Pre-Estimation Checks

Read this page before fitting UFXP. The method is fast because it uses empirical choice probabilities directly, so thin or degenerate support is the main thing to rule out first.

UFXP inverts empirical choice probabilities state by state, so its pre-estimation risks are CCP’s plus the usual linear-utility ones. Check these before fitting:

Check	Why it matters for UFXP
Feature rank	A rank-deficient design leaves a direction of theta undetermined; the closed-form solve flags it through converged_.
Feature condition number	Ill-conditioning inflates the variance of the closed-form solve.
State coverage	Conditions are scored only at visited states; unvisited states drop out, and very thin coverage leaves few usable conditions.
Action support per state	A state where one action is never taken makes the log-odds inversion degenerate at that state.
Transition row sums	Transition tensors must be row-stochastic in the (n_actions, n_states, n_states) orientation.
Reward normalization	One action’s utility should anchor the normalization (the reference action).

Canonical Simulation Checks

Values from the canonical synthetic run (see Simulation Study):

Check	Value	Status
Feature rank	4 / 4	pass
Feature condition number	4.51	pass
Observed states	21 / 21	pass
State-action coverage	1.000	pass
Minimum action share	0.325	pass

Common Risk Patterns

Concentrated panels are the pattern to watch. When most trajectories visit a narrow corridor of states (a gridworld walked corner to corner, a mileage process that rarely runs high), the choice-probability estimates at the edges are noisy or absent. The optimal weighting handles this gracefully. Thin states are downweighted by their sample share rather than trusted. But no weighting can recover information the data never carried. If coverage is thin everywhere, prefer NFXP, which pools all observations through the likelihood.