mirt (version 0.1-19)

simdata: Simulate response patterns from an underlying multivariate normal distribution

Description

Simulates response patterns for compensetory and noncompensatory MIRT models from multivariate normally distributed factor ($\theta$) scores, or from a user input matrix of $\theta$'s.

Usage

simdata(a, d, N, sigma = NULL, mu = NULL, guess = 0, partcomp = FALSE, 
  factor.loads = FALSE, Theta = NULL)

Arguments

a

a matrix of slope parameters. If slopes are to be constrained to zero then use NA. a may also be a similar matrix specifying factor loadings if factor.loads = TRUE

d

a matrix of intercepts. The matrix should have as many columns as the item with the largest number of categories, and filled empty locations with NA

N

sample size

guess

a vector of guessing parameters for each item; only applicable for dichotomous items. Must be either a scalar value that will affect all of the dichotomous items, or a vector with as many values as to be simulated items

sigma

a covariance matrix of the underlying distribution. Default is the identity matrix

mu

a mean vector of the underlying distribution. Defualt is a vector of zeros

partcomp

a logical vector used to sepcify which items are to be treated as parially compensatory items (see Reckase, 2009), and single values are repeated for each item. Note that when simulating noncompensatory data the slope parameters must equal the number of i

factor.loads

logical; are the slope parameters in a in the factor loadings metric?

Theta

a user specified matrix of the underlying ability parameters, where nrow(Theta) == N and ncol(Theta) == ncol(a)

Details

Returns a data matrix simulated from the parameters.

References

Reckase, M. D. (2009). Multidimensional Item Response Theory. New York: Springer.

Examples

###Parameters from Reckase (2009), p. 153
a <- matrix(c(
 .7471, .0250, .1428,
 .4595, .0097, .0692,
 .8613, .0067, .4040,
1.0141, .0080, .0470,
 .5521, .0204, .1482,
1.3547, .0064, .5362,
1.3761, .0861, .4676,
 .8525, .0383, .2574,
1.0113, .0055, .2024,
 .9212, .0119, .3044,
 .0026, .0119, .8036,
 .0008, .1905,1.1945,
 .0575, .0853, .7077,
 .0182, .3307,2.1414,
 .0256, .0478, .8551,
 .0246, .1496, .9348,
 .0262, .2872,1.3561,
 .0038, .2229, .8993,
 .0039, .4720, .7318,
 .0068, .0949, .6416,
 .3073, .9704, .0031,
 .1819, .4980, .0020,
 .4115,1.1136, .2008,
 .1536,1.7251, .0345,
 .1530, .6688, .0020,
 .2890,1.2419, .0220,
 .1341,1.4882, .0050,
 .0524, .4754, .0012,
 .2139, .4612, .0063,
 .1761,1.1200, .0870),30,3,byrow=TRUE)

d <- matrix(c(.1826,-.1924,-.4656,-.4336,-.4428,-.5845,-1.0403,
  .6431,.0122,.0912,.8082,-.1867,.4533,-1.8398,.4139,
  -.3004,-.1824,.5125,1.1342,.0230,.6172,-.1955,-.3668,
  -1.7590,-.2434,.4925,-.3410,.2896,.006,.0329),ncol=1)

mu <- c(-.4, -.7, .1)
sigma <- matrix(c(1.21,.297,1.232,.297,.81,.252,1.232,.252,1.96),3,3)

dataset1 <- simdata(a, d, 2000)
dataset2 <- simdata(a, d, 2000, mu = mu, sigma = sigma)

###An example of a mixed item, bifactor loadings pattern with correlated specific factors
# can use factor loadings metric
a <- matrix(c(
.8,.4,NA,
.4,.4,NA,
.7,.4,NA,
.8,NA,.4,
.4,NA,.4,
.7,NA,.4),ncol=3,byrow=TRUE)

#first three items are dichotomous, next two have 4 categories, and the last has 3
d <- matrix(c(
-1.0,NA,NA,
 1.5,NA,NA,
 0.0,NA,NA,
3.0,2.0,-0.5,
2.5,1.0,-1,
2.0,0.0,NA),ncol=3,byrow=TRUE)

sigma <- diag(3)
sigma[2,3] <- sigma[3,2] <- .25

dataset <- simdata(a,d,1000,sigma=sigma,factor.loads=TRUE)

####Compensatory item example
a <- matrix(c(
  1,NA,
1.5,NA,
 NA, 1,
 NA,1.6,
1.5,.5,
 .7, 1), ncol=2,byrow=TRUE)

#notice that the compensatory items have the same number of intercepts as 
#factors influencing the item
d <- matrix(c(
-1.0,NA,
 1.5,NA,
 0.0,NA,
 3.0,NA,
2.5,1.0,
2.0, -1),ncol=2,byrow=TRUE)

compdata <- simdata(a,d,3000, partcomp = c(F,F,F,F,T,T))