🤖 AI Summary
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.
📝 Abstract
For a set of binary response variables, conditional mean models characterize the expected value of a response variable given the others and are popularly applied in longitudinal and network data analyses. The quadratic exponential binary distribution is a natural choice in this context. However, maximum likelihood estimation of this distribution is computationally demanding due to its intractable normalizing constant, while the pseudo-likelihood, though computationally convenient, tends to severely underestimate the standard errors. In this work, we investigate valid estimation methods for the quadratic exponential binary distribution and its regression counterpart. We show that, when applying the generalized estimating equations to the pseudo-likelihood, using the independence working correlation yields consistent estimates, whereas using dependent structures, such as compound symmetric or autoregressive correlations, may introduce non-ignorable biases. Theoretical properties are derived, supported by simulation studies. For illustration, we apply the proposed approach to the carcinogenic toxicity of chemicals data and the constitutional court opinion wringing data.