orlm: Fitting multivariate regression models with order...
In daniel-gerhard/goric: Generalized Order-Restricted Information Criterion

Description Usage Arguments Details Value References See Also Examples

View source: R/orlm.R

This is a modification of the lm function, fitting (multivariate) linear models with order constraints on the model coefficients.

orlm(formula, data, constr, rhs, nec, control = orlmcontrol())

## S3 method for class 'formula'
orlm(formula, data, constr, rhs, nec,
  control = orlmcontrol())

`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.
`constr`	matrix with constraints; with rows as constraint definition, columns should be in line with the parameters of the model
`rhs`	vector of right hand side elements; Constr \; θ ≥q rhs; number should equal the number of rows of the constr matrix
`nec`	number of equality constraints; a numeric value treating the first nec constr rows as equality constraints, or a logical vector with `TRUE` for equality- and `FALSE` for inequality constraints.
`control`	a list of control arguments; see `orlmcontrol` for details.

The contraints in the hypothesis of interest are defined by Constr, rhs, and nec. The first nec constraints are the equality contraints: Constr[1:nec, 1:tk] θ = rhs[1:nec]; and the remaing ones are the inequality contraints: Constr[nec+1:c_m, 1:tk] θ ≥q rhs[nec+1:c_m]. Two requirements should be met:

The first nec constraints must be the equality contraints (i.e., Constr[1:nec, 1:tk] θ = rhs[1:nec]) and the remaining ones the inequality contraints (i.e., Constr[nec+1:c_m, 1:tk] θ ≥q rhs[nec+1:c_m]).
When rhs is not zero, Constr should be of full rank (after discarding redundant restrictions).

an object of class orlm

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.

solve.QP, goric

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

# unrestricted linear model
cm1 <- matrix(0, nrow=1, ncol=4)
fm1 <- orlm(y ~ grp-1, data=dat, constr=cm1, rhs=0, nec=0)

# order restriction (increasing means)
cm2 <- rbind(c(-1,1,0,0),
             c(0,-1,1,0),
             c(0,0,-1,1))
fm2 <- orlm(y ~ grp-1, data=dat, constr=cm2,
            rhs=rep(0,nrow(cm2)), nec=0)

# order restriction (increasing at least by delta=1)
fm3 <- orlm(y ~ grp-1, data=dat, constr=cm2,
            rhs=rep(1,nrow(cm2)), nec=0)

# larger than average of the neighboring first 2 parameters
cm4 <- rbind(c(-0.5,-0.5,1,0),
             c(0,-0.5,-0.5,1))
fm4 <- orlm(y ~ grp-1, data=dat, constr=cm4,
            rhs=rep(0,nrow(cm4)), nec=0)

# equality constraints (all parameters equal)
fm5 <- orlm(y ~ grp-1, data=dat, constr=cm2,
            rhs=rep(0,nrow(cm2)), nec=nrow(cm2))
            
# alternatively
fm5 <- orlm(y ~ grp-1, data=dat, constr=cm2,
            rhs=rep(0,nrow(cm2)), nec=c(TRUE,TRUE,TRUE))
            
# constraining the 1st and the 4th parameter
# to their true values, and the 2nd and 3rd between them
cm6 <- rbind(c( 1,0,0,0),
             c(-1,1,0,0),
             c(0,-1,0,1),
             c(-1,0,1,0),
             c(0,0,-1,1),
             c(0,0, 0,1))
fm6 <- orlm(y ~ grp-1, data=dat, constr=cm6,
            rhs=c(1,rep(0,4),5), nec=c(TRUE,rep(FALSE,4),TRUE))
            
            
###############################################################
## 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)

# 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))