Computation of Maximum Likelihood Estimates in Association Models
关联模型中最大似然估计的计算AI 解读 ↓
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关联模型中最大似然估计的计算
- 研究问题
- 交叉分类数据的关联模型带有非线性参数约束，如何更可靠、快速地计算最大似然估计，并获得渐近标准差？
- 方法与思路
- 作者利用解除约束不改变模型概率的性质，将似然比与约束偏离平方和组合成目标函数，再用修改的 Newton–Raphson 法求解。
- 材料陈述的贡献
- 摘要称该算法较可靠且快速，并能估计参数的渐近标准差；关键思路是利用参数欠识别下模型概率估计仍不变的性质。
- 阅读关注点
- 应核对目标函数的具体形式、解除约束后参数如何规范化、迭代增大的证明，以及标准差计算如何处理欠识别。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化；迭代增大不代表全局收敛，摘要未给出速度比较或可靠性的具体范围。
原文摘要
In association models for cross-classified data, computation of maximum likelihood estimates (MLE's) is relatively difficult due to the nonlinear constraints on the parameters. Currently available procedures based on the scoring algorithm for constrained maximum likelihood are relatively unreliable, and other cyclic procedures are relatively slow and do not provide estimated asymptotic standard deviations as by-products of calculations. To facilitate computations, it is noted that in standard association models, removal of constraints results in underidentification of parameters but does not affect the model itself, so that the MLE's of cell probabilities and conditional probabilities are unaffected. Given this observation, maximum likelihood estimation may be accomplished by unconstrained maximization of an objective function with two components: a log-likelihood ratio and a sum of squares representing deviations of parameters from their constraints. The objective function is then maximized by using a modification of the Newton-Raphson algorithm that ensures that successive iterations increase the objective function whenever a local maximum has not been reached. The proposed algorithm is shown to be reliable and relatively rapid. In addition, it is shown that the proposed technique may be used to estimate asymptotic standard deviations of parameter estimates. Use of the algorithm in practice is illustrated through some standard examples of association models.