LRSM {eRm} | R Documentation |

This function computes the parameter estimates of a linear rating scale model (LRSM) for polytomuous item responses by using CML estimation.

```
LRSM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE,
etaStart)
```

`X` |
Input data matrix or data frame; rows represent individuals (N in total), columns represent items. Missing values are inserted as |

`W` |
Design matrix for the LRSM. If omitted, the function will compute W automatically. |

`mpoints` |
Number of measurement points. |

`groupvec` |
Vector of length N which determines the group membership of each subject, starting from 1 |

`se` |
If |

`sum0` |
If |

`etaStart` |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |

Through appropriate definition of `W`

the LRSM can be viewed as a more parsimonous
RSM, on the one hand, e.g. by imposing some cognitive base operations
to solve the items. One the other hand, linear extensions of the Rasch model
such as group comparisons and repeated measurement designs can be computed.
If more than one measurement point is examined, the item responses for the 2nd, 3rd, etc.
measurement point are added column-wise in X.

If `W`

is user-defined, it is nevertheless necessary to
specify `mpoints`

and `groupvec`

. It is important that first the time contrasts and
then the group contrasts have to be imposed.

Available methods for LRSM-objects are:
`print`

, `coef`

,
`model.matrix`

, `vcov`

,`summary`

, `logLik`

, `person.parameters`

.

Returns an object of class `'eRm'`

containing:

`loglik` |
Conditional log-likelihood. |

`iter` |
Number of iterations. |

`npar` |
Number of parameters. |

`convergence` |
See |

`etapar` |
Estimated basic item parameters (item and category parameters). |

`se.eta` |
Standard errors of the estimated basic item parameters. |

`betapar` |
Estimated item (easiness) parameters. |

`se.beta` |
Standard errors of item parameters. |

`hessian` |
Hessian matrix if |

`W` |
Design matrix. |

`X` |
Data matrix. |

`X01` |
Dichotomized data matrix. |

`groupvec` |
Group membership vector. |

`call` |
The matched call. |

Patrick Mair, Reinhold Hatzinger

Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.

Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.

Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.

```
#LRSM for two measurement points
#20 subjects, 2*3 items, W generated automatically,
#first parameter set to 0, no standard errors computed.
res <- LRSM(lrsmdat, mpoints = 2, groupvec = 1, sum0 = FALSE, se = FALSE)
res
```

[Package *eRm* version 1.0-2 Index]