# one-sided t-test for iht `conTestC` tests linear inequality restricted hypotheses for (robust) linear models by a one-sided t-test. This method is based on the union-intersection principle. It is called by the `conTest` function if all restrictions are equalities. For more information see details. ```r ## S3 method for class 'restriktor' conTestC(object, ...) ``` ## Arguments - `object`: an object of class `restriktor`. - ``...``: no additional arguments for now. ## Details Hypothesis test Type C: * Test H0: at least one restriction false ("\<") against HA: all constraints strikty true ("\>"). This test is based on the intersection-union principle. Note that, this test only makes sense in case of no equality constraints. The null-distribution of hypothesis test Type C is based on a t-distribution (one-sided). Its power can be poor in case of many inequalty constraints. Its main role is to prevent wrong conclusions from significant results from hypothesis test Type A. ## Returns 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. - **test**: same as input. - **Ts**: test-statistic value. - **df.residual**: the residual degrees of freedom. - **pvalue**: tail probability for `Ts`. - **b.unrestr**: unrestricted regression coefficients. - **b.restr**: restricted regression coefficients. - **Sigma**: variance-covariance matrix of unrestricted model. - **R2.org**: unrestricted R-squared. - **R2.reduced**: restricted R-squared. - **boot**: "no", not used (yet). - **model.org**: original model. ## References Silvapulle, M.J. and Sen, P.K. (2005, chapter 5.). **Constrained Statistical Inference**. Wiley, New York ## Author(s) Leonard Vanbrabant and Yves Rosseel ## See Also quadprog , `iht` ## Examples ```r ## 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, type = "C") # another way is to first fit the restricted model fit.restr1 <- restriktor(fit1.lm, constraints = myConstraints1) iht(fit.restr1, type = "C") # 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, type = "C") ```

conTestC function