Description Usage Arguments Details Value References See Also Examples

`orgls`

is used to fit generalised least square models analogously to the function `gls`

in package `nlme`

but with order restrictions on the parameters.

1 2 3 4 5 6 |

`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 orgls 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; |

`nec` |
number of equality constraints; a numeric value treating the first nec constr rows as equality constraints, or a logical vector with |

`weights` |
a |

`correlation` |
a |

`control` |
a list of control arguments; see |

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 orgls

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
# generating example data
library(mvtnorm)
# group means
m <- c(0,5,5,7)
# compound symmetry structure of residuals
# (10 individuals per group, rho=0.7)
cormat <- kronecker(diag(length(m)*10), matrix(0.7, nrow=length(m), ncol=length(m)))
diag(cormat) <- 1
# different variances per group
sds <- rep(c(1,2,0.5,1), times=10*length(m))
sigma <- crossprod(diag(sds), crossprod(cormat, diag(sds)))
response <- as.vector(rmvnorm(1, rep(m, times=10*length(m)), sigma=sigma))
dat <- data.frame(response,
grp=rep(LETTERS[1:length(m)], times=10*length(m)),
ID=as.factor(rep(1:(10*length(m)), each=length(m))))
## set of gls models:
# unconstrained model
m1 <- orgls(response ~ grp-1, data = dat,
constr=rbind(c(0,0,0,0)), rhs=0, nec=0,
weights=varIdent(form=~1|grp),
correlation=corCompSymm(form=~1|ID))
# simple order
m2 <- orgls(response ~ grp-1, data = dat,
constr=rbind(c(-1,1,0,0),c(0,-1,1,0),c(0,0,-1,1)), rhs=c(0,0,0), nec=0,
weights=varIdent(form=~1|grp),
correlation=corCompSymm(form=~1|ID))
# equality constraints
m3 <- orgls(response ~ grp-1, data = dat,
constr=rbind(c(-1,1,0,0),c(0,-1,1,0),c(0,0,-1,1)), rhs=c(0,0,0), nec=3,
weights=varIdent(form=~1|grp),
correlation=corCompSymm(form=~1|ID))
``` |

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