| summary.bgeva {bgeva} | R Documentation |
bgeva summary
Description
It takes a fitted bgeva object produced by bgeva() and produces some summaries from it.
Usage
## S3 method for class 'bgeva'
summary(object,s.meth="svd",sig.lev=0.05,...)
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 {\bf 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 {\bf V}_f^{r-} denote
the rank r pseudoinverse of {\bf 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 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
Examples
## see examples for bgeva