This function computes the parameter estimates of a linear logistic test model (LLTM) for binary item responses by using CML estimation.

1 2 |

`X` |
Input 0/1 data matrix or data frame; rows represent individuals (N in total),
columns represent items. Missing values have to be inserted as |

`W` |
Design matrix for the LLTM. 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. If |

`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 LLTM can be viewed as a more parsimonous
Rasch model, 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 LLTM-objects are:

`print`

, `coef`

,
`model.matrix`

, `vcov`

,`summary`

, `logLik`

, `person.parameters`

.

Returns on object of class `eRm`

containing:

`loglik` |
Conditional log-likelihood. |

`iter` |
Number of iterations. |

`npar` |
Number of parameters. |

`convergence` |
See |

`etapar` |
Estimated basic item parameters. |

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

,`LPCM`

1 2 3 4 5 6 7 8 9 10 11 | ```
#LLTM for 2 measurement points
#100 persons, 2*15 items, W generated automatically
res1 <- LLTM(lltmdat1, mpoints = 2)
res1
summary(res1)
#Reparameterized Rasch model as LLTM (more pasimonious)
W <- matrix(c(1,2,1,3,2,2,2,1,1,1),ncol=2) #design matrix
res2 <- LLTM(lltmdat2, W = W)
res2
summary(res2)
``` |

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