Description Details Value Acknowledgements Author(s) References See Also Examples

Package `ic.infer`

implements estimation and testing for multivariate normal
expectations with linear equality- and inequality constraints. This also includes
inference on linear models with linear equality- and inequality constraints on the
parameters. Decomposition of R-squared is also included for these models.

Function `ic.est`

estimates the constrained expectation of a multivariate normal
random vector, function `ic.test`

conducts related tests.

Function `orlm`

estimates constrained parameters in normal linear models based on
a linear model object or a covariance matrix. The function offers the possibility of
bootstrapping the estimates. Tests and confidence intervals are provided by a summary
function.

Function `or.relimp`

decomposes the $R^2$-values analogously to metric
`lmg`

in package relaimpo for unconstrained linear models.
However, `or.relimp`

is far less comfortable
to use und subject to severe limitations, since automatic selection of restrictions
for sub models is not in all cases trivial.

The package makes use of various other R packages: quadprog is used for
constrained estimation, mvtnorm in calculation of weights for null distributions
of test statistics, kappalab for averaging over orderings in function `or.relimp`

,
and boot for bootstrapping.

The theory behind inequality-constrained estimation and testing as well as
functionality of the package are explained in a vignette (Link from within dynamic help:
../doc/ic.infer.pdf) that is based on Groemping (2010).
The vignette can also be opened from the command line by `vignette("ic.infer")`

.

The output of function `ic.est`

belongs to S3 class `orest`

.

The output of function `ic.test`

belongs to S3 class `ict`

.

The output of function `orlm`

belongs to S3 classes `orlm`

and `orest`

.

All these classes offer print and summary methods.

The output of function `or.relimp`

is a named vector.

This package uses as an internal function the function `nchoosek`

from vsn,
authored by Wolfgang Huber, available under LGPL.

It also uses modifications of numerical routines that were provided by John Fox in R-help.

Thanks go to Wiley for permission of incorporating the grades data from Table 1.3.1 of Robertson, Wright and Dykstra (1988) into the package.

Ulrike Groemping, BHT Berlin

Groemping, U. (2010). Inference With Linear Equality And Inequality
Constraints Using R: The Package ic.infer. *Journal of Statistical Software*,
Forthcoming.

Kudo, A. (1963). A multivariate analogue of the one-sided test.
*Biometrika* **50**, 403–418

Robertson T, Wright F, Dykstra R (1988). *Order-Restricted Inference*.
Wiley, New York.

Sasabuchi, S. (1980) A test of a multivariate normal mean with composite
hypotheses determined by linear inequalities. *Biometrika*
**67**, 429–429

Shapiro, A. (1988). Towards a unified theory of inequality-constrained
testing in multivariate analysis. *International Statistical Review*
**56**, 49–62

Silvapulle, M.J. and Sen, P.K. (2004). *Constrained Statistical Inference*.
Wiley, New York

See also `ic.est`

, `ic.test`

, `orlm`

,
`or.relimp`

, packages boot, kappalab,
mvtnorm, quadprog, and relaimpo

1 2 3 4 5 6 7 8 | ```
## unrestricted linear model for grade point averages
limo <- lm(meanGPA~.-n, weights=n, data=grades)
summary(limo)
## restricted linear model with restrictions that better HSR ranking
## cannot deteriorate meanGPA
orlimo <- orlm(lm(meanGPA~.-n, weights=n, data=grades), index=2:9,
ui=make.mon.ui(grades$HSR))
summary(orlimo, brief=TRUE)
``` |

ic.infer documentation built on Jan. 27, 2018, 1:04 a.m.

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