# summary.bgeva: bgeva summary In bgeva: Binary Generalized Extreme Value Additive Models

## Description

It takes a fitted bgeva object produced by bgeva() and produces some summaries from it.

## Usage

 1 2 3 4 ## S3 method for class 'bgeva' summary(object,s.meth="svd",sig.lev=0.05,...) 

## Arguments

 object A fitted bgeva object as produced by bgeva(). s.meth Matrix decomposition used to determine the matrix root of the covariance matrix. See the documentation of mvtnorm for further details. 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).

Consider also using the version of the model implemented in the gamlss() function of the SemiParBIVProbit package, where p-value calculations are more rigorous.

## 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 [email protected]

## 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.

bgevaObject, plot.bgeva

## Examples

 1 ## see examples for bgeva 

### Example output

Loading required package: mgcv