Conducting Environmental Impact Assessment in Developing Countries (United Nations University, 1999, 375 p.)
 4. EIA methods
 4.3 Matrix
 (introduction...) 4.3.1 Descriptive matrix 4.3.2 Symbolized matrix 4.3.3 Numeric and scaled matrices 4.3.4 The component interaction matrix 4.3.5 Advantages of the matrix approach 4.3.6 Limitations of the matrix approach

### 4.3.4 The component interaction matrix

The component interaction matrix (CIM) developed by Ross was first used in an EIA of five alternative sites for the transshipment of lumber on the Nanaimo estuary, British Columbia. The uniqueness of the area under consideration prompted an investigation of secondary impacts in an attempt to present the full implications of the project proposals.

In a CIM, the environment is represented by a list of environmental components, arranged along both horizontal and vertical axes. Direct dependencies between the components are identified and marked as "1'' in the appropriate cells. Interdependencies up to the nth order (i.e., all higher order dependencies) can be determined by the use of a matrix powering procedure.

The Canadian CIM above used 21 environmental components, and 120 first-order dependencies were identified. Matrix manipulation (powering) was performed until fifth-order dependencies had been discovered. From the information revealed by the powering process, a minimum link matrix was derived. All cells of the original CIM were used to contain integer values denoting the length (in terms of intervening nodes) of the shortest linkages connecting the two components. A disruption matrix was also formulated in which the impacts of each project alternative on all primary dependencies were scored on an ordinal scale from 0 to 3.

Provided that the initial identification of dependencies is explicit, the values (derived by mathematical procedures) in the minimum link matrix are substantive. The processes of matrix multiplication are not complicated, but they are tedious for large matrices and would normally require the use of a computer. It is unfortunate that, while the minimum link matrix can indicate the existence and length of a linkage between any two components, the structure of these linkages is not exposed.

The results of the component interaction analysis were not readily incorporated into the overall assessment of the transshipment project. In fact, the ad hoc assessment report of the five Nanaimo Port site proposals made little use of the results displayed in the component interaction, minimum link, and disruption matrices.

The CIM has been reviewed by Clark et al. (1981) and Bisset, but has not received much positive comment. The minimum link matrix is useful as a means of communicating the complex structure of the environmental systems likely to be affected by a project.