A comparative analysis of the reduced major axis technique of fitting lines to bivariate data

Leduc, Daniel J.

doi:10.1139/x87-107

Cited by 42 publications

(13 citation statements)

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“…Iterative approaches are therefore required. Several equation forms have been proposed and discussed (Barker and Diana, 1974;Borcherds and Sheth, 1995;Brauers and Finlayson-Pitts, 1997;Bruzzone and Moreno, 1998;Chong, 1991Chong, , 1994Christian and Tucker, 1984;Christian et al, 1986;Gonzalez et al, 1992;Irwin and Quickenden, 1983;Jones, 1979;Kalantar, 1990Kalantar, , 1991Krane and Schecter, 1982;Leduc, 1987;Lybanon, 1984ab, 1985Macdonald and Thompson, 1992;MacTaggart and Farwell, 1992;Markovsky and Van Huffel, 2007;Moreno, 1996;Neri et al, 1990Neri et al, , 1991Orear, 1982;Pasachoff, 1980;Pearson, 1901;Press et al, 1992a,b;Reed, 1990;Riu and Rius, 1995;Squire et al, 1990;Williamson, 1968;York, 1966York, , 1969York et al, 2004). This list is large to provide a comprehensive reference for the reader.…”

Section: Methods When Both X and Y Have Errorsmentioning

confidence: 99%

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008

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Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least-squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheetbased template is made available that employs one method for bivariate fitting.

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Section: Methods When Both X and Y Have Errorsmentioning

confidence: 99%

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008

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“…In such conditions, the use of regression techniques like the first axis of PCA or least-squares regression, should be avoided; they are sensitive to outliers and tend to overstress the importance of, in this case, extreme values of either density or weight on the general trajectory of the population. A non-parametric regression technique like Theil's incomplete regression, or another scaleindependent technique (like geometric mean regression) should be preferred for assessing the overall slope of the size/density trajectory of a population over time (see Leduc 1987).…”

Section: Discussion the Self-thinning Trajectory In Roadside Populationsmentioning

confidence: 99%

Density‐dependent mortality, growth and size inequality in roadside populations of the annual herb Galium aparine L.

Puntieri

Hall

1996

Ecological Research

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Biomass, plant size, plant density and the inequality of sizes were assessed for autumn-emerging roadside populations dominated by Galium aparine during early stages of growth in two independent studies. A third data set dealt with the survival of labelled seedlings belonging to different cohorts of emergence. One data set showed that the slope of the log-log size/density relationship for all plant species present in the samples was closer to -1.5 and that for G. aparine was closer to -1.0 in five separate populations. Biomass increase and density decrease was not found to take place in any of these simultaneously. The size inequality of G. aparine tended to increase or to remain constant during periods of high mortality, and in the early harvests it was negatively related to population density. The second data set revealed simultaneous decreases of both biomass and density of G. aparine and of all plant species during a period of a month soon after emergence, and a higher size inequality of G. aparine in those patches where plant density (and that of G. aparine) was lower. The labelling of seedlings indicated density-dependent mortality and a higher probability of survival for seedlings emerging very early. The size/density relationship of roadside populations dominated by 6:. aparine may follow a trajectory over time similar to that predicted by the 3/2 power law of self-thinning, but this species seems to have a weak size hierarchy development and limited individual growth at high population densities. The importance of plant architecture in relation to this response is discussed.

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“…Because our primary interest was to investigate the functional relationship between two variables, i.e., ln(QMD) and ln(N), instead of least-square regression, we employed reduced major axis regression (RMA), which has been documented to perform better when the primary interest is the values of the equation parameters themselves [60]. Solomon and Zhang [35] used this regression method to produce the self-thinning line for three mixed softwood forest types (hemlock-red spruce, spruce-fir, and cedar-black spruce) in the northeastern US.…”

Section: Selection Of Full Stocked Plots and Regression Methodsmentioning

confidence: 99%

Does the Slope of the Self-thinning Line Remain a Constant Value across Different Site Qualities?—An Implication for Plantation Density Management

Zeng

Wörns

et al. 2017

Forests

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Abstract:The self-thinning rule is regarded as one of the most important principles in plantation management. This rule, involving the assumption of a constant slope coefficient, has been universally applied when regulating stand density. In this study, we hypothesized that the slope coefficient can change significantly with changes in site quality. To test this hypothesis, we first grouped forest plots into 5 categories based on site index. Second, we produced the self-thinning line represented by the Reineke function for each of the 5 site categories, selecting fully stocked plots using reduced major axis regression. Third, the slope coefficients for the different categories were tested for significant differences. The results indicated that in general, the slope was significantly different with different site quality. In addition, we observed that the slope of the self-thinning line exhibited a steeper trend for sites of lower quality, which indicated increased self-thinning or reduced self-tolerance. Finally, we concluded that it is imperative to produce specific self-thinning lines for different site quality categories.

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A comparative analysis of the reduced major axis technique of fitting lines to bivariate data

Cited by 42 publications

References 0 publications

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

Density‐dependent mortality, growth and size inequality in roadside populations of the annual herb Galium aparine L.

Does the Slope of the Self-thinning Line Remain a Constant Value across Different Site Qualities?—An Implication for Plantation Density Management

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