Pre-Estimation Checks

Read this page before fitting NFXP. These checks are gates for structural interpretation: passing them does not prove the model, but failing them makes the reward estimate hard to read.

NFXP maximizes the conditional log likelihood over the reward parameters, so identification and numerical stability need to hold before optimization starts. Run these checks before treating a result as structural evidence.

Check	Why it matters
Feature rank	Rank below the number of parameters means theta is not identified.
Feature condition number	A high condition number signals unstable estimates.
Transition row sums	Each transition row must be a valid probability distribution.
Transition orientation	NFXP expects transitions in the \((A, S, S)\) orientation.
State coverage	Unobserved states produce weak or degenerate likelihood regions.
Action support	Rare actions leave their payoff weakly identified.
Reward normalization	Reward level and scale need a valid anchor.

Canonical Simulation Checks

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

Check	Value	Status
Feature rank	4 / 4	pass
Feature condition number	4.512	pass
Transition row error	2.42e-8	pass
Observed states	21 / 21	pass
State-action coverage	1.000	pass
Action shares	0.345, 0.330, 0.325	pass
Minimum action share	0.325	pass
Exit and absorbing anchor	true	pass

Common Risk Patterns

Feature matrices with state-only features copied identically across actions collapse the action-specific payoff differences, leaving them unidentified. Data with almost no replacement choices can fit in-sample behavior while leaving the replacement cost weakly identified. Transition matrices with the wrong orientation produce plausible arrays but wrong economics. When state coverage is thin, UFXP’s optimal weighting handles missing states more gracefully; NFXP pools all observations through the likelihood and degrades more slowly in coverage.