Evans R J, Forcina A
Statistical Laboratory, University of Cambridge, UK.
Comput Stat Data Anal. 2013 Oct 1;66:1-7. doi: 10.1016/j.csda.2013.02.001.
The two main algorithms that have been considered for fitting constrained marginal models to discrete data, one based on Lagrange multipliers and the other on a regression model, are studied in detail. It is shown that the updates produced by the two methods are identical, but that the Lagrangian method is more efficient in the case of identically distributed observations. A generalization is given of the regression algorithm for modelling the effect of exogenous individual-level covariates, a context in which the use of the Lagrangian algorithm would be infeasible for even moderate sample sizes. An extension of the method to likelihood-based estimation under -penalties is also considered.
本文详细研究了两种用于将约束边际模型拟合到离散数据的主要算法，一种基于拉格朗日乘数，另一种基于回归模型。结果表明，这两种方法产生的更新是相同的，但在观测值同分布的情况下，拉格朗日方法更有效。本文给出了回归算法的一种推广，用于对外生个体水平协变量的效应进行建模，在这种情况下，即使样本量适中，使用拉格朗日算法也是不可行的。本文还考虑了该方法在惩罚似然估计下的扩展。
