Native-scale covariance parameters and standard errors

Returns descriptor-defined native covariance parameters with delta-method standard errors computed from the fitted covariance-parameter uncertainty matrix.

Usage

covparams_mmes_se(object, term = NULL, rel_step = 1e-6)

Arguments

object: A fitted object of class "mmes".
term: Optional covariance-term name or numeric index. By default, all random and residual covariance terms are returned.
rel_step: Positive relative step used to numerically differentiate each CovarianceFactor native reporting callback.

Details

The fitted theta_se matrix describes uncertainty in the reported covPar coordinates. For each covariance structure, covparams_mmes_se numerically evaluates the Jacobian of its descriptor's native reporting callback and applies the multivariate delta method, $$V_{native} = J V_{covPar} J^{\mathsf T}.$$ Consequently, coupled transformations use the complete covariance information. For example, the standard error of a dsm() level variance accounts for uncertainty and covariance in both the overall variance and its variance ratio. Likewise, usm() standard errors account for all relevant normalized Cholesky parameters.

The transformation is available for every built-in CovarianceFactor family supported by covparams_mmes(); user-defined ownm() structures use their descriptor-provided native_report callback.

Parameters marked fixed in the covariance descriptor contribute no independent sampling uncertainty: their rows and columns in theta_se are excluded before transformation. A native quantity involving both fixed and free parameters can still have a nonzero standard error through its free parameters. Both fixed and estimated native quantities are returned.

The same table is stored automatically in object$covParNativeSE by mmes().

Value

A data frame containing term, factor, parameter, estimate, StdError, and Zratio. A zero standard error is reported for a fully fixed native quantity, with Zratio=NA.

Examples

if (FALSE) { # \dontrun{
fit <- mmes(Yield ~ Env,
            random = ~ vsm(dsm(Env), ism(Name)),
            rcov = ~ units, data = DT_example)
covparams_mmes_se(fit)
fit$covParNativeSE
} # }