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. \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
## 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
}
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