vcov: Extract covariance or correlation components from a fitted...

In spaMM: Mixed-Effect Models, with or without Spatial Random Effects

Extract covariance or correlation components from a fitted model object

Description

summary(<fit object>)$beta_table returns the table of fixed-effect coefficients as it is printed by summary, including standard errors and t-values.

vcov returns the variance-covariance matrix of the fixed-effects coefficients.

Corr by default returns correlation matrices of random effects (though see Details for user-defined correlation models).

VarCorr returns (co)variance parameters of random effects, and optionally the residual variance(s), from a fit object, in a data frame format roughly consistent with the method of objects of class "lme", in particular including columns with consistent names for easier extraction. One may have to consult the summary of the object to check the meaning of the contents of this data frame (e.g., of 'variance' coefficients for non-gaussian random effects). Other extractors to consider are get_ranPars and get_inits_from_fit, the latter providing parameters in a form suitable for initializing a fit.

The covariance matrix of residuals of a fit can be obtained as a block of the hat matrix
(get_matrix(., which="hat_matrix")). This is (as other covariances matrices above) a matrix of expected values, generally assuming that the fitted model is correct and that its parameters are “well” estimated, and should not to be confused with the computation of diagnostic correlations among inferred residuals of a fit.

Usage

## S3 method for class 'HLfit'
vcov(object, ...)
## S3 method for class 'HLfit'
VarCorr(x, sigma = 1, add_residVars=TRUE, verbose=TRUE, ...)
Corr(object, A=TRUE, cov2cor.=TRUE, ...)

Arguments

object, x

A fitted model object, inheriting from class "HLfit", as returned by the fitting functions in spaMM.

add_residVars	Boolean; whether to include residual variance information in the returned table.
sigma	ignored argument, included for consistency with the generic function.
A	Boolean: Whether to return the correlation matrix described by the AL matrix product, when there is an A matrix (as for IMRF terms; see random-effects).
cov2cor.	Boolean: Whether to convert covariance matrices to correlation matrices (see Details).
verbose	Boolean: Whether to print some notes.
...	Other arguments that may be needed by some method.

Details

Any matrix returned by the Corr extractor is by default the unconditional correlation matrix of a vector “ALv” of random effects (as defined in random-effects).

But it may also be an heteroscedastic matrix for some random effects if cov2cor. is set to FALSE. In particular, the IMRF and MaternIMRFa models are by default defined in terms of the inverse of an heteroscedastic covariance matrix (with tcrossprod factor L), and of a A matrix of weights. The product AL will be the tcrossprod factor of a covariance matrix rather than a correlation matrix, unless a non-default normalization was requested when declaring the random-effect terms. User-defined random-effects models may also be heteroscedastic. In all these cases Corr will by default return the correlation matrix, by applying cov2cor to the tcrossproduct.

Value

vcov returns a matrix.

Corr returns a list, for the different random effect terms. For each random-effect term with nontrivial correlation structure, the returned element is a matrix, returned in base matrix format or in some class from Matrix. Otherwise the it is an information message.

VarCorr returns either NULL (if no variance to report, as for a poisson GLM) or a data frame with columns for the grouping factor, term, variance of random effect, standard deviation (the root of the variance), and optionally for correlation of random effect in random-coefficient terms. Information about the residual variance is optionally included as the last row(s) of the data frame, when relevant (gaussian- or Gamma-response models with single scalar parameter; beware the meaning of the residual variance parameter for Gamma-response models).

Some variance parameters may be removed from the VarCorr output, with a message, such as the slope of the linear predictor describing the correlation model of an adjacency term (see autoregressive). The rare user of such parametrization should not consider this as a stable feature.

See Also

get_inits_from_fit and get_ranPars. get_matrix(., which="beta_v_cov") for the joint covariance matrix of estimates/predictions of fixed effect coefficients and random effects.

Examples

data("wafers")
m1 <- HLfit(y ~ X1+X2+(1|batch), resid.model = ~ 1 ,data=wafers, method="ML")
vcov(m1)

# Example from VarCorr() documentation in 'nlme' package
data("Orthodont",package = "nlme")
sp1 <- fitme(distance ~ age+(age|Subject), data = Orthodont, method="REML")
VarCorr(sp1)

spaMM documentation built on Aug. 30, 2023, 1:07 a.m.