sim_hmcdm {hmcdm}

Simulate responses from the specified model (entire cube)

Description

Simulate a cube of responses from the specified model for all persons on items across all time points. Currently available models are DINA, rRUM, and NIDA.

Usage

sim_hmcdm(
  model,
  alphas,
  Q_matrix,
  Design_array,
  itempars = NULL,
  r_stars = NULL,
  pi_stars = NULL,
  Svec = NULL,
  Gvec = NULL
)

Arguments

model

The cognitive diagnostic model under which the item responses are generated

alphas

An N-by-K-by-L array of attribute patterns of all persons across L time points

Q_matrix

A J-by-K of Q-matrix

Design_array

A N-by-J-by-L array indicating whether item j is administered to examinee i at l time point.

itempars

A J-by-2 mat of item parameters (slipping: 1st col, guessing: 2nd col).

r_stars

A J-by-K mat of item penalty parameters for missing skills.

pi_stars

A length J vector of item correct response probability with all requisite skills.

Svec

A length K vector of slipping probability in applying mastered skills

Gvec

A length K vector of guessing probability in applying mastered skills

Value

An array of item responses from the specified model of examinees across all time points.

Examples

## DINA ##
N = nrow(Design_array)
J = nrow(Q_matrix)
thetas_true = rnorm(N, 0, 1.8)
lambdas_true <- c(-2, .4, .055)
Alphas <- sim_alphas(model="HO_joint", 
                    lambdas=lambdas_true, 
                    thetas=thetas_true, 
                    Q_matrix=Q_matrix, 
                    Design_array=Design_array)
itempars_true <- matrix(runif(J*2,.1,.2), ncol=2)

Y_sim <- sim_hmcdm(model="DINA",Alphas,Q_matrix,Design_array,
                   itempars=itempars_true)
                   
## rRUM ##
J = nrow(Q_matrix)
K = ncol(Q_matrix)
Smats <- matrix(runif(J*K,.1,.3),c(J,K))
Gmats <- matrix(runif(J*K,.1,.3),c(J,K))
r_stars <- Gmats / (1-Smats)
pi_stars <- apply((1-Smats)^Q_matrix, 1, prod)

Y_sim <- sim_hmcdm(model="rRUM",Alphas,Q_matrix,Design_array,
                   r_stars=r_stars,pi_stars=pi_stars)

## NIDA ##
K = ncol(Q_matrix)
Svec <- runif(K,.1,.3)
Gvec <- runif(K,.1,.3)

Y_sim <- sim_hmcdm(model="NIDA",Alphas,Q_matrix,Design_array,
                   Svec=Svec,Gvec=Gvec)