Three-Way Nested Data for Age Determination Techniques Applied to Cetaceans
In the previous case study, we showed how multiple samples from bacteria in honey bees from the same hive gave a nested data structure, and mixed modelling techniques were applied to allow for correlations between observations from the same hive. The bee
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Three-Way Nested Data for Age Determination Techniques Applied to Cetaceans E.N. Ieno, P.L. Luque, G.J. Pierce, A.F. Zuur, M.B. Santos, N.J. Walker, A.A. Saveliev, and G.M. Smith
20.1 Introduction In the previous case study, we showed how multiple samples from bacteria in honey bees from the same hive gave a nested data structure, and mixed modelling techniques were applied to allow for correlations between observations from the same hive. The bee data provided an example of two-way nested data, and the underlying theory for this was discussed in Chapter 5. In this chapter, we go one step further and use three-way nested data, which extends the two-way approach discussed in Chapter 5. The underlying theory builds on the approach used for two-way data, and we recommend reading Chapter 5 before starting this chapter as we assume familiarity with the theory, model selection, and R code for two-way nested data. We use a subset of the data analysed in Luque (2008), who compared the results from three staining methods to determine the age of cetaceans stranded in Spain and Scotland. The data are nested in the sense that samples derive from multiple species, and from each species, we have various specimens (individual animals). From each specimen, several teeth were sectioned and tooth sections were stained using three staining methods (the Mayer Haematoxylin, Ehlrich Haematoxylin, and Toluidine Blue methods), giving three age estimates from each tooth. A diagram of the nested structure is given in Fig. 20.1. The three age observations per specimen (obtained by the three staining methods) are likely to be correlated, but we may also expect correlation between age readings within the same species (if, for example, different species have different lifespans and/or different age classes tend to become stranded and thus become the source of samples). The response variable is the estimated age of the animal. Available explanatory variables are sex (male or female), location of stranding (Scotland or Spain), and stain (Mayer Haematoxylin, Ehlrich Haematoxylin, and Toluidine Blue). In Chapter 4 of West et al. (2006), a three-way nested data set on mathematic scores for students within multiple classes and multiple schools is analysed. From a E.N. Ieno (B) Highland Statistics Ltd., Newburgh, AB41 6FN, United Kingdom
A.F. Zuur et al., Mixed Effects Models and Extensions in Ecology with R, Statistics for Biology and Health, DOI 10.1007/978-0-387-87458-6 20, C Springer Science+Business Media, LLC 2009
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Fig. 20.1 Sketch of the nested structure of the data. Six cetacean species were sampled. These were Delphinus delphis, Lagenorhynchus acutus, Phocoena phocoena, Stenella coeruleoalba, Stenella frontalis, and Tursiops truncatus. For each species, various specimens (animals) were available. The number of specimens per species range between 3 and 25. From each specimen, three estimated age readings were obtained by the three staining methods (labeled as 1, 2, and 3 in the graph)
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