restriktor (version 0.1-80.711)

goric: Generalized Order-Restrikted Information Criterion Weights

Description

The goric function computes GORIC weights, which are comparable to the Akaike weights.

Usage

goric(object, …, complement = FALSE, bound = NULL, 
             digits = max(3, getOption("digits") - 2), debug = FALSE)
# S3 method for goric
print(x, digits = max(3, getOption("digits") - 2), …)

Arguments

object

a fitted restriktor object of class conLM, conMLM, conRLM and conGLM.

x

an object of class goric.

…

further fitted restriktor objects of class conLM, conMLM, conRLM and conGLM.

complement

logical; if TRUE the complement is computed. The complement can only be computed for one restriktor object at a time.

bound

not used yet.

digits

the number of significant digits to use when printing.

debug

if TRUE, debugging information is printed out.

Value

The function returns a dataframe with the log-likelihood, penalty term, goric, and the GORIC weights values.

Details

The GORIC values themselves are not interpretable and the interest lie in their differences. The GORIC weights reflect the support of each hypothesis in the set. To compare two hypotheses (and not one to the whole set), one can examine the ratio of the two corresponding GORIC weights. To avoid selecting a weakly supported hypothesis as the best one, the unconstrained hypothesis is usually included as safeguard.

In case of one order-constrained hypothesis, say H1, the complement Hc can be computed as competing hypothesis. The complement is defined as Hc = not H1.

References

Kuiper, R.M., Hoijtink, H., and Silvapulle, M.J. (2011). An Akaike-type information criterion for model selection under inequality constraints. Biometrika, 98, 2, 495--501.

Examples

# NOT RUN {
library(MASS)
## lm
## unrestricted linear model for ages (in months) at which an 
## infant starts to walk alone.

# prepare data
DATA <- subset(ZelazoKolb1972, Group != "Control")
  
# fit unrestrikted linear model
fit1.lm <- lm(Age ~ Group, data = DATA)

# some artificial restrictions
fit1.con <- restriktor(fit1.lm, constraints = "GroupPassive > 0;  GroupPassive < GroupNo")
fit2.con <- restriktor(fit1.lm, constraints = "GroupPassive > 0;  GroupPassive > GroupNo")
fit3.con <- restriktor(fit1.lm, constraints = "GroupPassive == 0; GroupPassive < GroupNo")
fit4.con <- restriktor(fit1.lm) # unrestricted model

goric(fit1.con, fit2.con, fit3.con, fit4.con)

# fit1.con verus the complement
goric(fit1.con, complement = TRUE)


## mlm
# generate data
n <- 30
mu <- c(1,2,3,4)
Sigma <- matrix(5,4,4)
  diag(Sigma) <- c(10,10,10,10)
# 4 Y's.
Y <- mvrnorm(n, mu, Sigma)

# fit unrestricted multivariate linear model
fit2.mlm <- lm(Y ~ 1)

# constraints
myConstraints2 <- rbind(c(-1,1,0,0), c(0,-1,1,0), c(0,0,-1,1))

# fit restricted multivariate linear model
fit5.con <- restriktor(fit2.mlm, constraints = myConstraints2)

# fit5.con verus the complement
goric(fit5.con, complement = TRUE)
# }