eRm (version 0.15-5)

sim.locdep: Simulation locally dependent items

Description

This utility function returns a 0-1 matrix violating the local independence assumption.

Usage

sim.locdep(persons, items, it.cor = 0.25, seed = NULL,
   cutpoint = "randomized")

Arguments

persons

Either a vector of person parameters or an integer indicating the number of persons (see details).

items

Either a vector of item parameters or an integer indicating the number of items (see details).

it.cor

Either a single correlation value between 0 and 1 or a positive semi-definite VC matrix.

seed

A seed for the random number generated can be set.

cutpoint

Either "randomized" for a randomized tranformation of the model probability matrix into the model 0-1 matrix or an integer value between 0 and 1 (see details).

encoding

UTF-8

Details

If persons or items is an integer value, the corresponding parameter vector is drawn from N(0,1). The cutpoint argument refers to the transformation of the theoretical probabilities into a 0-1 data matrix. A randomized assingment implies that for each cell an additional random number is drawn. If the model probability is larger than this value, the person gets 1 on this particular item, if smaller, 0 is assigned. Alternatively, a numeric probability cutpoint can be assigned and the 0-1 scoring is carried out according to the same rule. The argument it.cor reflects the pair-wise inter-item correlation. If this should be constant across the items, a single value between 0 (i.e. Rasch model) and 1 (strong violation) can be specified. Alternatively, a symmetric VC-matrix of dimension number of items can be defined.

References

Jannarone, R. J. (1986). Conjunctive item response theory kernels. Psychometrika, 51, 357-373. Su'arez-Falc'on, J. C., & Glas, C. A. W. (2003). Evaluation of global testing procedures for item fit to the Rasch model. British Journal of Mathematical and Statistical Society, 56, 127-143.

See Also

sim.rasch, sim.2pl, sim.xdim

Examples

#simulating locally-dependent data
#500 persons, 10 items, inter-item correlation of 0.5
X <- sim.locdep(500, 10, it.cor = 0.5)

#500 persons, 4 items, correlation matrix specified
sigma <- matrix(c(1,0.2,0.2,0.3,0.2,1,0.4,0.1,0.2,0.4,1,0.8,0.3,0.1,0.8,1),
   ncol = 4)
X <- sim.locdep(500, 4, it.cor = sigma)