CDM (version 1.4-16)

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 errors, 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)

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

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)

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 it

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.

Value

• A list with following entries
• dat
  A matrix of simulated dichotoumos response data according to the specified CDM model.
• alpha
  Simulated attributes

References

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

See Also

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.

Examples

## simulate DINA and 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 <- sim.din(N = 200, q.matrix, slip, 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 <- sim.din(N = 200, q.matrix, slip, 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 )
sim.din(  q.matrix = q.matrix , alpha = alpha )