Show simple item record

dc.contributor.authorRoberts, David W.
dc.date.accessioned2019-03-05T15:33:26Z
dc.date.available2019-03-05T15:33:26Z
dc.date.issued2018-12
dc.identifier.citationRoberts, David W.. "Statistical Analysis of Maximally Similar Sets in Ecological Research." Mathematics 6, no. 12 (December 2018): 317-329. DOI:10.3390/math6120317.en_US
dc.identifier.issn2227-7390
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/15312
dc.description.abstractMaximally similar sets (MSSs) are sets of elements that share a neighborhood in a high-dimensional space defined by a symmetric, reflexive similarity relation. Each element of the universe is employed as the kernel of a neighborhood of a given size (number of members), and elements are added to the neighborhood in order of similarity to the current members of the set until the desired neighborhood size is achieved. The set of neighborhoods is then reduced to the set of unique, maximally similar sets by eliminating all sets that are permutations of an existing set. Subsequently, the within-MSS variability of candidate explanatory variables associated with the elements is compared to random sets of the same size to estimate the probability of obtaining variability as low as was observed. Explanatory variables can be compared for effect size by the rank order of within-MSS variability and random set variability, correcting for statistical power as necessary. The analyses performed identify constraints, as opposed to determinants, in the triangular distribution of pair-wise element similarity. In the example given here, the variability in spring temperature, summer temperature, and the growing degree days of forest vegetation sample units shows the greatest constraint on forest composition of a large set of candidate environmental variables.en_US
dc.language.isoenen_US
dc.rightsCC BY: This license lets you distribute, remix, tweak, and build upon this work, even commercially, as long as you credit the original creator for this work. This is the most accommodating of licenses offered. Recommended for maximum dissemination and use of licensed materials.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/legalcodeen_US
dc.titleStatistical Analysis of Maximally Similar Sets in Ecological Researchen_US
dc.typeArticleen_US
mus.citation.extentfirstpage317en_US
mus.citation.extentlastpage329en_US
mus.citation.issue12en_US
mus.citation.journaltitleMathematicsen_US
mus.citation.volume6en_US
mus.identifier.categoryLife Sciences & Earth Sciencesen_US
mus.identifier.categoryPhysics & Mathematicsen_US
mus.identifier.doi10.3390/math6120317en_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentEcology.en_US
mus.relation.universityMontana State University - Bozemanen_US
mus.data.thumbpage6en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

CC BY: This license lets you distribute, remix, tweak, and build upon this work, even commercially, as long as you credit the original creator for this work. This is the most accommodating of licenses offered. Recommended for maximum dissemination and use of licensed materials.
Except where otherwise noted, this item's license is described as CC BY: This license lets you distribute, remix, tweak, and build upon this work, even commercially, as long as you credit the original creator for this work. This is the most accommodating of licenses offered. Recommended for maximum dissemination and use of licensed materials.