Data Simulation Tool for DINA, DINO and mixed DINA and DINO Data
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.
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)N |
A numeric value specifying the number N of requested
response patterns. If |
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 |
Sigma |
A matrix of dimension |
rule |
An optional character string or vector of character strings
specifying the model rule that is used. The character strings must be
of |
alpha |
A matrix of attribute patterns which can be given as an input
instead of underlying latent variables. If |
A list with following entries
dat |
A matrix of simulated dichotomous response data according to the specified CDM model. |
alpha |
Simulated attributes |
Rupp, A. A., Templin, J. L., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.
Data-sim for artificial date set simulated with the help of this
method; plot.din, the S3 method for plotting objects of
the class din; summary.din, the S3
method for summarizing objects of the class din, which
creates objects of the class summary.din;
print.summary.din, the S3 method for printing
objects of the class summary.din; din,
the main function for DINA and DINO parameter estimation,
which creates objects of the class din. See also
CDM-package for general information about this package.
See sim_model for a general simulation function.
#############################################################################
## 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$alpha )
## [,1] [,2]
## [1,] 1 1
## [2,] 1 1
## [3,] 1 1
## [4,] 1 1
## [5,] 1 1
## [6,] 1 0
# simulate data based on given attributes
# -> 5 persons with 2 attributes -> see the Q-matrix above
alpha <- matrix( c(1,0,1,0,1,1,0,1,1,1),
nrow=5,ncol=2, byrow=TRUE )
CDM::sim.din( q.matrix=q.matrix, alpha=alpha )
## Not run:
#############################################################################
# EXAMPLE 2: Simulation based on attribute vectors
#############################################################################
set.seed(76)
# define Q-matrix
Qmatrix <- matrix(c(1,0,1,0,1,0,0,1,0,1,0,1,1,1,1,1), 8, 2, byrow=TRUE)
colnames(Qmatrix) <- c("Attr1","Attr2")
# define skill patterns
alpha.patt <- matrix(c(0,0,1,0,0,1,1,1), 4,2,byrow=TRUE )
AP <- nrow(alpha.patt)
# define pattern probabilities
alpha.prob <- c( .20, .40, .10, .30 )
# simulate alpha latent responses
N <- 1000 # number of persons
ind <- sample( x=1:AP, size=N, replace=TRUE, prob=alpha.prob)
alpha <- alpha.patt[ ind, ] # (true) latent responses
# define guessing and slipping parameters
guess <- c(.26,.3,.07,.23,.24,.34,.05,.1)
slip <- c(.05,.16,.19,.03,.03,.19,.15,.05)
# simulation of the DINA model
dat <- CDM::sim.din(N=0, q.matrix=Qmatrix, guess=guess,
slip=slip, alpha=alpha)$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
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.