ic.infer {ic.infer}

Package for inequality-constrained estimation and testing

Description

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.

Details

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").

Value

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.

Acknowledgements

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.

Author(s)

Ulrike Groemping, BHT Berlin

References

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

See also ic.est, ic.test, orlm, or.relimp, packages boot, kappalab, mvtnorm, quadprog, and relaimpo

Examples

## 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)