Simulation locally dependent items
This utility function returns a 0-1 matrix violating the local independence assumption.
Either a vector of person parameters or an integer indicating the number of persons (see details).
Either a vector of item parameters or an integer indicating the number of items (see details).
Either a single correlation value between 0 and 1 or a positive semi-definite VC matrix.
A seed for the random number generated can be set.
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.
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.
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.
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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)