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 include 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