bgeva (version 0.3-1)

summary.bgeva: bgeva summary

Description

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

Usage

# S3 method for 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.

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.

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 $\hat{\mathbf{f}}$ and ${\mathbf{V}}_f$ denote the vector of values of a smooth term evaluated at the original covariate values and the corresponding Bayesian covariance matrix, and let ${\mathbf{V}}_f^{r-}$ denote the rank $r$ pseudoinverse of ${\mathbf{V}}_f$. The statistic used is $T={\hat{\mathbf{f}}}^{\prime }{\mathbf{V}}_f^{r-}\hat{\mathbf{f}}$. 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.

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

## see examples for bgeva