),
  psi = psi,
  x = x,
  d = d
)

# Example 3: Item Responses -------------------------------------------------

# Generate person parameters for the nominal response model
xi <- cbind(eta = rnorm(N, mean = 0.00, sd = 1.00))

# Generate item parameters for the nominal response model
psi <- cbind(
  lambda1 = rnorm(n, mean = -0.50, sd = 0.50),
  lambda2 = rnorm(n, mean = -0.50, sd = 0.50),
  lambda3 = rnorm(n, mean = -0.50, sd = 0.50),
  lambda4 = rnorm(n, mean = 1.50, sd = 0.50),
  zeta1 = rnorm(n, mean = -0.50, sd = 0.50),
  zeta2 = rnorm(n, mean = -0.50, sd = 0.50),
  zeta3 = rnorm(n, mean = -0.50, sd = 0.50),
  zeta4 = rnorm(n, mean = 1.50, sd = 0.50)
)

# Simulate uncontaminated data
r <- sim(psi, xi)$r

# Modify contaminated data by replacing 40% of the copier responses with
# source responses
for (v in 1:length(c)) {
  ci <- sample(1:n, size = n * 0.40)
  r[c[v], ci] <- r[s[v], ci]
}

# Detect answer copying
out <- detect_ac(
  method = c("OMG_R", "GBT_R"),
  psi = psi,
  r = r
)