Effective dimensionality of environmental indicators: a principal component analysis with bootstrap confidence intervals

In this paper, a principal component analysis (PCA) is performed on 14 selected environmental indicators with «bootstrapped» confidence intervals. The term «bootstrap» refers to the process of randomly re-sampling the original sample set to generate new data sets and using these new data sets to make estimates of the statistic of interest. The objective is to derive some quasi-confidence intervals for the statistics when the underlying statistical distributions of the statistics are unknown. The analysis indicates that the first four principal components, which together account for more than 60% of the total variance in the original 14 variables, appear to be statistically significant based on the bootstrapped eigenvalue method, although the bootstrapped eigenvector method seems to be more conservative by identifying only the first two components as the significant ones. The first four principal components have large coefficients (eigenvectors) in absolute values with air, biodiversity, land and water indicators, respectively. All these suggest that there is large redundancy in the existing environmental indicators. Consequently, to avoid overwhelming and confusing indicator-users including decision makers and the general public, developing four sub-indices representing air, water, land and biodiversity should be the primary focus, which would probably capture the most important aspects of the environment.