# vcov: Calculate Variance-Covariance Matrix for a Fitted Smooth... In npreg: Nonparametric Regression via Smoothing Splines

 vcov R Documentation

## Calculate Variance-Covariance Matrix for a Fitted Smooth Model

### Description

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`).

### Usage

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

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

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

### Arguments

 `object` an object of class "gsm" output by the `gsm` function, "sm" output by the `sm` function, or "ss" output by the `ss` function `...` other arugments (currently ignored)

### Details

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).

### Value

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

### Author(s)

Nathaniel E. Helwig <helwig@umn.edu>

### References

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.4135/9781526421036885885")}

Nychka, D. (1988). Bayesian confience intervals for smoothing splines. Journal of the American Statistical Association, 83(404), 1134-1143. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.2517-6161.1983.tb01239.x")}

`ss`, `sm`, `gsm` for model fitting

`boot.ss`, `boot.sm`, `boot.gsm` for bootstrapping

### Examples

``````## 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
}
``````

npreg documentation built on May 29, 2024, 4:17 a.m.