simcdm (version 0.1.2)

sim_dina_class: Simulate Binary Responses for a DINA Model

Description

Generate the dichotomous item matrix for a DINA Model.

Usage

sim_dina_class(N, J, CLASS, ETA, gs, ss)

Value

A dichotomous item matrix with dimensions \(N \times J\).

Arguments

N

Number of Observations

J

Number of Assessment Items

CLASS

Does the individual possess all the necessary attributes?

ETA

\(\eta\) Matrix containing indicators.

gs

A vec describing the probability of guessing or the probability subject correctly answers item \(j\) when at least one attribute is lacking.

ss

A vec describing the probability of slipping or the probability of an incorrect response for individuals with all of the required attributes

Author

Steven Andrew Culpepper and James Joseph Balamuta

See Also

sim_dina_attributes() and sim_dina_items()

Examples

# Set 
N       = 100
rho     = 0
K       = 3

# Fixed Number of Assessment Items for Q
J = 18

# Specify Q
qbj = c(4, 2, 1, 4, 2, 1, 4, 2, 1, 6, 5, 3, 6, 5, 3, 7, 7, 7)

# Fill Q Matrix
Q = matrix(, J, K)
for (j in seq_len(J)) {
  Q[j,] = attribute_inv_bijection(K, qbj[j])
}

# Item parm vals
ss = gs = rep(.2, J)

# Generating attribute classes depending on correlation
if (rho == 0) {
  PIs = rep(1 / (2 ^ K), 2 ^ K)
  CLs = c(seq_len(2 ^ K) %*% rmultinom(n = N, size = 1, prob = PIs)) - 1
}

if (rho > 0) {
  Z = matrix(rnorm(N * K), N, K)
  Sig = matrix(rho, K, K)
  diag(Sig) = 1
  X = Z %*% chol(Sig)
  thvals = matrix(rep(0, K), N, K, byrow = T)
  Alphas = 1 * (X > thvals)
  CLs = Alphas %*% attribute_bijection(K)
}

# Simulate data under DINA model
ETA = sim_eta_matrix(K, J, Q)
Y_sim = sim_dina_class(N, J, CLs, ETA, gs, ss)