vcov | R Documentation |

Returns the variance-covariance matrix for the basis function coefficients from a fit smoothing spline (fit by `ss`

), smooth model (fit by `sm`

), or generalized smooth model (fit by `gsm`

).

## S3 method for class 'ss' vcov(object, ...) ## S3 method for class 'sm' vcov(object, ...) ## S3 method for class 'gsm' vcov(object, ...)

`object` |
an object of class "gsm" output by the |

`...` |
other arugments (currently ignored) |

The variance-covariance matrix is calculated using the Bayesian interpretation of a smoothing spline. Unlike the classic treatments (e.g., Wahba, 1983; Nychka, 1988), which interpret the smoothing spline as a Bayesian estimate of a Gaussian process, this treatment applies the Bayesian interpretation directly on the coefficient vector. More specifically, the smoothing spline basis function coefficients are interpreted as Bayesian estimates of the basis function coefficients (see Helwig, 2020).

Returns the (symmetric) matrix such that cell (*i,j*) contains the covariance between the *i*-th and *j*-th elements of the coefficient vector.

Nathaniel E. Helwig <helwig@umn.edu>

Helwig, N. E. (2020). Multiple and Generalized Nonparametric Regression. In P. Atkinson, S. Delamont, A. Cernat, J. W. Sakshaug, & R. A. Williams (Eds.), SAGE Research Methods Foundations. doi: 10.4135/9781526421036885885

Nychka, D. (1988). Bayesian confience intervals for smoothing splines. *Journal of the American Statistical Association, 83(404)*, 1134-1143. doi: 10.2307/2290146

Wahba, G. (1983). Bayesian "confidence intervals" for the cross-validated smoothing spline. *Journal of the Royal Statistical Society. Series B, 45(1)*, 133-150. doi: 10.1111/j.2517-6161.1983.tb01239.x

`ss`

, `sm`

, `gsm`

for model fitting

`boot.ss`

, `boot.sm`

, `boot.gsm`

for bootstrapping

## for 'ss' objects this function is defined as function(object, ...){ Sigma <- tcrossprod(object$fit$cov.sqrt) rownames(Sigma) <- colnames(Sigma) <- names(object$fit$coef) Sigma } ## for 'sm' and 'gsm' objects this function is defined as function(object, ...){ Sigma <- tcrossprod(object$cov.sqrt) rownames(Sigma) <- colnames(Sigma) <- names(object$coefficients) Sigma }

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.