Ecological Archives E089-082-A2
نویسندگان
چکیده
Lindsay A. Turnbull, Cloé Paul-Victor, Bernhard Schmid, and Drew W. Purves. 2008. Growth rates, seed size, and physiology: Do small-seeded species really grow faster? Ecology 89:1352–1363. Appendix B. PARAMETER ESTIMATION FOR THE DAILY GROWTH MODEL. The likelihood analysis used measurements of aboveand belowground biomass of individual plants, growing in different temperature and nutrient regimes, to estimate the parameters in the daily growth model (see main text and Eqs. 1 4). The first step of a likelihood analysis is to define the log-likelihood of the data X, given the model, and parameter values , (hereafter referred to as the likelihood only). Given the definition of , the analysis proceeds by finding the parameters θ that maximize (the so-called maximumlikelihood estimates, or MLEs), and the confidence intervals on each parameter. In special cases involving simple models and simple error structures (e.g., linear regression), the MLEs and confidence intervals can be found analytically. For complex, nonlinear models, such as those employed here, this is not possible, and computational methods are needed to explore different parameter sets. Nonetheless, the underlying approach in these more complex cases is formally identical to simpler, more familiar statistical methods, including (for example) linear regression and ANOVA. For an introduction to likelihood analysis in ecology see Hilborn and Mangel (1997). θ ( | ) X θ ( | ) X θ ( | ) X θ
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