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

Abstract

The statistical analysis of annual growth of Posidonia oceanica is traditionally carried out through Gaussian linear models applied to untransformed, or log-transformed, data. In this paper, we claim that there are good reasons for re-considering this established practice, since real data on annual growth often violate the assumptions of Gaussian linear models, and show that the class of Generalized Linear Models (GLMs) represents a useful alternative for handling such violations. By analyzing Sicily PosiData-1, a real dataset on P. oceanica growth data gathered in the period 2000–2002 along the coasts of Sicily, we find that in the majority of cases Normality is rejected and the effect of age on growth is nonlinear. AGLM with Gamma distribution and identity or log link appears to be a satisfactory choice in most cases. Furthermore, when back-dating techniques are employed, each plant provides a longitudinal set of dependent data, and a proper statistical analysis should take such dependence into account. We show that the class of Generalized Linear Mixed Models (GLMM), an extension of GLM’s, provides an effective way to analyze longitudinal P. oceanica growth data. Again, by using examples taken from Sicily PosiData-1, we show that misleading results can be obtained if dependence is ignored and that other techniques, like sub-sampling, are not a good option for overcoming the so-called ‘‘pseudo-replications’’ problem.