Linear combinations of environmental variables
Dummy Environmental variables
Transforming environmental variables
Since the statistical significance of a CCA analysis is determined by a randomization
test, there is no need to transform data to fulfill statistical assumptions. However,
transformations can be used to dampen the influence of outliers. The choice of
transformation impacts the location of sample scores, species scores, and
environmental scores. A dampening transformation (e.g. square root) tend to make
samples and species more evenly spread out. Only rarely will transformation of
environmental variables change the overall interpretation of an ordination.
References cited
See also selected references for self education.
Roberts, D. W. 1986. Ordination on the basis of fuzzy set theory. Vegetatio 66:123 
Linear combinations of environmental variables
An environmental variable cannot be a linear combination of other variables. For
example, sediments can be defined by  % clay, % sand, and % silt, which must add
to 100%. Thus if you give the % of clay and sand then the % silt in the sample can
be calculated as 100   %clay   %sand. The % silt is a linear combination of the other
variables. Data that includes linear combinations will produce a singular matrix which
cannot be solved. ECOM will remove variables to avoid this problem. However, you
should avoid this problem by eliminating unnecessary variables (eg only include two
of the 3 particle types ), as ECOM  will not detect situations where rounding errors
result in a situation where the linear combination is not exact; eg when you have
entered 33.3% for all 3 sediment variables. If this occurs then the results can be
unreliable as the numerical methods might not find an accurate solution.
This problem also occurs with the use of dummy variables.
See also:
Selecting Environmental variables
Dummy Environmental variables
Transforming environmental variables
Dummy Environmental variables
Some aspects of the environment cannot be described using continuous variables. For
example land use is better described by categorical variables. Categorical variables
need to be coded as dummy variables if they are to be used in either CCA or RDA.
Dummy variables are binary; they take the value 1 or 0.
For every categorical variable with K categories, only K 1 dummy variables can be
included in the analysis (see 
Linear combinations of environmental variables
For example, suppose in a study of a chalk stream fauna at 5 sites we categorise the
stream bed as unmodified, recently dredged or dredged more than 10 years ago, then
these data can be entered as two variables as follows:
Copyright 2004  PISCES Conservation Ltd

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