This function computes posterior mode estimates of the parameters of a flexible Cox model
with structured additive predictors using a Newton-Raphson algorithm. Integrals are solved
numerically. Moreover, optimum smoothing variances are computed using a stepwise optimization,
see also the details section of function `bfit`

.

opt_Cox(x, y, start, weights, offset,
criterion = c("AICc", "BIC", "AIC"),
nu = 0.1, update.nu = TRUE,
eps = .Machine$double.eps^0.25, maxit = 400,
verbose = TRUE, digits = 4, ...)
cox_mode(x, y, start, weights, offset,
criterion = c("AICc", "BIC", "AIC"),
nu = 0.1, update.nu = TRUE,
eps = .Machine$double.eps^0.25, maxit = 400,
verbose = TRUE, digits = 4, ...)

## Arguments

x |
The `x` list, as returned from function
`bamlss.frame` and transformed by function `surv_transform` ,
holding all model matrices and other information that is used for
fitting the model. |

y |
The model response, as returned from function `bamlss.frame` . |

start |
A named numeric vector containing possible starting values, the names are based on
function `parameters` . |

weights |
Prior weights on the data, as returned from function `bamlss.frame` . |

offset |
Can be used to supply model offsets for use in fitting,
returned from function `bamlss.frame` . |

criterion |
Set the information criterion that should be used, e.g., for smoothing
variance selection. Options are the corrected AIC `"AICc"` , the `"BIC"` and
`"AIC"` . |

nu |
Calibrates the step length of parameter updates of one Newton-Raphson update. |

update.nu |
Should the updating step length be optimized in each iteration
of the backfitting algorithm. |

eps |
The relative convergence tolerance of the backfitting algorithm. |

maxit |
The maximum number of iterations for the backfitting algorithm |

verbose |
Print information during runtime of the algorithm. |

digits |
Set the digits for printing when `verbose = TRUE` . |

… |
Currently not used. |

## Value

A list containing the following objects:

fitted.valuesA named list of the fitted values of the modeled parameters
of the selected distribution.

parametersThe estimated set regression coefficients and smoothing variances.

edfThe equivalent degrees of freedom used to fit the model.

logLikThe value of the log-likelihood.

logPostThe value of the log-posterior.

hessianThe Hessian matrix evaluated at the posterior mode.

convergedLogical, indicating convergence of the backfitting algorithm.

timeThe runtime of the algorithm.

## References

Umlauf N, Klein N, Zeileis A (2016). Bayesian Additive Models for Location
Scale and Shape (and Beyond). *(to appear)*

## See also

## Examples

## Please see the examples of function sam_Cox()!