goric: Calculate GORIC

Description

The goric function calculates the order-restricted log likelihood, the penalty of the generalised order restricted information criterion (GORIC), the GORIC values, differences to the minimum GORIC value, and the GORIC weights for a set of hypotheses, where the penalty is based on \(iter\) iterations. The hypothesis with the lowest GORIC value is the preferred one. The GORIC weights reflect the support of each hypothesis in the set. To compare two hypotheses (and not one to the whole set), one should examine the ratio of the two corresponding GORIC weights. To safequard for weak hypotheses (i.e., hypotheses not supported by the data), one should include a model with no constraints (the so-called unconstrained model).

Usage

goric(object, ..., iter = 1e+05, type = "GORIC", dispersion = 1,
  mc.cores = 1)
# S3 method for orlm
goric(object, ..., iter = 1e+05, type = "GORIC",
  mc.cores = 1)
# S3 method for orgls
goric(object, ..., iter = 1e+05, type = "GORIC",
  mc.cores = 1)
# S3 method for list
goric(object, ..., iter = 1e+05, type = "GORIC",
  dispersion = 1, mc.cores = 1)
# S3 method for orglm
goric(object, ..., iter = 1e+05, type = "GORIC",
  dispersion = 1, mc.cores = 1)

Arguments

object

an object of class orlm, orgls, orglm, or a list of these objects

...

further objects of class orlm, orgls, or orglm

iter

number of iterations to calculate GORIC penalty terms

type

if "GORIC" (default), the penalty term for the generalized order restriction information criterion is computed; with "GORICCa" or "GORICCb" small sample corrections for the penalty term are applied

dispersion

dispersion parameter to scale GORIC analogously to QAIC in generalized linear models

mc.cores

number of cores using a socket cluster implemented in package parallel

Value

a data.frame with the information criteria or a single penalty term

References

Kuiper R.M., Hoijtink H., Silvapulle M.J. (2011). An Akaike-type Information Criterion for Model Selection Under Inequality Constraints. Biometrika, 98, 495--501.
Kuiper R.M., Hoijtink H., Silvapulle M.J. (2012). Generalization of the Order-Restricted Information Criterion for Multivariate Normal Linear Models. Journal of Statistical Planning and Inference, 142, 2454-2463. doi:10.1016/j.jspi.2012.03.007.
Kuiper R.M. and Hoijtink H. (submitted). A Fortran 90 Program for the Generalization of the Order-Restricted Information Criterion. Journal of Statictical Software.

Examples

Run this code

# NOT RUN {
## Example from Kuiper, R.M. and Hoijtink, H. (Unpublished).
# A Fortran 90 program for the generalization of the 
# order restricted information criterion.
# constraint definition
cmat <- cbind(diag(3), 0) + cbind(0, -diag(3))
constr <- kronecker(diag(3), cmat)
constr

# no effect model
(fm0 <- orlm(cbind(SDH, SGOT, SGPT) ~ dose-1, data=vinylidene,
            constr=constr, rhs=rep(0, nrow(constr)), nec=nrow(constr)))

# order constrained model (increasing serum levels with increasing doses)
fm1 <- orlm(cbind(SDH, SGOT, SGPT) ~ dose-1, data=vinylidene,
            constr=constr, rhs=rep(0, nrow(constr)), nec=0)
summary(fm1)

# unconstrained model
(fmunc <- orlm(cbind(SDH, SGOT, SGPT) ~ dose-1, data=vinylidene,
              constr=matrix(0, nrow=1, ncol=12), rhs=0, nec=0))

# calculate GORIC
# (only small number of iterations to decrease computation time, default: iter=100000)
goric(fm0, fm1, fmunc, iter=1000)
# }