Dray S., Chessel D., Thioulouse J. (2003). Co-inertia analysis and the linking of ecological data tables. Ecology, 84:3078--3089.

Ecological studies often require studying the common structure of a pair of data tables. Co-inertia analysis is a multivariate method for coupling two tables. It is often neglected by ecologists who prefer the widely used methods of redundancy analysis and canonical correspondence analysis. We present the co-inertia criterion for measuring the adequacy between two data sets. Co-inertia analysis is based on this criterion as are canonical correspondence analysis or canonical correlation analysis, but the latter two have additional constraints. Co-inertia analysis is very flexible and allows many possibilities for coupling. Co-inertia analysis is suitable for quantitative and/or qualitative or fuzzy environmental variables. Moreover, various weighting of sites and various transformations and/or centering of species data are available for this method. Hence, more ecological considerations can be taken into account in the statistical procedures. Moreover, the principle of this method is very general and can be easily extended to the case of distance matrices or to the case of more than two tables. Simulated ecological data are used to compare the co-inertia approach with other available methods.

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