Starshaped Mean Residual Life Modeling of Rural STEM Teacher Retention

Thomas M. Menino Convention & Exhibition Center 

Rural STEM teacher shortages motivate survival models capturing early-career attrition and student achievement impacts. We adapt the starshaped mean equilibrium life (SMEL) framework-defined by nondecreasing mean residual life ratio m(t)/t-to model teacher careers as burn-in-to-equilibrium processes. We embed SMEL in proportional mean residual life (PMRL) regression and estimate a three-parameter Weibull baseline via Bayesian inference using the No-U-Turn Sampler. Monte Carlo studies under decreasing, increasing, and bathtub hazards with up to 40% censoring show SMEL-PMRL maintains minimal bias and reduces integrated Brier scores by ~20% relative to Cox, accelerated failure time, and standard Weibull models. Applied to 2018-2023 NSF Noyce data on 169 rural Texas STEM teachers and 3,214 students, the model reveals a 32% rural penalty in expected tenure, a 38\% drop in remaining tenure during years 1-3, and positive effects of Noyce scholarships and rural-origin backgrounds. Joint teacher--student modeling links persistence beyond year 3 to substantial achievement gains, illustrating how SMEL-PMRL yields interpretable, policy-relevant metrics for timing retention interventions.

mean residual life

survival analysis

Bayesian methods

teacher retention

rural STEM education

PMRL regression 

Section on Nonparametric Statistics