Methods for cross point analysis of double-demand functions in assessing animal preferences

• Two novel approaches for cross point analysis of double demand experiments to assess animal preferences.
• The two novel approaches are compared with two existing approaches from the literature.
• The novel approaches require less population parameters, are more straightforward, have clear interpretation for parameters, are more robust .
• Moreover the novel approaches are numerically less demanding.
• We provide programs for the novel approaches in SAS and GenStat.

Cross point analysis of double demand functions provides a compelling way to quantify the strength of animal preferences for two simultaneously presented resources. During daily sessions, animals have to work to gain access to (a portion of) either resource, e.g. by pressing one of two panels a required number of times (the workload). Each panel is linked to one of the simultaneously presented resources. Workloads are varied over sessions and resources. Per session, for each resource the number of times that an animal is rewarded by access to the resource is observed. Four statistical approaches for analysis of these observations, including two novel approaches, are presented and discussed. The two novel approaches are based on relative numbers of rewards, i.e. analyses of proportions, while the other two methods that have been used before are based on absolute numbers of rewards, i.e. analyses of counts. Data from an experiment investigating preferences of Holstein-Friesian bull calves for two types of roughage (chopped and long hay) will be used to illustrate the calculations. The rationale of the four statistical approaches is given, and their pros and cons are discussed. The two novel approaches will be recommended for future practical use; they are directly tuned to the essential property of a double-demand experiment that animals have a choice between resources and consequently comprise considerably less population parameters than the other two approaches, allowing for more direct and clear interpretation. The novel approaches are less sensitive to model assumptions (more robust), and associated computer algorithms for fitting these models to the data are more reliable.