The box-cox transformation and non-iterative estimation methods for ordinal log-linear models

Recently Beh and Farver investigated and evaluated three non-iterative procedures for estimating the linear-by-linear parameter of an ordinal log-linear model. The study demonstrated that these non-iterative techniques provide estimates that are, for most types of contingency tables, statistically indistinguishable from estimates from Newton's unidimensional algorithm. Here we show how two of these techniques are related using the Box–Cox transformation. We also show that by using this transformation, accurate non-iterative estimates are achievable even when a contingency table contains sampling zeros.