An Algorithm and Fortran Program for Multivariate LAD ? (?1 of ?2) Regression

Kaufman, E. H.; Taylor, G. D.; Mielke, Paul W.; Berry, Kenneth J.

doi:10.1007/s00607-001-1440-y

Cited by 19 publications

(7 citation statements)

References 13 publications

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“…The method can also be used for tetrahedral coordinates plus luminance ( and as four variables). The multivariate analysis we recommend (Mielke & Berry, 2002b,c) is based on a combination of multivariate multiple least sum of Euclidean distances (LSED) regression analyses (Kaufman et al ., 2002; Mielke & Berry, 2003) and the Euclidean distance version of multi‐response permutation procedures (MRPP) described in Chapter 2 of Mielke & Berry (2001). This method has two desirable features: (1) it satisfies the congruence principle (Mielke, 1985; Mielke & Berry, 2001; see pages 19–20), i.e.…”

Section: Comparing Entire Colour Patternsmentioning

confidence: 99%

“…For the two‐group analyses considered here, the null hypothesis is that all points are randomly ordered or, consequentially, the within‐group points were distributed in the same way as the between‐group points. Computational algorithms are available for MRPP (Mielke & Berry, 2001), LSED (Kaufman et al ., 2002; Mielke & Berry, 2003), and the composite LSED‐MRPP residual analysis (Mielke & Berry, 2002b,c). We develop these methods further in this paper.…”

Section: Comparing Entire Colour Patternsmentioning

confidence: 99%

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Comparing entire colour patterns as birds see them

Endler

Mielke

2005

Biological Journal of the Linnean Society

687

1,061

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Colour patterns and their visual backgrounds consist of a mosaic of patches that vary in colour, brightness, size, shape and position. Most studies of crypsis, aposematism, sexual selection, or other forms of signalling concentrate on one or two patch classes (colours), either ignoring the rest of the colour pattern, or analysing the patches separately. We summarize methods of comparing colour patterns making use of known properties of bird eyes. The methods are easily modifiable for other animal visual systems. We present a new statistical method to compare entire colour patterns rather than comparing multiple pairs of patches. Unlike previous methods, the new method detects differences in the relationships among the colours, not just differences in colours. We present tests of the method's ability to detect a variety of kinds of differences between natural colour patterns and provide suggestions for analysis. © 2005 The Linnean Society of London, Biological Journal of the Linnean Society, 2005, 86, 405–431.

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Section: Comparing Entire Colour Patternsmentioning

confidence: 99%

Section: Comparing Entire Colour Patternsmentioning

confidence: 99%

Comparing entire colour patterns as birds see them

Endler

Mielke

2005

Biological Journal of the Linnean Society

687

1,061

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“…The coefficients required by the linear model were obtained by least sum of absolute (LAD) or Euclidean (LSED) distance rather than by ordinary least squares (OLS), implementing linear programming techniques (Kaufman et al, 2002). The residuals obtained after fitting the regression model were analysed implementing multiresponse permutation procedures (MRPP) to test for group differences examining differences among the medians of the different groups (Berry and Mielke, 1999;Mielke and Berry, 2007).…”

Section: Experimental Design and Statistical Analysismentioning

confidence: 99%

Trade-off between camouflage and sexual dimorphism revealed by UV digital imaging: the case of Australian Mallee Dragons (Ctenophorus fordi)

Garcia

Rohr

Dyer

2013

Journal of Experimental Biology

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SUMMARYColour patterns displayed by animals may result from the balance of the opposing requirements of sexual selection through display and natural selection through camouflage. Currently, little is known about the possibility of the dual purpose of an animal colour pattern in the UV region of the spectrum, which is potentially perceivable by both predators and conspecifics for detection or communication purposes. Here, we implemented linearised digital UV photography to characterise and quantify the colour pattern of an endemic Australian Agamid lizard classically regarded as monomorphic when considering data from the visible region of the spectrum. Our results indicate a widespread presence of UV elements across the entire body of the lizards and these patterns vary significantly in intensity, size and frequency between sexes. These results were modelled considering either lizard or avian visual characteristics, revealing that UV reflectance represents a trade-off between the requirements of sexual displaying to conspecifics and concealment from avian predators. Supplementary material available online at

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“…, x,,. An algorithm to obtain the unstandardzed Pjk values is given by Kaufman, et al (2002). In comparison to alternative multivariate multiple regression models that minimize only the multivariate multiple regression model based on the least sum of Euclidean &stances does not vary with coordinate rotation and possesses the desired geometrical attribute of satisfying the triangle inequahty of a metric (Welke, 1987;Mielke & Berry, 2001, pp.…”

mentioning

confidence: 99%

“…In comparison to alternative multivariate multiple regression models that minimize only the multivariate multiple regression model based on the least sum of Euclidean &stances does not vary with coordinate rotation and possesses the desired geometrical attribute of satisfying the triangle inequahty of a metric (Welke, 1987;Mielke & Berry, 2001, pp. 4, 23, 237;Kaufman, et al, 2002). If variations do occur with coordinate rotation, then the probabhty (P) value of a statistical analysis may depend on its arbitrary orientation in the data space.…”

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confidence: 99%