A Multivariate Ordering of Vegetation Data Based on Gaussian Type Gradient Response Curves

Ihm, Peter; Groenewoud, H. van

doi:10.2307/2258600

Cited by 61 publications

(20 citation statements)

References 17 publications

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“…Second, in weighted average ordination (Ellenberg, 1948;Whittaker, 1956) sample positions are assigned only on the basis of species weights (and vice versa) so that clustering the samples can have no effect on their relative positions in the ordination. Third, Gaussian ordination (Gauch et al, 1974;Ihm & van Groenewoud, 1975) should be improved by heavy sampling toward the ends of the gradient since such a dispersion of samples gives maximum information about the more poorly defined curves.…”

Section: Introductionmentioning

confidence: 99%

Effects of sample distribution along gradients on eigenvector ordination

Mohler

1981

Vegetatio

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In general, disproportionately heavy sampling of the ends of a gradient increases the interpretability of eigenvector ordinations. More specifically, correspondence analysis (CA) and detrended correspondence analysis (DCA) best reproduce the original positions of samples in simulated coenoclines when samples are clustered toward the ends of the axis. Principal components analysis (PCA) reproduces the original sample positions less well than either CA or DCA and shows no improvement as samples are increasingly clustered toward the ends of the axis. PCA and CA show less curvature of one dimensional data into the second axis when sampling favors the ends of the axis.

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Section: Introductionmentioning

confidence: 99%

Effects of sample distribution along gradients on eigenvector ordination

Mohler

1981

Vegetatio

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“…In ecology a similar method called Gaussian ordination (Ihm & van Groenewoud, 1975) has been in use for quite some time. Some attempts have also been made to establish the relationship between unfolding analysis, Gaussian ordination, and correspondence analysis (Escoufier, 1987;Heiser, 1981Heiser, , 1987Ihm & van Groenewoud, 1984;ter Braak, 1986).…”

Section: Relations To Other Methodsmentioning

confidence: 99%

Analysis of contingency tables by ideal point discriminant analysis

Takane

1987

Psychometrika

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Cross-classified data are frequently encountered in behavioral and social science research. The loglinear model and dual scaling (correspondence analysis) are two representative methods analyzing such data. An alternative method, based on ideal point discriminant analysis (DA), proposed for analysis of contingency tables, which in a certain sense encompasses the two existing methods. A variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and/or as direct constraints on model parameters. This, along with maximum likelihood estimation of the model parameters, allows interesting model comparisons. This is illustrated by the analysis of several data sets.

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“…where s i is a site-specific parameter (Ihm and Groenewoud 1975;ter Braak 1988) or s i = 1, so that there are no site specific parameters (ter Braak 1985(ter Braak , 1986, h j is a species-specific parameter denoting the maximum expected abundance, x i is a site score, often interpreted as a latent environmental variable, u j is a species score, often interpreted as a latent trait and, in this model, the optimum for the jth species and σ j is the niche width of the jth species. The link with the correspondence analysis methods is strongest when σ j = σ and when this constant σ is small compared to the range of the site scores (ter Braak 1985), i.e.…”

Section: Appendix A1: Model-based Derivationsmentioning

confidence: 99%

“…Indeed, rewriting model (27) in an exponential form and using a first order Taylor expansion in terms of b te u j x i yields the reconstitution formula of correspondence analysis (Greenacre 1984;Ihm and Groenewoud 1975):…”

Section: Appendix A1: Model-based Derivationsmentioning

confidence: 99%

Algorithms and biplots for double constrained correspondence analysis

2018

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Correspondence analysis with linear external constraints on both the rows and the columns has been mentioned in the ecological literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by defining the method as maximizing the fourth-corner correlation between linear combinations, by providing novel algorithms, which demonstrate relationships with related methods, and by making a detailed study of possible biplots and associated approximations. The method is illustrated using ecological data on the abundances of species in sites and where the species are characterized by traits and sites by environHandling Editor: Bryan F. J. Manly. Electronic supplementary material 123Environ Ecol Stat mental variables. The trait data and environment data form the external constraints and the question is which traits and environmental variables are associated, how these associations drive species abundances and how they can be displayed in biplots. With microbiome data becoming widely available, these and related multivariate methods deserve more study as they might be routinely used in the future.

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A Multivariate Ordering of Vegetation Data Based on Gaussian Type Gradient Response Curves

Cited by 61 publications

References 17 publications

Effects of sample distribution along gradients on eigenvector ordination

Effects of sample distribution along gradients on eigenvector ordination

Analysis of contingency tables by ideal point discriminant analysis

Algorithms and biplots for double constrained correspondence analysis

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