  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 this model type. Conventionally,
for the power-related sample size calculations a deviation from the null
hypothesis (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.
