restriktor (version 0.2-250)

goric: Generalized Order-Restrikted Information Criterion (Approximation) Weights

Description

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

Usage

goric(object, ..., comparison = c("unconstrained", "complement", "none"), 
      VCOV = NULL, sample.nobs = NULL, type = "goric", bound = NULL, debug = FALSE)
# S3 method for goric
print(x, digits = max(3, getOption("digits") - 4), …)
# S3 method for goric
summary(object, brief = TRUE, digits = max(3, getOption("digits") - 4), …)
# S3 method for goric
coef(object, …)

Arguments

object

an object containing the outcome of a statistical analysis. Currently, the following objects can be processed:

• a fitted object of class restriktor.

• a fitted unconstrained object of class lm, rlm or glm.

• a numeric vector containing the unconstrained estimates resulting from any statistical analysis.

x

an object of class goric.

…

this depends on the class of the object. If object is of class restriktor, further objects of class restriktor can be passed. If object is of class lm, rlm or glm, the constraints can be passed. If object is of class numeric, the constraints can be passed. See details for more information.

comparison

if "unconstrained" (default) the unconstrained model is included in the set of models. If "complement" then the restricted object is compared against its complement. Note that the complement can only be computed for one model/hypothesis at a time (for now). If "none" the model is only compared against the models provided by the user.

VCOV

variance-coviance matrix. Only needed if object is of class numeric and type = "gorica".

sample.nobs

not used for now.

type

if "goric" (default), the generalized order-restricted information criterion value is computed. If "gorica" the log-likihood is computed using the multivariate normal distribution function.

bound

not used yet.

digits

the number of significant digits to use when printing.

debug

if TRUE, debugging information is printed out.

brief

if FALSE, an extended overview is printed.

Value

The function returns a dataframe with the log-likelihood, penalty term, GORIC(A) values and the GORIC(A) weights. Furthermore, a dataframe is returned with the relative GORIC(A) weights.

Details

The GORIC(A) values themselves are not interpretable and the interest lie in their differences. The GORIC(A) 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(A) 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.

If the object(s) is of class restriktor the constraints are automatically extracted. Otherwise, the constraint syntax can be parsed via the …. If the object is an unconstrained model of class lm, rlm or glm, then the constraints can be specified in two ways, see restriktor. Note that if the constraints are written in matrix notation, then the constraints for each model/hypothesis is put in a named list. For example, h1 <- list(constraints = "x1 > 0", rhs = 0, neq = 0). The rhs and neq are not required if they are equal to 0. If type = "gorica", then the object might be a (named) numeric vector. The constraints can again be specified in two ways, see restriktor. For examples, see below.

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.

Vanbrabant, L. and Kuiper, R. (n.d.). Giving the complement a compliment: Evaluating a theory-based hypothesis against its complement using the GORIC.

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 versus the complement
goric(fit1.con, comparison = "complement")


## GORICA
# generate data
n <- 10
x1 <- rnorm(n)
x2 <- rnorm(n)
y <- 1 + x1 + x2 + rnorm(n)
# fit unconstrained linear model
fit.lm <- lm(y ~ x1 + x2)

# extract unconstrained estimates
est <- coef(fit.lm)
# unconstrained variance-covariance matrix
VCOV <- vcov(fit.lm)

## constraint syntax (character)
h1 <- "x1 > 0"
h2 <- "x1 > 0; x2 > 0"
# use fitted unconstrained linear model
out <- goric(fit.lm, h1, h2, type = "gorica")
# use unconstrained estimates
out <- goric(est, VCOV = VCOV, h1, h2, type = "gorica")

## constraint syntax (matrix notation)
h1 <- list(constraints = c(0,1,0))
h2 <- list(constraints = rbind(c(0,1,0), c(0,0,1)))
out <- goric(fit.lm, h1, h2, type = "gorica")
out <- goric(est, VCOV = VCOV, h1, h2, type = "gorica")


## 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)
# }