simcdmWithin this document, we highlight the different features of the simcdm package as it relates to simulating cognitive diagnostic modeling data.
For consistency, we aim to use the following notation.
Denoting individuals:
Denoting items:
Denoting attributes:
Denoting the skill/attribute “Q” matrix:
To use simcdm, please load the package.
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 / AttributesSimulate 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 1Create the ideal response matrix for each trait (\(J\) items by \(2^K\) latent classes).
# Set a seed for reproducibility
set.seed(4421)
# Simulate an eta matrix
eta = sim_eta_matrix(K, J, Q)
eta## [,1] [,2] [,3] [,4]
## [1,] 0 0 1 1
## [2,] 0 0 1 1
## [3,] 0 1 0 1
## [4,] 0 1 0 1
## [5,] 0 1 0 1
## [6,] 0 1 0 1
## [7,] 0 0 0 1
## [8,] 0 0 1 1
## [9,] 0 0 1 1
## [10,] 0 1 0 1Generate 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 0Simulations 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)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 0Simulate 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 0The 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),]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