Modeling Posidonia oceanica growth data: from linear to generalized linear mixed models

The statistical analysis of annual growth of Posidonia oceanica is traditionally carried out through Gaussian linearmodels applied to untransformed, or log-transformed, data. In this paper, we claim that there are good reasons forre-considering this established practice, since real data on annual growth often violate the assumptions of Gaussianlinear models, and show that the class of Generalized Linear Models (GLMs) represents a useful alternative for handlingsuch violations. By analyzing Sicily PosiData-1, a real dataset on P. oceanica growth data gathered in the period2000–2002 along the coasts of Sicily, we find that in the majority of cases Normality is rejected and the effect of age ongrowth is nonlinear. AGLM with Gamma distribution and identity or log link appears to be a satisfactory choice in mostcases. Furthermore, when back-dating techniques are employed, each plant provides a longitudinal set of dependentdata, and a proper statistical analysis should take such dependence into account. We show that the class of GeneralizedLinear Mixed Models (GLMM), an extension of GLM’s, provides an effective way to analyze longitudinal P. oceanicagrowth data. Again, by using examples taken from Sicily PosiData-1, we show that misleading results can be obtained ifdependence is ignored and that other techniques, like sub-sampling, are not a good option for overcoming the so-called‘‘pseudo-replications’’ problem.