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.
restriktor estimates the parameters of an univariate
and multivariate linear model (
lm), robust estimation of the
linear model (
rlm) or a generalized linear model (
subject to linear equality and/or inequality restriktions. The real
work horses are 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.
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.
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
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
The output of function
conTest belongs to S3 class
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
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.
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## 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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