These authors describe a statistical analytical technique, “nonlinear regression”, that potentially provides more information than linear regression techniques including ANCOVA. The basic linear regression formula includes the intercept and the slope as parameters; nonlinear regression adds an exponent parameter. In this paper, these parameters are referred to as k1 (intercept), k2 (slope), and k3 (exponent), in the formula
y = k1 + k2x^k3
where y is the response variable and x is the explanatory variable.These authors tested their technique on three example datasets from previous studies. The first example is most thoroughly examined, and involves a plant competition experiment. One key feature of all of the example analysis is the dataset must be paired, such that each data point on the x axis corresponds to a partner data point on the y axis. In the plant competition example, individual plants that did not experience competition are paired with individuals that did, because each pair of plants was grown in a communal pot that was treated at the pot level with manipulations such as fertilizer application. The continuous dataset is plant size, measured as the absolute gain in mass over the course of the growing season.
The exponent parameter k3 can take on any value between negative and positive infinity, to describe curves that may be accelerating, saturating, or straight. At values of 1 or -1, k3 is not informative as a parameter, and should be discarded from the model. This analysis is based on a model-building and model-testing technique, where models with various values for the three parameters are tested against null models and each other in an iterative fashion to find the model that best fits the data.
This approach is likely to be useful in the analysis of some of the data collected at Alexandra Fjord in 2009.
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