General log-linear models are widely used to express the association in multivariate frequency data on contingency tables. The paper focuses on the power analysis for testing the goodness-of-fit hypothesis for these models. Conventionally, for the power-related sample size calculations a deviation from the null hypothesis, aka effect size, is specified by means of the chi-square goodness-of-fit index. It is argued that the odds ratio is a more natural measure of effect size, with the advantage of having a data-relevant interpretation. Therefore, a class of log-affine models that are specified by odds ratios whose values deviate from those of the null by a small amount can be chosen as an alternative. Being expressed as sets of constraints on odds ratios, both hypotheses are represented by smooth surfaces in the probability simplex, and thus, the power analysis can be given a geometric interpretation as well. A concept of geometric power is introduced and a Monte-Carlo algorithm for its estimation is proposed. The framework is applied to the power analysis of goodness-of-fit in the context of multinomial sampling. An iterative scaling procedure for generating distributions from a log-affine model is described and its convergence is proved. To illustrate, the geometric power analysis is carried out for data from a clinical study.

翻译：通用对数线性模型广泛应用于表达列联表中多元频率数据的关联性。本文聚焦于检验这些模型的拟合优度假设的检验效能分析。传统上，在基于检验效能的样本量计算中，偏离零假设的效应量（即效应大小）通过卡方拟合优度指数来指定。本文认为优势比是一种更自然的效应量度量，其优势在于具有数据相关的可解释性。因此，可以选择一类由优势比值偏离零假设微小量指定的对数仿射模型作为备择假设。由于两种假设均被表示为优势比上的约束条件集，它们在概率单纯形中表现为光滑曲面，因此检验效能分析亦可赋予几何解释。本文提出了几何检验效能的概念，并设计了其蒙特卡洛估计算法。该框架被应用于多项抽样情境下的拟合优度检验效能分析。本文描述了从对数仿射模型生成分布的迭代尺度化算法，并证明了其收敛性。为说明该方法，本文对一项临床研究数据执行了几何检验效能分析。