# Most Likely Transformations

### Description

Likelihood-based model estimation in conditional transformation models

### Usage

1 2 |

### Arguments

`model` |
a conditional transformation model as specified by |

`data` |
a |

`weights` |
an optional vector of weights |

`offset` |
an optional vector of offset values |

`fixed` |
a named vector of fixed regression coefficients; the names need to correspond to column names of the design matrix |

`theta` |
optional starting values for the model parameters |

`pstart` |
optional starting values for the distribution function evaluated at the data |

`scale` |
a logical indicating if (internal) scaling shall be applied to the model coefficients |

`dofit` |
a logical indicating if the model shall be fitted to the
data ( |

`optim` |
a list of functions implementing suitable optimisers |

`...` |
additional arguments, currently ignored |

### Details

This function fits a conditional transformation model by searching for the most likely transformation as described in Hothorn et al. (2016).

### Value

An object of class `mlt`

with corresponding methods.

### References

Torsten Hothorn, Lisa Moest, Peter Buehlmann (2016), Most Likely Transformations, http://arxiv.org/abs/1508.06749

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
### set-up conditional transformation model for conditional
### distribution of dist given speed
dist <- numeric_var("dist", support = c(2.0, 100), bounds = c(0, Inf))
speed <- numeric_var("speed", support = c(5.0, 23), bounds = c(0, Inf))
ctmm <- ctm(response = Bernstein_basis(dist, order = 4, ui = "increasing"),
interacting = Bernstein_basis(speed, order = 3))
### fit model
(mltm <- mlt(ctmm, data = cars))
### plot data
plot(cars)
### predict quantiles and overlay data with model via a "quantile sheet"
q <- predict(mltm, newdata = data.frame(speed = 0:24), type = "quantile",
p = 2:8 / 10, K = 500)
tmp <- apply(q, 1, function(x) lines(0:24, x, type = "l"))
``` |