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

Package `restriktor`

implements estimation, testing and evaluating of linear equality and
inequality restriktions about parameters and effects for univariate and multivariate
normal models and generalized linear models.

Package: | restriktor |

Type: | Package |

Version: | 0.2-800 |

Date: | 2020-02-25 |

License: | GPL (>=2) |

LazyLoad: | yes |

Function `restriktor`

estimates the parameters of an univariate
and multivariate linear model (`lm`

), robust estimation of the
linear model (`rlm`

) or a generalized linear model (`glm`

)
subject to linear equality and/or inequality restriktions. The real
work horses are the `conLM`

, `conMLM`

, the `conRLM`

,
and the `conGLM`

functions. A major advantage of restriktor
is that the constraints can be specified by a text-based description.
This means that users do not have to specify the complex constraint matrix
(comparable with a contrast matrix) themselves.

The function `restriktor`

offers the possibility to compute
(model robust) standard errors under the restriktions. The
parameter estimates can also be bootstrapped, where bootstrapped
standard errors and confidence intervals are available via the
summary function. Moreover, the function computes the Generalized
Order-restricted Information Criterion (GORIC), which is a
modification of the AIC and a generalization of the ORIC.

The function `iht`

(alias `conTest`

) conducts restricted
hypothesis tests. F, Wald/LRT and score test-statistics are available.
The null-distribution of these test-statistics takes the form of a
mixture of F-distributions. The mixing weights (a.k.a. chi-bar-square
weights or level probabilities) can be computed using the multivariate
normal distribution function with additional Monte Carlo steps or via
a simulation approach. Bootstrap methods are available to calculate the
mixing weights and to compute the p-value directly. Parameters estimates
under the null- and alternative-hypothesis are available from the
summary function.

The function `goric`

(generalized order-restricted information
criterion) computes GORIC values, weights and relative-weights or GORICA
(generalized order-restricted information crittion approximation) values,
weights and relative weights. The GORIC(A) values are comparable to the AIC
values. The function offers the possibility to evaluate an order-restricted
hypothesis against its complement, the unconstrained hypothesis or against
a set of hypotheses. For now, only one order-restricted hypothesis can be
evaluated against its complement but work is in progress to evaluate a set
of order-restricted hypothesis against its complement.

The package makes use of various other R packages: quadprog is used for restricted estimation, boot for bootstrapping, ic.infer for computing the mixing weights based on the multivariate normal distribution, lavaan for parsing the constraint syntax.

The output of function `restriktor`

belongs to S3 class
`conLM`

, `conMLM`

, `conRLM`

or `conGLM`

.

The output of function `conTest`

belongs to S3 class `conTest`

.

These classes offer print and summary methods.

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

from ic.infer, which is originally from
vsn, authored by Wolfgang Huber, available under LGPL.

The output style of the `iht`

print function is strongly
inspired on the summary of the `ic.test`

function from the
ic.infer package.

Leonard Vanbrabant and Yves Rosseel - Ghent University

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

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.

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

Schoenberg, R. (1997). Constrained Maximum Likelihood. *Computational
Economics*, **10**, 251–266.

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

Silvapulle, M. (1992a). Robust tests of inequality constraints and one-sided
hypotheses in the linear model. *Biometrika*, **79**, 621–630.

Silvapulle, M. (1992b). Robust wald-type tests of one-sided hypotheses in
the linear model. *Journal of the American Statistical Association*,
**87**, 156–161.

Silvapulle, M. (1996). Robust bounded influence tests against one-sided
hypotheses in general parametric models. *Statistics & probability
letters*, **31**, 45–50.

Silvapulle, M.J. and Sen, P.K. (2005). *Constrained Statistical Inference*.
Wiley, New York

Vanbrabant, L. and Kuiper, R. (n.d.). Giving the complement a compliment: Evaluating a theory-based hypothesis against its complement using the GORIC.

See also `restriktor`

, `iht`

,
packages boot, goric, ic.infer,
mvtnorm, and quadprog.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## Data preparation
## Ages (in months) at which an infant starts to walk alone.
DATA <- ZelazoKolb1972
idx <- which(DATA$Group == "Control")
DATA <- DATA[-idx, ]
## unrestricted linear model
fit.lm <- lm(Age ~ -1 + Group, data = DATA)
summary(fit.lm)
## restricted linear model with restriktions that the walking
## exercises would not have a negative effect of increasing the
## mean age at which a child starts to walk.
myConstraints <- ' GroupActive < GroupPassive;
GroupPassive < GroupNo '
fit.con <- restriktor(fit.lm, constraints = myConstraints)
summary(fit.con)
``` |

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