Simulation locally dependent items

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Description

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

Usage

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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).

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

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#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)

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