Assessment of preference among a range of options using log ratio analysis

Animals generally exhibit preference from among the resources available to them. Preference data are compositional, since they describe the proportion of some resource, such as time or energy, which has been allocated to each option, and the sum of these proportions must be 1. The unit-sum constraint places a restriction on the types of analysis that are appropriate. The method of log ratios provides a transformation that leads to analyses in which the unit-sum constraint is automatically satisfied. This paper describes a form of log ratio analysis that allows estimation of the relative preferences for the options available and the influence on these preferences of the conditions under which the options are presented. The method is most suitable for application to data from controlled experiments in which options are presented in pairs, as equal availability of rile choices can best be achieved and standard regression techniques call be used to fit the proposed models. The proposed analysis is demonstrated by a simple example in which the main difficulty of log ratio analysis, namely, unutilized options, is addressed and overcome.