spaMM (version 4.1.20)

numInfo: Information matrix

Description

Computes by numerical derivation the observed information matrix for (ideally) all parameters for main response model, that is, the matrix of second derivatives of negative log likelihood. Residual dispersion parameters are not handled beyond scalar phi values. The default value of the which argument shows all classes of parameters that should be handled, including random-effect parameters (lambda, ranCoefs, corrPars, and hyper), residual dispersion parameters (phi, NB_shape for negbin1 and negbin2, and beta_prec for beta_resp), and fixed-effect coefficients (beta).

Usage

numInfo(fitobject, transf = FALSE, 
        which = NULL, 
        check_deriv = TRUE,          
        verbose=FALSE, ...)

Value

A matrix.

Arguments

fitobject

Fit object returned by a spaMM fitting function.

transf

Whether to perform internal computations on a transformed scale (but computation on transformed scale may be implemented for fewer classes of models than default computation).

which

NULL, or character vector giving the sets of parameters with respect to which derivatives are to be computed. The NULL default is equivalent to c("lambda", "ranCoefs", "corrPars", "hyper", "phi", "NB_shape", "beta_prec", "beta") for ML fits, and to the same except "beta" (fixed effects) for REML fits.

check_deriv

Boolean; whether to perform some checks for possible problems (see Details).

verbose

Boolean: whether to print (as a list) the estimates of the parameters for which the Hessian will be computed, additional information about possibly ignored parameters, possible misuse of REML fits, and a (sort of) progress bar if the procedure is expected to last more than a few seconds.

...

Arguments passed to numDeriv::hessian and numDeriv::grad.

Details

The computation of a second derivatives is not necessarily meaningful if a first derivative does not vanish at the parameter estimates. This may occur in particular when the objective function (say, marginal likelihood) is maximized at a boundary of the parameter space (say, at zero for lambda estimates). Further, for such values at a boundary, only one-sided derivatives can be computed, and this is not handled by numDeriv::hessian. So, some checks may be requested to detect non-zero gradients and parameters estimated at their boundaries. The boundary checks are currently performed for lambda and ranCoefs estimates, if check_deriv is set to TRUE or to NULL. Other parameters are not (yet) checked, so numInfo may sometimes fails when such other parameter estimates are at a boundary. If check_deriv is set to TRUE, an additional systematic check of the gradient with respect to all target parameters is performed. These checks remain experimental, and defaults may change in a later version, with little notice.

Examples

data("wafers")
lmmfit <- fitme(y ~X1+X2+X1*X3+X2*X3+I(X2^2)+(1|batch),data=wafers)
numinfo <- numInfo(lmmfit)
(SEs <- sqrt(diag(solve(numinfo))))
#
# => beta SEs here equal to conditional SEs shown by fit summary.
# Other SEs can be compared to the approximate ones 
# for log(phi) and log(lambda), given by 
#
# update(lmmfit, control=list(refit=TRUE))
#
# => 1118*0.5289 and 10840*0.1024

data("blackcap")
maternfit <- fitme(migStatus ~ means+ Matern(1|longitude+latitude),data=blackcap) 
numInfo(maternfit)