10.4.3. Multilevel analysis

Clustering of losses results in over-dispersed data, but clustering might very well be a biologically relevant phenomenon. A method to investigate correlations between groups of observations is to perform multilevel analysis by means of fitting models that contain random effects (random effects models and mixed models). Classic examples of multilevel analysis include schools or hospitals as random factors in an analysis of dependent variables on the level of students or patients respectively. In the case of colony losses, suitable data levels for random effects are often spatial in nature, as colonies are clustered by beekeepers, beekeepers are clustered in regions or habitat types and the latter are clustered within countries.

See Twisk (2010) and Zuur et al. (2009) for practical application of multilevel analysis methods. Rodríguez (2008) is also useful.  A good online resource for multilevel analysis can be found at the homepage of the University of Bristol Centre for Multilevel Modelling (at http://www.bristol.ac.uk/cmm/ ).