Estimation of Contrasts of Log-Frequencies

Analyses Based on Log-Frequencies In bio-assay, if X is bn(p), it may be required to estimate a = log 0 where 0 = p/(l p), a very simple constant since ax = log p log (1 p). Similarly in the analysis of multiway contingency tables, when a hierarchical logistic or log-linear model is to be fitted, the parameters of interest will be contrasts in log-frequencies for all saturation models and some unsaturated models. A discussion of some of the models is to be found in Cox (1970). Haldane (1955) and Anscombe (1956) independently suggested the use of log [(X + ')/(n + 1)] to estimate log (p). The bias incurred is of the order of 11-2 when n is large.