Ordination or gradient analysis, in

multivariate analysis Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., '' multivariate random variables''. Multivariate statistics concerns understanding the differ ...

, is a method complementary to

data clustering Cluster analysis or clustering is the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each o ...

, and used mainly in

exploratory data analysis In statistics, exploratory data analysis (EDA) is an approach of data analysis, analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or ...

(rather than in

hypothesis testing A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. T ...

). In contrast to cluster analysis, ordination

orders Order, ORDER or Orders may refer to: * A socio-political or established or existing order, e.g. World order, Ancien Regime, Pax Britannica * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * H ...

quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or latent variables, are then characterized numerically and/or graphically in a

biplot Biplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot. A biplot overlays a ''score plot'' with a ''loading plot''. A biplot allows information on both samples and variables of a d ...

. The first ordination method,

principal components analysis Principal component analysis (PCA) is a Linear map, linear dimensionality reduction technique with applications in exploratory data analysis, visualization and Data Preprocessing, data preprocessing. The data is linear map, linearly transformed ...

, was suggested by Karl Pearson in 1901.

Methods

Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis,

correspondence analysis Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical ...

(CA) and its derivatives (

detrended correspondence analysis Detrended correspondence analysis (DCA) is a multivariate statistics, statistical technique widely used by ecology, ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify Community (ecol ...

, canonical correspondence analysis, and redundancy analysis, belong to the first group). The second group includes some distance-based methods such as non-metric

multidimensional scaling Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of n objects in a set into a configuration of n points mapped into an ...

, and machine learning methods such as T-distributed stochastic neighbor embedding and

nonlinear dimensionality reduction Nonlinear dimensionality reduction, also known as manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds which cannot be adequately captured by linear de ...

. The third group includes model-based ordination methods, which can be considered as multivariate extensions of

Generalized Linear Models In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by ...

. Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects. Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods.

Applications

Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant

community ecology In ecology, a community is a group or association of populations of two or more different species occupying the same geographical area at the same time, also known as a biocoenosis, biotic community, biological community, ecological communit ...

. It is also used in

genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinians, Augustinian ...

and

systems biology Systems biology is the computational modeling, computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological system ...

for

microarray A microarray is a multiplex (assay), multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of biological interactions. It is a two-dimensional array on a Substrate (materials science), solid substrate—usu ...

data analysis and in

psychometrics Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and rela ...

References

External links

#General #*http://ordination.okstate.edu/ The Ordination Web Page - Ordination Methods for Ecologists #*https://www.davidzeleny.net/anadat-r/doku.php/en:start #*https://link.springer.com/article/10.1007/s11192-015-1744-x #Specific Techniques #*http://www.statsoft.com/textbook/stcoran.html #*http://www.statsoft.com/textbook/stmulsca.html #*http://www.statsoft.com/textbook/glosfra.html #*https://link.springer.com/article/10.1007/s11192-015-1744-x Ordination method for articles, using year of publication, impact factor and number of citations. #Software #*http://home.centurytel.net/~mjm/pcordwin.htm #*http://www.microcomputerpower.com/catalog/canoco.html #*http://www.brodgar.com #*http://www.VisuMap.com #*https://cran.r-project.org/web/packages/vegan/vegan.pdf R package for classical ordination methods #*https://cran.r-project.org/package=seriation R package for ordering objects #*https://cran.r-project.org/web/packages/gllvm/index.html R package for model-based ordination #*https://cran.r-project.org/web/packages/VGAM/index.html R package for model-based ordination #*https://cran.r-project.org/web/packages/boral/index.html R package for model-based ordination Dimension reduction

Methods

Applications

See also

References

Further reading

External links