We present a detailed discussion of the theoretical properties of quadratic inference function estimators of the parameters in marginal linear regression models. We consider the effect of the choice of working correlation on fundamental questions including the existence of quadratic inference function estimators, their relationship with generalized estimating equations estimators, and the robustness and asymptotic relative efficiency of quadratic inference function and generalized estimating equations estimators. We show that the quadratic inference function estimators do not always exist and propose a way to handle this. We then show that they have unbounded influence functions and can be more or less asymptotically efficient than generalized estimating equations estimators. We also present empirical evidence to demonstrate these results. We conclude that the choice of working correlation can have surprisingly large effects.

中文翻译：

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工作相关性对纵向数据拟合模型的影响

我们详细讨论了边际线性回归模型中参数的二次推理函数估计器的理论特性。我们考虑工作相关性的选择对基本问题的影响，包括二次推理函数估计量的存在性、它们与广义估计方程估计量的关系，以及二次推理函数和广义估计方程估计量的鲁棒性和渐近相对效率。我们证明二次推理函数估计器并不总是存在，并提出了一种处理这个问题的方法。然后我们证明它们具有无界影响函数，并且可以比广义估计方程估计器或多或少地渐近有效。我们还提供了经验证据来证明这些结果。我们得出的结论是，工作相关性的选择可能会产生令人惊讶的巨大影响。