iht() function

The iht() function is for informative hypothesis testing. The minimal requirement is a fitted restriktor() object. The remaining options, can be changed to your personal preferences.

iht(object, type = "summary", test = "F", neq.alt = 0,
    boot = "no", R = 9999, p.distr = rnorm,
    parallel = "no", ncpus = 1L, cl = NULL, seed = 1234,
    verbose = FALSE, control = NULL, ...)

For example, the syntax might look as follows:

iht(restr.ANOVA)

Hypothesis tests

Type A: Test H0: all restrictions with equalities ("=") active against HA: at least one inequality restriction (">") strictly true.

Type B: Test H0: all restrictions with inequalities (">") (including some equalities ("=")) active against HA: at least one restriction false (some equality restrictions may be maintained).

Type C: Test H0: at least one restriction false ("<") against HA: all restrictions strictly true (">"). This test is based on the union-intersection principle. Note that, this test only makes sense in case of no equality constraints.

Type global: equal to Type A but H0 contains additional equality constraints. This test is analogue to the global F-test in lm, where all coefficients but the intercept equal 0.

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 inequality restrictions. Its main role is to prevent wrong conclusions from significant results from hypothesis test Type A.

The exact finite sample distributions of the non-robust F-, score- and LR-test statistics based on restricted OLS estimates and normally distributed errors, are a mixture of F-distributions under the null hypothesis (Wolak, 1987). In agreement with Silvapulle (1992), we found that the results based on these mixtures of F-distributions approximate the tail probabilities of the robust tests better than their asymptotic distributions. Therefore, all p-values for hypothesis test Type "A", "B" and "global" are computed based on mixtures of F-distributions.

Note that, in case of equality constraints only, the null-distribution of the (robust) F-test statistics is based on an F-distribution. The (robust) Wald- and (robust) score-test statistics are based on chi-square distributions.

By default, the iht() function prints an overview of all available hypothesis tests.

iht(fit.ANOVA, constraints = myConstraints)


Restriktor: restricted hypothesis tests ( 14 residual degrees of freedom ):


Multiple R-squared remains 0.985 

Constraint matrix:
   GroupActive GroupNo GroupPassive    op rhs active
1:          -1       0            1    >=   0     no
2:           0       1           -1    >=   0     no


Overview of all available hypothesis tests:

Global test: H0: all parameters are restricted to be equal (==)
         vs. HA: at least one inequality restriction is strictly true (>)
       Test statistic: 5.9780,   p-value: 0.02834

Type A test: H0: all restrictions are equalities (==) 
         vs. HA: at least one inequality restriction is strictly true (>)
       Test statistic: 5.9780,   p-value: 0.02834

Type B test: H0: all restrictions hold in the population
         vs. HA: at least one restriction is violated
       Test statistic: 0.0000,   p-value: 1

Type C test: H0: at least one restriction is false or active (==) 
         vs. HA: all restrictions are strictly true (>)
       Test statistic: 1.0627,   p-value: 0.1529

Note: Type C test is based on a t-distribution (one-sided), 
      all other tests are based on a mixture of F-distributions.

Instead of an overview of all available hypothesis tests, separate hypothesis tests can be obtained, which provide more detailed information, such as the restricted estimates under the null- and alternative-hypothesis. The results for hypothesis test Type A can be requested as follows:

iht(fit.ANOVA, constraints = myConstraints, type = "A")

By default, the iht() function uses the F-bar test-statistic. In addition, a likelihood ratio (LR) test and a score-test are available and can be obtained by adding the argument test = "score" or "LRT" to the iht() function.

iht(fit.ANOVA, constraints = myConstraints, type = "A", test = "score")

Explaining the iht() arguments