- Restriktor is an open-source project, which means that the R code is no black-box and available online at GitHub.

Restriktor is developed for applied users. This means that we have tried to come up with a user-friendly constraint syntax. In R, categorical predictors are represented by 'factors'. For example, the ‘Group’ variable with three factor levels: 'Low', 'Medium', and 'High'. Then, the constraints can be specified using the factor level names. In case of a continuous variable the constraints can be specified using the variable name. For example, the categorical variable 'Group' and one continuous predictor 'x1' the constraints syntax might look as follows:

`myConstraints <- ' GroupLow < GroupMedium GroupMedium < GroupHigh x1 > 0 '`

In addition, we have tried to provide all the necessary tools and output to evaluate the order-constrained hypothesis. The main tools are the

`restriktor()`

function and the`conTest()`

function. The restriktor() function is used for estimating the restricted estimates and the conTest() function is for testing the order-constrained hypothesis. For example, the output of the restriktor() function might look as follows:`Restriktor: restricted linear model: Residuals: Min 1Q Median 3Q Max -2.877222 -0.773776 0.005096 0.755305 2.978666 Coefficients: Estimate Std. Error t value Pr(>|t|) group1 0.945747 0.075464 12.533 < 2.2e-16 *** group2 0.945747 0.075464 12.533 < 2.2e-16 *** group3 1.058034 0.106722 9.914 < 2.2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.0672 on 297 degrees of freedom Standard errors: standard Multiple R-squared reduced from 0.4656 to 0.4623 Generalized Order-Restricted Information Criterion: Loglik Penalty Goric -443.6900 2.8333 893.0466`

- support for linear inequality constraints, linear equality constraints, or a combination of both.
- support for the robust (rlm) and generalized linear model (glm).
- (robust) standard error under the constraints.
- bootstrapped standard errors (standard and model-based).
- hypothesis tests: global/omnibus, Type A, Type B, and Type C.
- test-statistics: F/Wald, score and likelihood ratio.
- parametric and model-based bootstrapped p-values.
- two methods to compute the chi-square-bar mixing weights: (1) based on the multivariate normal distribution function with additional Monte Carlo steps, or (2) based entirely on Monte Carlo simulation.
- model selection under (in)equality constraints. (GORIC)
- ...