sim.din: Data Simulation Tool for DINA, DINO and mixed DINA and DINO Data

Description

sim.din can be used to simulate dichotomous response data according to a CDM model. The model type DINA or DINO can be specified item wise. The number of items, the sample size, and two parameters for each item, the slipping and guessing parameters, can be set explicitly.

Usage

sim.din(N=0, q.matrix, guess=rep(0.2, nrow(q.matrix)),
    slip=guess, mean=rep(0, ncol(q.matrix)), Sigma=diag(ncol(q.matrix)),
    rule="DINA", alpha=NULL)

Value

A list with following entries

dat: A matrix of simulated dichotomous response data according to the specified CDM model.
alpha: Simulated attributes

Arguments

N: A numeric value specifying the number \(N\) of requested response patterns. If alpha is specified, then N is set by default to 0.
q.matrix: A required binary \(J \times K\) matrix describing which of the \(K\) attributes are required, coded by 1, and which attributes are not required, coded by 0, to master the items.
guess: An optional vector of guessing parameters. Default is 0.2 for each item.
slip: An optional vector of slipping parameters. Default is 0.2 for each item.
mean: A numeric vector of length ncol(q.matrix) indicating the mean vector of the continuous version of the dichotomous skill vector. Default is rep(0, length=ncol(q.matrix)). That is, having a probability of 0.5 for possessing each of the attributes.
Sigma: A matrix of dimension ncol(q.matrix) times ncol(q.matrix) specifying the covariance matrix of the continuous version of the dichotomous skill vector (i.e., the tetrachoric correlation of the dichotomous skill vector). Default is diag( 1, ncol(q.matrix)). That is, by default the possession of the attributes is assumed to be uncorrelated.
rule: An optional character string or vector of character strings specifying the model rule that is used. The character strings must be of "DINA" or "DINO". If a vector of character strings is specified, implying an itemwise condensation rule, the vector must be of length \(J\), which is the number of used items. The default is the condensation rule "DINA" for all items.
alpha: A matrix of attribute patterns which can be given as an input instead of underlying latent variables. If alpha is not NULL, then mean and Sigma are ignored.

References

Rupp, A. A., Templin, J. L., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Examples

Run this code

#############################################################################
## EXAMPLE 1: simulate DINA/DINO data according to a tetrachoric correlation
#############################################################################

# define Q-matrix for 4 items and 2 attributes
q.matrix <- matrix(c(1,0,0,1,1,1,1,1), ncol=2, nrow=4)

# Slipping parameters
slip <- c(0.2,0.3,0.4,0.3)

# Guessing parameters
guess <- c(0,0.1,0.05,0.2)

set.seed(1567) # fix random numbers
dat1 <- CDM::sim.din(N=200, q.matrix, slip=slip, guess=guess,
  # Possession of the attributes with high probability
  mean=c(0.5,0.2),
  # Possession of the attributes is weakly correlated
  Sigma=matrix(c(1,0.2,0.2,1), ncol=2), rule="DINA")$dat
head(dat1)

set.seed(15367) # fix random numbers
res <- CDM::sim.din(N=200, q.matrix, slip=slip, guess=guess, mean=c(0.5,0.2),
         Sigma=matrix(c(1,0.2,0.2,1), ncol=2), rule="DINO")

# extract simulated data
dat2 <- res$dat
# extract attribute patterns
head( res$alpha )
  ##        [,1] [,2]
  ##   [1,]    1    1
  ##   [2,]    1    1
  ##   [3,]    1    1
  ##   [4,]    1    1
  ##   [5,]    1    1
  ##   [6,]    1    0

#  simulate data based on given attributes
#          -> 5 persons with 2 attributes -> see the Q-matrix above
alpha <- matrix( c(1,0,1,0,1,1,0,1,1,1),
    nrow=5,ncol=2, byrow=TRUE )
CDM::sim.din(  q.matrix=q.matrix, alpha=alpha )

if (FALSE) {
#############################################################################
# EXAMPLE 2: Simulation based on attribute vectors
#############################################################################
set.seed(76)
# define Q-matrix
Qmatrix <- matrix(c(1,0,1,0,1,0,0,1,0,1,0,1,1,1,1,1), 8, 2, byrow=TRUE)
colnames(Qmatrix) <- c("Attr1","Attr2")
# define skill patterns
alpha.patt <- matrix(c(0,0,1,0,0,1,1,1), 4,2,byrow=TRUE )
AP <- nrow(alpha.patt)
# define pattern probabilities
alpha.prob <- c( .20, .40, .10, .30 )
# simulate alpha latent responses
N <- 1000     # number of persons
ind <- sample( x=1:AP, size=N, replace=TRUE, prob=alpha.prob)
alpha <- alpha.patt[ ind, ]    # (true) latent responses
# define guessing and slipping parameters
guess <- c(.26,.3,.07,.23,.24,.34,.05,.1)
slip <- c(.05,.16,.19,.03,.03,.19,.15,.05)
# simulation of the DINA model
dat <- CDM::sim.din(N=0, q.matrix=Qmatrix, guess=guess,
              slip=slip, alpha=alpha)$dat
# estimate model
res <- CDM::din( dat, q.matrix=Qmatrix )
# extract maximum likelihood estimates for individual classifications
est <- paste( res$pattern$mle.est )
# calculate classification accuracy
mean( est==apply( alpha, 1, FUN=function(ll){ paste0(ll[1],ll[2] ) } ) )
  ##   [1] 0.935

#############################################################################
# EXAMPLE 3: Simulation based on already estimated DINA model for data.ecpe
#############################################################################

dat <- CDM::data.ecpe$data
q.matrix <- CDM::data.ecpe$q.matrix

#***
# (1) estimate DINA model
mod <- CDM::din( data=dat[,-1], q.matrix=q.matrix, rule="DINA")

#***
# (2) simulate data according to DINA model
set.seed(977)
# number of subjects to be simulated
n <- 3000
# simulate attribute patterns
probs <- mod$attribute.patt$class.prob   # probabilities
patt <- mod$attribute.patt.splitted      # response patterns
alpha <- patt[ sample( 1:(length(probs) ), n, prob=probs, replace=TRUE), ]
# simulate data using estimated item parameters
res <- CDM::sim.din(N=n, q.matrix=q.matrix, guess=mod$guess$est, slip=mod$slip$est,
              rule="DINA", alpha=alpha)
# extract data
dat <- res$dat
}