Describing the problem - Linear Example

PD profile for \(X^1\) (expected value).

(same_group_y_mean_filled %*% same_group_x1_dist_matrix) |> round(digits = 2)

##      [,1]
## [1,] 0.95
## [2,] 0.95
## [3,] 0.95
## [4,] 0.95
## [5,] 0.95

Now, the obtained profile indicates no effect of X1, which is not true.