Description Usage Arguments Details Value Warning Author(s) References See Also Examples

Based on given observations a matrix is created that creates a basis e.g. of splines or a markov random field that is evaluated for each observation. Additionally a penalty matrix is generated. Shape constraint p-spline bases can also be specified.

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`x` |
Data vector, matrix or data frame. In case of '2dspline', or 'krig' |

`type` |
Character string defining the type of base that is generated for the given variable(s) |

`B_size` |
Number of basis functions of psplines. Default is 20. |

`B` |
For the 'special' |

`P` |
Square matrix that has to be provided in 'special' case and with 'markov' |

`bnd` |
Object of class |

`center` |
Logical to state whether the basis shall be centered in order to fit additive models with one central intercept. |

`by` |
An optional variable defining varying coefficients, either a factor or numeric variable. Per default treatment coding is used. Note that the main effect needs to be specified in a separate basis. |

`constraint` |
Character string defining the type of shape constraint that is imposed on the spline curve. The last option 'flatend' results in constant functions at the covariate edges. |

`...` |
Currently not used. |

Possible `types`

of bases:

- pspline
Penalized splines made upon

`B_size`

equidistant knots with degree 3. The penalization matrix consists of differences of the second order, see`diff`

.- 2dspline
Tensor product of 2 p-spline bases with the same properties as above.

- markov
Gaussian markov random field with a neighbourhood structure given by

`P`

or`bnd`

.

- krig
'kriging' produces a 2-dimensional base, which is calculated as exp(-r/phi)*(1+r/phi) where

`phi`

is the maximum euclidean distance between two knots divided by a constant.- random
A 'random' effect is like the 'markov' random field based on a categorial variable, and since there is no neighbourhood structure, P = I.

- ridge
In a 'ridge' regression, the base is made from the independent variables while the goal is to determine significant variables from the coefficients. Therefore no penalization is used (P = I).

- special
In the 'special' case,

`B`

and`P`

are user defined.- parametric
A parametric effect.

- penalizedpart_pspline
Penalized splines made upon

`B_size`

equidistant knots with degree 3. The penalization matrix consists of differences of the second order, see`diff`

. Generally a P-spline of degree 3 with 2 order penalty can be splited in a linear trend and the deviation of the linear trend. Here only the wiggly deviation of the linear trend is kept. It is possible to combine it with the same covariate of type`parametric`

List consisting of:

`B ` |
Matrix of the evaluated base, one row for each observation, one column for each base element. |

`P ` |
Penalty square matrix, needed for the smoothing in the regression. |

`x ` |
The observations |

`type` |
The |

`bnd` |
The |

`Zspathelp` |
Matrix that is also only needed with 'markov' |

`phi` |
Constant only needed with 'kriging' |

`center` |
The boolean value of the argument |

`by` |
The variable included in the |

`xname` |
Name of the variable |

`constraint` |
Part of the penalty matrix. |

`B_size` |
Same as input |

`P_orig` |
Original penalty |

`B_mean` |
Original mean of design matrix |

`param_center` |
Parameters of centering the covariate. |

`nbp` |
Number of penalized parameters in this covariate. |

`nbunp` |
Number of unpenalized parameters in this covariate. |

The `pspline`

is now centered around its mean. Thus different results compared to old versions of `expectreg`

occure.

Fabian Otto- Sobotka

Carl von Ossietzky University Oldenburg

http://www.uni-Oldenburg.de

Thomas Kneib, Elmar Spiegel

Georg August University Goettingen

http://www.uni-goettingen.de

Sabine Schnabel

Wageningen University and Research Centre

http://www.wur.nl

Paul Eilers

Erasmus Medical Center Rotterdam

http://www.erasmusmc.nl

Fahrmeir L and Kneib T and Lang S (2009)
* Regression *
Springer, New York

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