Fitting multivariate regression models with order restrictions

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Description

It determines the order-restricted maximum likelihood estimates and the corresponding log likelihood for the hypothesis of interest. Additionally it gives the (unconstrained) maximum likelihood estimates and the active contraints.

Usage

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orlmSet(formula, data, set, direction="increase", n=NULL, base=1,
        control = orlmcontrol())

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

set

either a character string (see constrSet), or a list with slots for constr, rhs, and nec similarly defined as in orlm

direction

direction of the order constraints

n

a (possibly named) vector of sample sizes for each group

base

column of the constraint matrix representing a control group

control

a list of control arguments; see orlmcontrol for details.

Details

This function is just a wrapper for repeated calls of orlm with different constraint definitions. Predefined lists with constraint-sets can be constructed with function constrSet.

Value

an object of class list

Author(s)

Daniel Gerhard and Rebecca M. Kuiper

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.

See Also

orlm, constrSet, goric

Examples

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########################
## Artificial example ##
########################

n <- 10
m <- c(1,2,4,5,2,1)
nm <- length(m)
dat <- data.frame(grp=as.factor(rep(1:nm, each=n)),
                  y=rnorm(n*nm, rep(m, each=n), 1))

(cs <- constrSet(table(dat$grp), set="sequence"))
oss <- orlmSet(y ~ grp-1, data=dat, set=cs)
oss
# the same as:
oss <- orlmSet(y ~ grp-1, data=dat, set="sequence")