Pre-Estimation Checks

Important Links

• NFXP Overview

• Quick Start

• Simulation Study

• Bus Engine Example

Read this page before fitting NFXP. These checks support structural interpretation. A satisfactory result does not prove the model. A poor result makes the reward estimate hard to interpret.

NFXP maximizes the conditional log likelihood over the reward parameters, so the model must be identified and numerically stable 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.

Example Diagnostics

These values come from the 200-state example in the Simulation Study:

Diagnostic	Value
Reward features	3
Design rank	3 / 3
Action-contrast rank	3 / 3
Observed states	186 / 200
Actions	2
Observations	7,500

Common Risk Patterns

Feature matrices that copy state-only features identically across actions have zero immediate reward contrasts. Those features can still affect dynamic choices when actions induce different future state distributions. Check the full dynamic design, not only the immediate contrast matrix. 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 uses optimal weighting for missing states. NFXP instead pools all observations through the likelihood.