mirt (version 1.6.1)

simdata: Simulate response patterns

Description

Simulates response patterns for compensatory 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, itemtype, sigma = NULL, mu = NULL, guess = 0,
  upper = 1, nominal = NULL, Theta = NULL, returnList = FALSE)

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

itemtype

a character vector of length nrow(a) (or 1, if all the item types are the same) specifying the type of items to simulate.

Can be 'dich', 'graded', 'gpcm','nominal', 'nestlogit', or 'partcomp', for dichotomous,

sigma

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

mu

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

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

upper

same as guess, but for upper bound parameters

nominal

a matrix of specific item category slopes for nominal models. Should be the dimensions as the intercept specification with one less column, with NA in locations where not applicable. Note that during estimation the first slope will be constra

Theta

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

returnList

logical; return a list containing the data, item objects defined by mirt containing the population parameters and item structure, and the latent trait matrix Theta? Default is FALSE

Details

Returns a data matrix simulated from the parameters, or a list containing the data, item objects, and Theta matrix.

References

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

Examples

###Parameters from Reckase (2009), p. 153

set.seed(1234)

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)*1.702

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)*1.702

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, itemtype = 'dich')
dataset2 <- simdata(a, d, 2000, itemtype = 'dich', mu = mu, sigma = sigma)

#mod <- mirt(dataset1, 3, method = 'MHRM')
#coef(mod)

###An example of a mixed item, bifactor loadings pattern with correlated specific factors

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)

d <- matrix(c(
-1.0,NA,NA,
 1.5,NA,NA,
 0.0,NA,NA,
0.0,-1.0,1.5,  #the first 0 here is the recommended constraint for nominal
0.0,1.0,-1, #the first 0 here is the recommended constraint for gpcm
2.0,0.0,NA),ncol=3,byrow=TRUE)

nominal <- matrix(NA, nrow(d), ncol(d))
#the first 0 and last (ncat - 1) = 2 values are the recommended constraints
nominal[4, ] <- c(0,1.2,2)

sigma <- diag(3)
sigma[2,3] <- sigma[3,2] <- .25
items <- c('dich','dich','dich','nominal','gpcm','graded')

dataset <- simdata(a,d,2000,items,sigma=sigma,nominal=nominal)

#mod <- bfactor(dataset, c(1,1,1,2,2,2), itemtype=c(rep('2PL', 3), 'nominal', 'gpcm','graded'))
#coef(mod)

####Unidimensional nonlinear factor pattern

theta <- rnorm(2000)
Theta <- cbind(theta,theta^2)

a <- matrix(c(
.8,.4,
.4,.4,
.7,.4,
.8,NA,
.4,NA,
.7,NA),ncol=2,byrow=TRUE)
d <- matrix(rnorm(6))
itemtype <- rep('dich',6)

nonlindata <- simdata(a,d,2000,itemtype,Theta=Theta)

#model <- mirt.model('
#F1 = 1-6
#(F1 * F1) = 1-3')
#mod <- mirt(nonlindata, model)
#coef(mod)

####2PLNRM model for item 4 (with 4 categories), 2PL otherwise

a <- matrix(rlnorm(4,0,.2))

#first column of item 4 is the intercept for the correct category of 2PL model,
#    otherwise nominal model configuration
d <- matrix(c(
-1.0,NA,NA,NA,
 1.5,NA,NA,NA,
 0.0,NA,NA,NA,
 1, 0.0,-0.5,0.5),ncol=4,byrow=TRUE)

nominal <- matrix(NA, nrow(d), ncol(d))
nominal[4, ] <- c(NA,0,.5,.6)

items <- c(rep('dich',3),'nestlogit')

dataset <- simdata(a,d,2000,items,nominal=nominal)

#mod <- mirt(dataset, 1, itemtype = c('2PL', '2PL', '2PL', '2PLNRM'), key=c(NA,NA,NA,1))
#coef(mod)
#itemplot(mod,4)

#return list of simulation parameters
listobj <- simdata(a,d,2000,items,nominal=nominal, returnList=TRUE)
str(listobj)