Construct a rating–position interaction term compatible with SIMEX

Construct and validate an interaction term between Glicko‑2 rating difference and board-position lopsidedness for logistic regressions of chess outcomes, and develop a methodology that remains compatible with the SIMEX measurement‑error calibration, recognizing that lopsided positions should attenuate the effect of rating difference and may require incorporating absolute skill as an additional covariate.

Background

The authors note that some positions are effectively decided, reducing the predictive power of rating differences. They argue this calls for an interaction term between rating difference and position lopsidedness.

However, they explicitly state that it is unclear how to construct such an interaction and warn it would interfere with SIMEX calibration. They also point out that absolute skill may matter from lopsided positions, implying additional model terms.