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.
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References
Brophy, C., Gibson, D., Wayne, P., & Connolly J. (2007). A modelling framework for analysing the reproductive output of individual plants grown in monoculture. Ecological Modelling, 207, 99–108.
Brophy, C., Gibson, D. J., Wayne, P. M., & Connolly J. (2008). How reproductive allocation and flowering probability of individuals in plant populations are affected by position in stand size hierarchy, plant size and CO2 regime. Journal of Plant Ecology, 1, 207–215.
Collett, D. (1993). Modelling binary data. London: Chapman & Hall/CRC.
Efron, B., & Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy. Statistical Science, 1, 54–77.
Efron B., & Tibshirani, R. (1993) An introduction to the bootstrap. New York: Chapman & Hall.
Harper, J. (1977). Population biology of plants. London: Academic.
Jawitz, J. (2004). Moments of truncated continuous univariate distributions. Advances in Water Resources, 27, 269–281.
McCulloch, C. (1994). Maximum likelihood variance components estimation for binary data. Journal of the American Statistical Association, 89, 330–335.
McCulloch, C., & Searle, S. (2001). Generalised, linear, and mixed models. In W. Shewhart & S. Wilks (Eds.), In probability and statistics. New York: Wiley.
McLachlann, P., & Peel, D. (2000). Finite mixture models. New York: Wiley.
Schmid, B., Polasek, W., Weiner, J., Krause, A., & Stoll, P. (1994). Modelling of discontinuous relationships in biology with censored regression. American Naturalist, 143, 494–507.
Wayne, P., Carnelli, A., Connolly, J., & Bazzaz, F. (1999). The density dependence of plant responses to elevated CO2. Journal of Ecology, 87, 183–192.
Acknowledgements
CB is the holder of an Environmental Protection Agency (Ireland) Doctoral Scholarship, JC has received support from an Enterprise Ireland International Collaboration grant for this work, and DG received support from the United States Department of Agriculture.
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Brophy, C., Gibson, D., Wayne, P.W., Connolly, J. (2014). A Mixture Model and Bootstrap Analysis to Assess Reproductive Allocation in Plants. In: MacKenzie, G., Peng, D. (eds) Statistical Modelling in Biostatistics and Bioinformatics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-04579-5_14
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DOI: https://doi.org/10.1007/978-3-319-04579-5_14
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