mirt (version 0.1-14)

simdata: Simulate response patterns from an underlying multivariate normal distribution

Description

Simulates response patterns from multivariate normally distributed factor scores.

Usage

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

Arguments

a

a matrix of slope parameters. If slopes are to be constrained to zero then use NA

d

a matrix of intercepts. The matrix should have as many columns as the item with the largest number of categories, and fill the 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

mu

a mean vector of the underlying distribution

factor.loads

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

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)