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The aggregation- and distance-based models are a collection of disjoint geometric objects that are attached to the vertices representing permissible preference states: e.four disconnected cubes in Figure 8 for distance-based specifications of. A random preference model is always a single polytope whose vertices are the permissible preference states: e.the irregular pyramid in Figure 9, for Random.

In its current classical (frequentist) form, QT est can test each of these models, stated as a Null Hypothesis, provided that, in the random preference and random utility case, the user provides the mathematical description of the relevant polytope and that the latter is full-dimensional.

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