# Simulate data from polytomous logit-normit (graded logistic) model

### Description

Simulate data from polytomous logit-normit (graded logistic) model

### Usage

1 | ```
simulpln(n,nitem,ncat,alphas,betas)
``` |

### Arguments

`n` |
Number of responses to generate. |

`nitem` |
Number of items. |

`ncat` |
Number of categories for the items. |

`alphas` |
A vector of length |

`betas` |
A vector of length |

### Details

Data from graded logistic models is generated under the following parameterization:

*
Pr(y_i = k_i| η) = {
1-Ψ (α_i,k + β_i*η) if k_i = 0,
Ψ (α_i,k + β_i*η) - Ψ (α_i,k+1 + β_i*η) if 0 < k_i < m-1,
Ψ (α_i,k+1 + β_i*η) if k_i = m-1}.
*

Where the items are *y_i, i = 1, …, n*, and response categories are *k=0, …, m-1*. *η* is the latent trait, *Ψ* is the logistic distribution function, *α* is an intercept (cutpoint) parameter, and *β* is a slope parameter. When the number of categories for the items is 2, this reduceds to the 2PL parameterization:

*Pr(y_i = 1| η) = Ψ (α_1 + β_i η)*

### Value

A data matrix in which each row represents a response pattern and the final column represents the frequency of each response pattern.

### Author(s)

Carl F. Falk cffalk@gmail.com, Harry Joe

### See Also

`nrmlepln`

`nrmlerasch`

`nrbcpln`

### Examples

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