rmvlogis | R Documentation |

Produces Bernoulli or Multinomial random variates under the Rasch, the two-parameter logistic, the three parameter, the graded response, and the generalized partial credit models.

rmvlogis(n, thetas, IRT = TRUE, link = c("logit", "probit"), distr = c("normal", "logistic", "log-normal", "uniform"), z.vals = NULL) rmvordlogis(n, thetas, IRT = TRUE, model = c("gpcm", "grm"), link = c("logit", "probit"), distr = c("normal", "logistic", "log-normal", "uniform"), z.vals = NULL)

`n` |
a scalar indicating the number of response patterns to simulate. |

`thetas` |
for |

`IRT` |
logical; if |

`model` |
from which model to simulate. |

`link` |
a character string indicating the link function to use. Options are logit and probit. |

`distr` |
a character string indicating the distribution of the latent variable. Options are Normal, Logistic, log-Normal, and Uniform. |

`z.vals` |
a numeric vector of length |

The binary variates can be simulated under the following parameterizations for the probability of correctly responding in
the *i*th item. If `IRT = TRUE`

* π_i = c_i +
(1 - c_i) g(beta_{2i} (z - beta_{1i})),*

whereas if `IRT = FALSE`

* π_i = c_i + (1 - c_i) g(beta_{1i} + beta_{2i} z),*

*z* denotes the latent variable,
*β_{1i}* and *β_{2i}* are the first and second columns of `thetas`

, respectively, and *g()*
is the link function. If `thetas`

is a three-column matrix then the third column should contain the guessing
parameters *c_i*'s.

The ordinal variates are simulated according to the generalized partial credit model or the graded response model depending
on the value of the `model`

argument. Check `gpcm`

and `grm`

to see how these models are defined,
under both parameterizations.

a numeric matrix with `n`

rows and columns the number of items, containing the simulated binary or ordinal variates.

For options `distr = "logistic"`

, `distr = "log-normal"`

and `distr = "uniform"`

the simulated random
variates for *z* simulated under the Logistic distribution with `location = 0`

and `scale = 1`

, the
log-Normal distribution with `meanlog = 0`

and `sdlog = 1`

and the Uniform distribution with `min = -3.5`

and `max = 3.5`

, respectively. Then, the simulated *z* variates are standardized, using the theoretical mean
and variance of the Logistic, log-Normal and Uniform distribution, respectively.

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

`gpcm`

,
`grm`

,
`ltm`

,
`rasch`

,
`tpm`

# 10 response patterns under a Rasch model # with 5 items rmvlogis(10, cbind(seq(-2, 2, 1), 1)) # 10 response patterns under a GPCM model # with 5 items, with 3 categories each thetas <- lapply(1:5, function(u) c(seq(-1, 1, len = 2), 1.2)) rmvordlogis(10, thetas)

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