sim.xdim {eRm} | R Documentation |

This utility function simulates a 0-1 matrix violating the unidimensionality assumption in the Rasch model.

```
sim.xdim(persons, items, Sigma, weightmat, seed = NULL,
cutpoint = "randomized")
```

`persons` |
Either a matrix (each column corresponds to a dimension) 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). |

`Sigma` |
A positive-definite symmetric matrix specifying the covariance matrix of the variables. |

`weightmat` |
Matrix for item-weights for each dimension (columns). |

`seed` |
A seed for the random number generated can be set. |

`cutpoint` |
Either |

If `persons`

is specified as matrix, `Sigma`

is ignored. If `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.

If `weightmat`

is not specified, a random indicator matrix is generated where each item is a measurement
of only one dimension. For instance, the first row for a 3D-model could be (0,1,0) which means
that the first item measures the second dimension only. This corresponds to the between-item
multidimensional model presented by Adams et al. (1997).

`Sigma`

reflects the VC-structure for the person parameters drawn from a multivariate
standard normal distribution. Thus, the diagonal elements are typically 1 and the lower the
covariances in the off-diagonal, the stronger the model violation.

Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1-23.

Glas, C. A. W. (1992). A Rasch model with a multivariate distribution of ability. In M. Wilson (Ed.), Objective Measurement: Foundations, Recent Developments, and Applications (pp. 236-258). Norwood, NJ: Ablex.

`sim.rasch`

, `sim.locdep`

, `sim.2pl`

```
# 500 persons, 10 items, 3 dimensions, random weights.
Sigma <- matrix(c(1, 0.01, 0.01, 0.01, 1, 0.01, 0.01, 0.01, 1), 3)
X <- sim.xdim(500, 10, Sigma)
#500 persons, 10 items, 2 dimensions, weights fixed to 0.5
itemvec <- runif(10, -2, 2)
Sigma <- matrix(c(1, 0.05, 0.05, 1), 2)
weights <- matrix(0.5, ncol = 2, nrow = 10)
X <- sim.xdim(500, itemvec, Sigma, weightmat = weights)
```

[Package *eRm* version 1.0-2 Index]