# penMSM.

### Description

L1 penalized estimation of multistate models.

### Usage

1 2 3 |

### Arguments

`type` |
character defining the type of penalty, either |

`d` |
data set with variables (mandatory) |

`X` |
design matrix. |

`PSM1` |
penalty structure matrix containing the penalty structure vectors |

`PSM2` |
penalty structure matrix containing the penalty structure vectors |

`lambda1` |
vector with penalty parameters for the respective penalty components (lasso part). |

`lambda2` |
vector with penalty parameters for the respective penalty components (fusion part). |

`w` |
vector containing weights for the respective penalty components. |

`betastart` |
vector containing starting values for beta. |

`nu` |
numeric value denoting the weight, i.e. a value between 0 and 1, of the Fisher scoring updates. |

`tol` |
relative update tolerance for stopping of the estimation algorithm. |

`max.iter` |
number of maximum iterations if tlerance is not reached. |

`trace` |
logical triggering printout of status information during the fitting process. . |

`diagnostics` |
logical triggering that Fisher matrix, score vector, and approximated penalty matrix are returned with the results. |

`family` |
character defining the likelihood to be used. |

`poissonresponse` |
response values for poisson likelihood (if used). |

`poissonoffset` |
offset values for poisson likelihood (if used). |

`constant.approx` |
constant for locally squared approximation of the absolute value penalty function. |

### Details

This function is the core function of this package. It implements L1 penalized estimation of multistate models, with the penalty applied to absolute effects and absolute effect differences on transition-type specific hazard rates.

### Value

A list with elements `B`

(matrix with estimated
effects), `aic`

(Akaike Information Criterion), `gcv`

(GCV
criterion), `df`

(degrees of freedom), and (if `diagnostics`

are requested)
`F`

(Fisher matrix), `s`

(score vector), and
`A`

(approximated penalty matrix).

### Author(s)

Holger Reulen

### Examples

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