Chapter 2 simcdm: Simulate Cognitive Diagnostic Model Data
2.1 Matrix Simulation
Simulations within this section are done underneath the following settings.
# Set a seed for reproducibility
set.seed(888)
# Setup Parameters
N = 15 # Number of Examinees / Subjects
J = 10 # Number of Items
K = 2 # Number of Skills / Attributes2.1.1 Attribute profile simulation
Generate latent attribute profile classes (\(2^K\) latent classes by \(K\) skills).
## [,1] [,2]
## [1,] 0 0
## [2,] 0 1
## [3,] 1 0
## [4,] 1 1Generate latent attribute profile class for each subject (\(N\) subjects by \(K\) skills).
# Set a seed for reproducibility
set.seed(5126)
# Create attributes for a subject
subject_alphas = sim_subject_attributes(N, K)
subject_alphas## [,1] [,2]
## [1,] 0 0
## [2,] 1 1
## [3,] 1 0
## [4,] 1 1
## [5,] 0 0
## [6,] 0 1
## [7,] 0 1
## [8,] 1 0
## [9,] 0 1
## [10,] 0 1
## [11,] 0 1
## [12,] 0 1
## [13,] 1 0
## [14,] 0 0
## [15,] 1 02.1.2 Identifiable Q Matrix Simulation
Simulate an identifiable \(Q\) matrix (\(J\) items by \(K\) skills).
# Set a seed for reproducibility
set.seed(1512)
# Simulate an identifiable Q matrix
Q = sim_q_matrix(J, K)
Q## [,1] [,2]
## [1,] 1 0
## [2,] 1 0
## [3,] 0 1
## [4,] 0 1
## [5,] 0 1
## [6,] 0 1
## [7,] 1 1
## [8,] 1 0
## [9,] 1 0
## [10,] 0 12.2 DINA Simulation
Simulations within this section are done underneath the following settings.
# Set a seed for reproducibility
set.seed(888)
# Setup Parameters
N = 15 # Number of Examinees / Subjects
J = 10 # Number of Items
K = 2 # Number of Skills / Attributes
# Assign slipping and guessing values for each item
ss = gs = rep(.2, J)
# Simulate identifiable Q matrix
Q = sim_q_matrix(J, K)
# Simulate subject attributes
subject_alphas = sim_subject_attributes(N, K)2.2.1 DINA Item Simulation
Simulate item data, \(Y\), under DINA model (\(N\) by \(J\))
# Set a seed for reproducibility
set.seed(2019)
# Simulate items under the DINA model
items_dina = sim_dina_items(subject_alphas, Q, ss, gs)
items_dina## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 1 0 0 0 1 1
## [2,] 1 1 1 0 1 1 1 1 0 1
## [3,] 0 0 0 0 1 0 0 0 1 1
## [4,] 1 1 1 0 0 0 1 1 1 0
## [5,] 1 1 1 1 1 1 1 1 1 1
## [6,] 1 1 1 1 0 1 0 1 0 1
## [7,] 0 0 0 1 1 0 0 0 0 1
## [8,] 1 0 1 1 1 0 0 1 0 1
## [9,] 1 1 1 1 0 1 1 1 1 1
## [10,] 0 1 0 1 1 0 0 0 1 1
## [11,] 1 1 1 1 1 1 1 0 1 1
## [12,] 0 0 0 0 1 0 0 0 1 0
## [13,] 0 0 0 0 1 0 0 0 1 1
## [14,] 1 0 0 1 1 0 0 0 0 0
## [15,] 1 1 0 1 0 0 1 1 0 02.2.2 DINA Attribute Simulation
Simulate attribute data under DINA model (\(N\) by \(J\))
# Set a seed for reproducibility
set.seed(51823)
# Simulate attributes under the DINA model
attributes = sim_dina_attributes(subject_alphas, Q)
attributes## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 1 0 0 0 1 1
## [2,] 1 1 1 1 1 1 1 1 1 1
## [3,] 0 0 0 1 1 0 0 0 1 1
## [4,] 1 1 1 0 0 0 1 1 0 0
## [5,] 1 1 1 1 1 1 1 1 1 1
## [6,] 1 1 1 1 1 1 1 1 1 1
## [7,] 0 0 0 1 1 0 0 0 1 1
## [8,] 1 1 1 1 1 1 1 1 1 1
## [9,] 1 1 1 1 1 1 1 1 1 1
## [10,] 0 0 0 1 1 0 0 0 1 1
## [11,] 1 1 1 1 1 1 1 1 1 1
## [12,] 0 0 0 1 1 0 0 0 1 1
## [13,] 0 0 0 1 1 0 0 0 1 1
## [14,] 0 0 0 0 0 0 0 0 0 0
## [15,] 1 1 1 0 0 0 1 1 0 02.3 rRUM Simulation
The rRUM simulations are done using the following settings.
# Set a seed for reproducibility
set.seed(888)
# Setup Parameters
N = 15 # Number of Examinees / Subjects
J = 10 # Number of Items
K = 2 # Number of Skills / Attributes
# The probabilities of answering each item correctly for individuals
# who do not lack any required attribute
pistar = rep(.9, J)
# Simulate an identifiable Q matrix
Q = sim_q_matrix(J, K)
# Penalties for failing to have each of the required attributes
rstar = .5 * Q
# Latent Class Probabilities
pis = c(.1, .2, .3, .4)
# Generate latent attribute profile with custom probability (N subjects by K skills)
subject_alphas = sim_subject_attributes(N, K, prob = pis)
# Equivalent to:
# class_alphas = attribute_classes(K)
# subject_alphas = class_alphas[sample(2 ^ K, N, replace = TRUE, prob = pis),]2.3.1 Simulate rRUM items
Simulate rRUM item data \(Y\) (\(N\) by \(J\))
# Set a seed for reproducibility
set.seed(912)
# Generate rRUM items
rrum_items = sim_rrum_items(Q, rstar, pistar, subject_alphas)
rrum_items## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 1 1 1 0 1 0 1 1 1 0
## [2,] 1 1 0 1 1 0 1 0 0 0
## [3,] 0 1 1 1 0 1 1 1 0 0
## [4,] 0 1 1 1 0 1 1 1 1 0
## [5,] 1 1 0 0 1 0 1 1 1 0
## [6,] 1 1 1 1 0 0 1 1 0 1
## [7,] 1 0 1 0 1 0 0 0 0 1
## [8,] 0 0 1 0 0 0 1 0 0 1
## [9,] 0 1 0 1 1 1 0 1 1 0
## [10,] 1 1 1 1 0 0 0 1 1 0
## [11,] 1 1 1 0 0 0 1 1 0 1
## [12,] 0 1 0 1 1 0 1 1 1 1
## [13,] 1 0 1 1 1 0 1 1 1 1
## [14,] 1 0 1 1 1 1 1 1 1 1
## [15,] 0 0 1 0 1 1 1 1 1 1