conTest_summary: function for computing all available hypothesis tests

Description

conTest_summary computes all available hypothesis tests and returns and object of class conTest for which a print function is available. The conTest_summary can be used directly and is called by the conTest function if type = "summary".

Usage

# S3 method for restriktor
conTest_summary(object, test = "F", ...)

Value

An object of class conTest, for which a print is available. More specifically, it is a list with the following items:

CON: a list with useful information about the constraints.
Amat: constraints matrix.
bvec: vector of right-hand side elements.
meq: number of equality constraints.
meq.alt: same as input neq.alt.
iact: number of active constraints.
type: same as input.
test: same as input.
Ts: test-statistic value.
df.residual: the residual degrees of freedom.
pvalue: tail probability for Ts.
b.eqrestr: equality restricted regression coefficients. Only available for type = "A" and type = "global", else b.eqrestr = NULL.
b.unrestr: unrestricted regression coefficients.
b.restr: restricted regression coefficients.
b.restr.alt: restricted regression coefficients under HA if some equality constraints are maintained.
Sigma: variance-covariance matrix of unrestricted model.
R2.org: unrestricted R-squared.
R2.reduced: restricted R-squared.
boot: same as input.
model.org: original model.

Arguments

object

an object of class restriktor.

test

test statistic; for information about the null-distribution see details.

for object of class lm; if "F" (default), the classical F-statistic is computed. If "Wald", the classical Wald-statistic is computed. If "score", the classical score test statistic is computed.
for object of class rlm; if "F" (default), a robust likelihood ratio type test statistic (Silvapulle, 1992a) is computed. If "Wald", a robust Wald test statistic (Silvapulle, 1992b) is computed. If "score", a score test statistic (Silvapulle, 1996) is computed.

...

the same arguments as passed to the iht function, except for type, of course.

Author

Leonard Vanbrabant and Yves Rosseel

References

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. and Silvapulle, P. (1995). A score test against one-sided alternatives. American statistical association, 90, 342--349.

Silvapulle, M. (1996) On an F-type statistic for testing one-sided hypotheses and computation of chi-bar-squared weights. Statistics and probability letters, 28, 137--141.

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

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

Wolak, F. (1987). An exact test for multiple inequality and equality constraints in the linear regression model. Journal of the American statistical association, 82, 782--793.

Examples

Run this code

## example 1:
# the data consist of ages (in months) at which an 
# infant starts to walk alone.

# prepare data
DATA1 <- subset(ZelazoKolb1972, Group != "Control")

# fit unrestricted linear model
fit1.lm <- lm(Age ~ -1 + Group, data = DATA1)

# the variable names can be used to impose constraints on
# the corresponding regression parameters.
coef(fit1.lm)

# constraint syntax: assuming that the walking 
# exercises would not have a negative effect of increasing the 
# mean age at which a child starts to walk. 
myConstraints1 <- ' GroupActive  < GroupPassive < GroupNo '

iht(fit1.lm, myConstraints1)


# another way is to first fit the restricted model
fit.restr1 <- restriktor(fit1.lm, constraints = myConstraints1)

iht(fit.restr1)

# Or in matrix notation.
Amat1 <- rbind(c(-1, 0,  1),
               c( 0, 1, -1))
myRhs1 <- rep(0L, nrow(Amat1)) 
myNeq1 <- 0

fit1.con <- restriktor(fit1.lm, constraints = Amat1,
                       rhs = myRhs1, neq = myNeq1)
iht(fit1.con)

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