Monotone likelihood is a common issue in political science duration modeling, often leading to divergent parameter estimates. This problem arises when covariate values change monotonically with respect to failure time. Using mathematical explanations and simulations, this article demonstrates how Firth's penalized maximum likelihood estimation provides solutions.

Data & Methods Used

• Mathematical exposition

• Monte Carlo simulations

• Empirical political science applications

Key Findings

• Conditions for acute monotone likelihood identified

• Guidance for applying duration modeling techniques provided to avoid divergence toward infinity

Why It Matters

This research helps prevent misinterpretation and model misspecification in analyzing political events.