An Accurate Standard Error Estimation for Quadratic Exponential Logistic Regressions by Applying Generalized Estimating Equations to Pseudo-Likelihoods
In quadratic exponential binary distribution (QIBD) regression models, standard errors estimated via pseudolikelihood are severely underestimated. To address this, we propose a novel standard error correction method that integrates pseudolikelihood estimation with generalized estimating equations (GEE). Theoretically, we prove that adopting an independence working correlation structure within the GEE framework ensures consistent parameter estimation, whereas misspecifying the dependence structure induces substantial bias. Through analytical derivation and extensive simulations across diverse dependency scenarios, our method demonstrably improves both accuracy and robustness of standard error estimation. Empirical applications to toxicological longitudinal data and constitutional court judgment network data confirm its strong performance under realistic, complex dependency structures. This work provides the first standard error estimator for QIBD-type models that simultaneously achieves computational efficiency and statistical reliability.