A Mixture Model and Bootstrap Analysis to Assess Reproductive Allocation in Plants

Abstract

In this paper we discuss issues that arise in predicting from complex models for the analysis of reproductive allocation (RA) in plants. Presenting models of RA requires prediction on the original scale of the data and this can present challenges if transformations are used in modelling. It is also necessary to estimate without bias the mean level of RA as this may reflect a plant’s ability to contribute in the next generation. Several issues can arise in modelling RA including the occurrence of zero values and the clustering of plants in stands which can lead to the need for complex modelling. We present a two-component finite mixture model framework for the analysis of RA data with the first component a censored regression model on the logarithmic scale and the second component a logistic regression model. Both components contain random error terms to allow for potential correlation between grouped plants. We implement the framework using data from an experiment carried out to assess environmental factors on reproductive allocation. We detail the issues that arose in predicting from the model and present a bootstrap analysis to generate standard errors for the predictions from and to test for comparisons among predictions.