Oracle Model Recovery

2021-06-12

Overview

Within this vignette, we will show how to estimate and recover the oracle model.

EDINA

The following model recovery routine is based on the de La Torre (2009).

Load Package

library("edm")

message("Running simulation with edm v",
        as.character(utils::packageVersion("edm")),
        sep = "")

Setup Simulation

# Assign simulation parameters
N = 200        # Sample Size
K = 5          # Number of Attributes
J = 30         # Number of Items
delta0 = rep(1, 2 ^ K)

# Creating Q matrix
Q = matrix(rep(diag(K), 2), 2 * K, K, byrow = TRUE)
for (mm in 2:K) {
  temp = combn(seq_len(K), m = mm)
  tempmat = matrix(0, ncol(temp), K)
  for (j in seq_len(ncol(temp)))
    tempmat[j, temp[, j]] = 1
  Q = rbind(Q, tempmat)
}
Q = Q[seq_len(J), ]

# Setting item parameters and generating attribute profiles
ss = gs = rep(.2, J)
PIs = rep(1 / (2 ^ K), 2 ^ K)
CLs = c((1:(2 ^ K)) %*% rmultinom(n = N, size = 1, prob = PIs))

# Defining matrix of possible attribute profiles
As = rep(0, K)
for (j in seq_len(K)) {
  temp = combn(1:K, m = j)
  tempmat = matrix(0, ncol(temp), K)
  for (j in seq_len(ncol(temp)))
    tempmat[j, temp[, j]] = 1
  As = rbind(As, tempmat)
}
As = as.matrix(As)

# Sample true attribute profiles
Alphas = As[CLs, ]

Simulate the Data

# Simulate data under DINA model
Y_sim = sim_dina(Alphas, Q, ss, gs)

Estimation Routine

# Estimating Q
burnin = 20000
chain_length = 10000
system.time({
  recovery_edina_model = edina(Y_sim, K, burnin, chain_length)
})

View Q Matrix

est_q_matrix = extract_q_matrix(recovery_edina_model)
est_binary_q_matrix = extract_q_matrix(recovery_edina_model, binary_q = TRUE)

Q
est_binary_q_matrix

ErRUM

Setup Simulation Parameters

set.seed(217)
# Define Simulation Parameters
N = 1000     # number of individuals
J = 6        # number of items
K = 2        # number of attributes

As = simcdm::pi_reference(K) # matrix where rows represent attribute classes

pis = c(.1, .2, .3, .4) # pi
Q = rbind(c(1,0),
           c(0,1),
           c(1,0),
           c(0,1),
           c(1,1),
           c(1,1))
pistar = rep(.9, J)    # pistar
rstar = .5 * Q          # rstar
alpha = As[sample(1:(K ^ 2), N, replace = TRUE, pis),]

Simulate ErRUM data under a model

# Simulate data
Y = sim_rrum(Q, rstar, pistar, alpha)

Estimate the simulated ErRUM model

# Recover simulation parameters with Gibbs Sampler
errum(Y, K)