33

ECOM II

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 

31.

7.3

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

7.4

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:

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