Pre-Estimation Checks

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.