# bgeva summary

### Description

It takes a fitted `bgeva`

object produced by `bgeva()`

and produces some summaries from it.

### Usage

1 2 3 4 |

### Arguments

`object` |
A fitted |

`s.meth` |
Matrix decomposition used to determine the matrix root of the covariance matrix. See the documentation of |

`sig.lev` |
Significance level used for intervals obtained via posterior simulation. |

`...` |
Other arguments. |

### Details

As in the package `mgcv`

, based on the results of Wood (2013), ‘Bayesian p-values’ are returned for the smooth terms. These have
better frequentist performance than their frequentist counterpart. Let *\hat{\bf f}*
and *V_f* denote the vector of values of a smooth term evaluated at the original covariate values and the
corresponding Bayesian covariance matrix, and let *V_f^{r-}* denote
the rank *r* pseudoinverse of *V_f*. The statistic used
is *T=\hat{\bf f}^\prime {\bf V}_f^{r-} \hat{\bf f}*. This is
compared to a chi-squared distribution with degrees of freedom given by *r*, which is obtained by
biased rounding of the estimated degrees of freedom. See Wood (2013) for further details.

Note that covariate selection can also be achieved using a single penalty shrinkage approach as shown in Marra and Wood (2011).

### Value

`tableP` |
It returns a table containing parametric estimates, their standard errors, z-values and p-values. |

`tableNP` |
It returns a table of nonparametric summaries for each smooth component including estimated degrees of freedom, estimated rank, approximate Wald statistic for testing the null hypothesis that the smooth term is zero, and p-value. |

`n` |
Sample size. |

`tau` |
Tail parameter of the link function. |

`formula` |
The original GAM formula used. |

`l.sp` |
Number of smooth components. |

`t.edf` |
Total degrees of freedom of the estimated model. |

### Author(s)

Maintainer: Giampiero Marra giampiero.marra@ucl.ac.uk

### References

Marra G. and Wood S.N. (2011), Practical Variable Selection for Generalized Additive Models. *Computational Statistics and Data Analysis*, 55(7), 2372-2387.

Wood, S.N. (2013). On p-values for smooth components of an extended generalized additive model. *Biometrika*, 100(1), 221-228.

### See Also

`bgevaObject`

, `plot.bgeva`

### Examples

1 | ```
## see examples for bgeva
``` |