vcov() is a generic function and functions with names beginning
in vcov. will be methods for this function.
# S3 method for aster
vcov(object, info = c("expected", "observed"), ...)
# S3 method for reaster
vcov(object, standard.deviation = TRUE, re.too = FALSE,
complete = TRUE, ...)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.
an object of class "aster" or class "reaster",
usually the object returned by a call to R function aster
or R function reaster.
the type of Fisher information used to compute the variance-covariance matrix.
if FALSE, then some of the parameters are
variance components, if TRUE, then the square roots of these
variance components.
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.
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.
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).
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. 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. tools:::Rd_expr_doi("10.1093/biomet/asm030").
aster, reaster, vcov
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]
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