Define x_j

Define x_j to use for the analytic derivatives of the variance-covariance matrix. x_j is derived based on the provided utility functions and design candidate using base model.matrix to automatically handle alternative specific attributes and interaction terms

define_x_j(utility, design_candidate)

Arguments

utility

A named list of utility functions. See the examples and the vignette for examples of how to define these correctly for different types of experimental designs.

design_candidate

The current design candidate under consideration

Value

The list x_j

Details

We can extract the attribute names for each utility function to allow us to place the correct restrictions on the design candidate. Specifically, we restrict all levels of unavailable attributes to zero for alternatives where they do not feature. This is to ensure that we do not give weight when deriving the variance-covariance matrix using derive_vcov. Furthermore, the Xs are "sorted" using the order of the candidate set, which ensures that when we calculate the sum of the probabilities times X, the correct columns are added together. See derive_vcov.