con_weights_boot {restriktor}

function for computing the chi-bar-square weights based on Monte Carlo simulation.

Description

The null-distribution of the test statistics under inequality constraints takes the form of mixtures of F-distributions. This function computes these mixing weights (a.k.a chi-bar-square weights and level probabilities). It can be used directly and is called by the conTest function.

Usage

con_weights_boot(VCOV, Amat, meq, 
                 R = 99999L, parallel = c("no", "multicore", "snow"),
                 ncpus = 1L, cl = NULL, seed = NULL, verbose = FALSE, ...)

Arguments

VCOV

variance-covariance matrix of the data for which the weights are to be calculated.

Amat

constraints matrix R (or a vector in case of one constraint) and defines the left-hand side of the constraint R\theta \ge rhs, where each row represents one constraint. The number of columns needs to correspond to the number of parameters estimated (\theta). The rows should be linear independent, otherwise the function gives an error. For more information about constructing the matrix R and rhs see restriktor.

meq

integer (default = 0) treating the number of constraints rows as equality constraints instead of inequality constraints. For example, if meq = 2, this means that the first two rows of the constraints matrix R are treated as equality constraints.

R

integer; number of bootstrap draws for mix.bootstrap. The default value is set to 99999.

parallel

the type of parallel operation to be used (if any). If missing, the default is set "no".

ncpus

integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs.

cl

an optional parallel or snow cluster for use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the conTest call.

seed

seed value.

verbose

logical; if TRUE, information is shown at each bootstrap draw.

...

no additional arguments for now.

Value

The function returns a vector with the mixing weights

Author(s)

Leonard Vanbrabant and Yves Rosseel

References

Silvapulle, M.J. and Sen, P.K. (2005, p.79). Constrained Statistical Inference. Wiley, New York.

Examples

W <- matrix(c(1,0.5,0.5,1),2,2)
Amat <- rbind(c(0,1))
meq <- 0L
# we only generate 99 bootstrap samples in this 
# example; in practice you may wish to use a much higher number.
wt.bar <- con_weights_boot(W, Amat, meq, R = 99)
wt.bar