vcov: Calculate Asymptotic Variance-Covariance Matrix for a Fitted...

In aster: Aster Models

Calculate Asymptotic Variance-Covariance Matrix for a Fitted Model Object

Description

vcov() is a generic function and functions with names beginning in vcov. will be methods for this function.

Usage

## S3 method for class 'aster'
vcov(object, info = c("expected", "observed"), ...)
## S3 method for class 'reaster'
vcov(object, standard.deviation = TRUE, re.too = FALSE,
  complete = TRUE, ...)

Arguments

object	an object of class "aster" or class "reaster", usually the object returned by a call to R function aster or R function reaster.
info	the type of Fisher information used to compute the variance-covariance matrix.
standard.deviation	if FALSE, then some of the parameters are variance components, if TRUE, then the square roots of these variance components.
re.too	if TRUE, treat the estimated random effects vector, the mode of the conditional distribution of random effects given observed data, as part of the estimates vector described by the returned variance-covariance matrix. If also standard.deviation is TRUE, then these estimates are standardized.
complete	If TRUE, the full variance-covariance matrix, including entries for parameters estimated to be zero (for which the entries will also be zero).
...	required by the generic function. Ignored by these methods.

Details

The method for objects aout of class "aster" returns what the theory always has been, the inverse of aout$fisher or aout$hessian, which are the same matrix for unconditional aster models or different matrices for unconditional aster models (Geyer, et al., 2007, Sections 3.1 and 3.2).

The method for objects rout of class "reaster" returns in the case re.too = FALSE (the default) more or less what it always has used for standard errors but not exactly. It does use the theory from Geyer, et al. (2013, equation (8) and the surrounding discussion) as it always has, but now uses second derivatives calculated by R function objfun, which is new (so standard errors are not exactly the same as before).

The method for objects rout of class "reaster" returns in the case re.too = TRUE something entirely new and unpublished, but which is just an application of the delta method. The vector of random effects estimates rout$b is a differentiable function of the parameter estimates rout$alpha and rout$nu, which means it is a straightforward application of the delta method to get the combined approximate asymptotic variance-covariance matrix for all three (vector) estimates. See Geyer (unpublished, equation (4.21 and the surrounding discussion for details).

Value

A matrix of the estimated approximate, large sample, covariances between the parameter estimates.

Entries for parameters estimated to be zero are zero, not because there is no sampling variability but rather because the sampling distribution is highly non-normal and one-sided so covariances are useless.

This returned matrix has dimension attributes, like any R matrix. For the function vcov.reaster, it also has attributes, which are some of is.alpha, is.b, is.nu, is.c, and is.sigma. These are all logical vectors that can serve as index vectors for the matrix.

• is.alpha extracts elements of the variance-covariance matrix for estimates of fixed effects.

• is.nu extracts elements of the variance-covariance matrix for estimates of variance components (if standard.deviation == FALSE was specified).

• is.b extracts elements of the variance-covariance matrix for estimates of random effects (if standard.deviation == FALSE & re.too = TRUE was specified).

• is.nu extracts elements of the variance-covariance matrix for estimates of square roots of variance components (if standard.deviation == TRUE was specified).

• is.c extracts elements of the variance-covariance matrix for standardized estimates of random effects (if standard.deviation == TRUE & re.too = TRUE was specified).

See reaster for more about these parameterizations.

References

Geyer, C.~J. (unpublished) Aster Theory. https://github.com/cjgeyer/AsterTheory. There are no version numbers, so cite the specific git commit by its SHA-1 checksum.

Geyer, C. J., Ridley, C. E., Latta, R. G., Etterson, J. R., and Shaw, R. G. (2013) Local Adaptation and Genetic Effects on Fitness: Calculations for Exponential Family Models with Random Effects. Annals of Applied Statistics, 7, 1778–1795. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/13-AOAS653")}.

Geyer, C. J., Wagenius, S., and Shaw, R. G. (2007) Aster Models for Life History Analysis. Biometrika, 94, 415–426. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/asm030")}.

See Also

aster, reaster, vcov

Examples

data(radish2)

pred <- c(0,1,2)
fam <- c(1,3,2)

rout <- reaster(resp ~ varb + fit : (Site * Region),
    list(block = ~ 0 + fit : Block, pop = ~ 0 + fit : Pop),
    pred, fam, varb, id, root, data = radish2)

vout <- vcov(rout, standard.deviation = FALSE, re.too = TRUE)
attributes(vout)
is.alpha <- attr(vout, "is.alpha")
vout[is.alpha, is.alpha]

aster documentation built on Dec. 8, 2025, 9:06 a.m.