- The application of principal component analysis (PCA) in pasture science
|Last update: November 24, 2010 12:30:47 PM|
THE APPLICATION OF PRINCIPAL COMPONENT ANALYSIS (PCA) IN PASTURE SCIENCE
P G Marais & P C V du Toit
Grootfontein Agricultural Development Institute, Private Bag X529 Middelburg 5900
Multivariate analyses of variance techniques are conceptually ideal for analysing data on vegetation cover, since they allow measurements such as frequency counts for a number of plant species to be dealt with in a single analysis as an inter-related set, rather than as several univariate analyses of variance. However, complex interactions can also result from interactions, that is, multicollinearity of many simple linear functions. Multicollinearity is the situation which arises in multiple regression when some or all of the explanatory variables are so highly correlated with one another that it becomes very difficult, if not impossible, to disentangle their influences and to obtain a reasonably precise estimate of their effects. Most multivariate techniques involve either side stepping the issue of multicollinearity of the variables by multiple regression techniques or by projecting weighted scores of these variables onto a common axis. Thereby comparing the different variables by determining a set of orthogonal axes that maximize the variance i.e. capture as much of the variance observed as possible on a single axis, the slope coefficients and the correlations for the individual variables can be additive. The latter, known as principal component analysis is used quite extensively in the analysis of ecological data. A study which modelled grazing index values for Nama Karoo plants, involved the estimation of the size of the plants, which included the measurements of, canopy spread cover, basal cover and height. The aboveground phytomass that was regarded as being available to the grazing animal was also measured. This approach of measurement and collection of plant material of Karoo bushes and grasses was considered to provide a fair estimate of the available forage on the veld, especially with the prediction of grazing capacities in mind. Fifty plants per species provided an acceptable mean measurement of size and available phytomass. Four experimental plots in the Nama Karoo with ten representative plant species per plot were used. The present study represents an effort to further our understanding of factors impacting interpretation of the concept of multicollinearity and the application of principal component analysis. PCA generates new variables (principal components) which are a linear function of the original variables. Differences between the principal components of grasses and Karoo bushes do excise as well as between plots.