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Mean and median bias reduction in generalized linear models

机译：广义线性模型中的均值和中位数偏差减少

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摘要

This paper presents an integrated framework for estimation and inference from generalized linear models using adjusted score equations that result in mean and median bias reduction. The framework unifies theoretical and methodological aspects of past research on mean bias reduction and accommodates, in a natural way, new advances on median bias reduction. General expressions for the adjusted score functions are derived in terms of quantities that are readily available in standard software for fitting generalized linear models. The resulting estimating equations are solved using a unifying quasi-Fisher scoring algorithm that is shown to be equivalent to iteratively reweighted least squares with appropriately adjusted working variates. Formal links between the iterations for mean and median bias reduction are established. Core model invariance properties are used to develop a novel mixed adjustment strategy when the estimation of a dispersion parameter is necessary. It is also shown how median bias reduction in multinomial logistic regression can be done using the equivalent Poisson log-linear model. The estimates coming out from mean and median bias reduction are found to overcome practical issues related to infinite estimates that can occur with positive probability in generalized linear models with multinomial or discrete responses, and can result in valid inferences even in the presence of a high-dimensional nuisance parameter.
机译：本文提出了一个综合框架，用于使用调整后的得分方程从广义线性模型进行估计和推断，从而导致均值和中位数偏差减少。该框架统一了以往关于平均偏差减少的研究的理论和方法论方面，并自然地适应了中位数偏差减少的新进展。调整后的得分函数的一般表达式是根据标准软件中容易获得的，用于拟合广义线性模型的数量得出的。使用统一的准费舍尔评分算法来求解所得的估计方程，该算法显示为具有经过适当调整的工作变量的迭代加权最小二乘方。建立了均值和中位数偏差减少的迭代之间的形式联系。当需要估计色散参数时，可使用核心模型不变性来开发一种新颖的混合调整策略。还显示了如何使用等效的Poisson对数线性模型完成多项式Lo​​gistic回归中的中位数偏差减少。发现均值和中位数偏差减少产生的估计值可以克服与无限估计值有关的实际问题，这些问题可能在具有多项式或离散响应的广义线性模型中以正概率发生，并且即使存在高估计值，也可以得出有效推论尺寸扰动参数。

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