sim_rrum_items: Generate data from the rRUM
In simcdm: Simulate Cognitive Diagnostic Model ('CDM') Data

Description Usage Arguments Value Author(s) References Examples

Randomly generate response data according to the reduced Reparameterized Unified Model (rRUM).

1	sim_rrum_items(Q, rstar, pistar, alpha)

`Q`	A `matrix` with J rows and K columns indicating which attributes are required to answer each of the items, where J represents the number of items and K the number of attributes. An entry of 1 indicates attribute k is required to answer item j. An entry of one indicates attribute k is not required.
`rstar`	A `matrix` a matrix with J rows and K columns indicating the penalties for failing to have each of the required attributes, where J represents the number of items and K the number of attributes. `rstar` and `Q` must share the same 0 entries.
`pistar`	A `vector` of length J indicating the probabiliies of answering each item correctly for individuals who do not lack any required attribute, where J represents the number of items.
`alpha`	A `matrix` with N rows and K columns indicating the subjects attribute acquisition, where K represents the number of attributes. An entry of 1 indicates individual i has attained attribute k. An entry of 0 indicates the attribute has not been attained.

Y A matrix with N rows and J columns indicating the indviduals' responses to each of the items, where J represents the number of items.

Steven Andrew Culpepper, Aaron Hudson, and James Joseph Balamuta

Culpepper, S. A. & Hudson, A. (In Press). An improved strategy for Bayesian estimation of the reduced reparameterized unified model. Applied Psychological Measurement.

Hudson, A., Culpepper, S. A., & Douglas, J. (2016, July). Bayesian estimation of the generalized NIDA model with Gibbs sampling. Paper presented at the annual International Meeting of the Psychometric Society, Asheville, North Carolina.

# Set seed for reproducibility
set.seed(217)

# Define Simulation Parameters
N = 1000 # number of individuals
J = 6 # number of items
K = 2 # number of attributes

# Matrix where rows represent attribute classes
As = attribute_classes(K) 

# Latent Class probabilities
pis = c(.1, .2, .3, .4) 

# Q Matrix
Q = rbind(c(1, 0),
          c(0, 1),
          c(1, 0),
          c(0, 1),
          c(1, 1),
          c(1, 1)
    )
    
# The probabiliies of answering each item correctly for individuals 
# who do not lack any required attribute
pistar = rep(.9, J)

# Penalties for failing to have each of the required attributes
rstar  = .5 * Q

# Randomized alpha profiles
alpha  = As[sample(1:(K ^ 2), N, replace = TRUE, pis),]

# Simulate data
rrum_items = sim_rrum_items(Q, rstar, pistar, alpha)