A New Linearized Formula for the Law of Total Effective Temperature and the Evaluation of Line-Fitting Methods with Both Variables Subject to Error
By T. Ikemoto, K. Takai. 2000
329 citations recorded by the source corpus.
Abstract In the quantitative analysis of experimental data regarding temperature-dependent development, the so-called law of total effective temperature is sometimes expressed in the linearized equation 1,: 1/D = −(t/k) + (1/k)T. D indicates the duration of development; T, temperature; t, the estimated developmental zero temperature; and k, the effective cumulative temperature. The method of fitting usually involves the regression of y = 1/D on x = T. Although the degree of fitting of equation 1, to data within optimum temperature ranges is fairly satisfactory, we have in the current study addressed three problems regarding the use of equation 1, and methods of fitting involving the regression of y on x. First, we found that the detection of optimum temperature ranges is frequently difficult with equation 1,. Second, in applying the method of regression of y on x with equation 1, the weights of the data points are disproportionate between those in the upper and lower parts of the line and they are not homogeneous along the temperature axis. The lower the temperature, the more disproportionate weight is burdened and the less weight is loaded. Third, in most of the data, errors in the x-variable are ignored. The second and third problems would in most cases result in a reduction in the slope of the line, a smaller t, and a larger k. Therefore, we proposed a new linearized formula: (DT) = k + tD. We further propose the use of the reduced major axis, obtained as the solution of the functional model among bivariate errors-in-variables models, in the method of fitting to data. We demonstrated that the majority of the problems raised above could be unraveled under this new approach based on statistical analysis.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d555945dd68c19743dc4e00c0624c46ddab38724
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Citations in the corpus
- Life history parameters for Nesidiocoris tenuis (Reuter) (Het., Miridae) under different temperature regimes (2009, methodology): “The thermal constant and lower threshold temperature for hatching times and nymphal development were determined using the linear model proposed by Ikemoto and Takai (2000), DT = k + tD.”
- The Utility of Coleoptera in Forensic Investigations (2009, methodology): “Such studies should sample according to published standards to produce robust developmental models ( Ikemoto and Takai 2001; Richards and Villet 2008).”
- Quantitative comparisons and models of time-averaging in bivalve and brachiopod shell accumulations (2010, result): “Although the two fitting methods yield very similar results in this case (data not shown), reduced major axis is more appropriate because both the x and y variables have errors associated with them (Griffiths 1998; Ikemoto and Takai 2000; Ayers 2001).”
- Intrinsic Optimum Temperature for Development of Insects and Mites (2005, methodology): “The reduced major axis lineÞtting method (see Ikemoto and Takai 2000) is also applicable to this step.”