A socially responsible consumption index based on non-linear dimensionality reduction and global sensitivity analysis

Higher-order factor analysis is a statistical method that consists of repeating steps of factor analysis. Studies of this type allow researchers and practitioners to visualize the hierarchical structure of the concept being studied. Unfortunately, the Socially Responsible Consumer (SRC) research community still remains unable to construct a second-order SRC index. Most researchers argue that the statistical requirements for the construction of the second-order index are not met. They typically try to construct the second-order index by applying linear factor analysis techniques. It is worth mentioning that this is a widespread practice in the social sciences. In this manuscript, we aim to show how better indices can be created by applying non-linear dimensionality reduction techniques. Specifically, we have modified the Unsupervised Extreme Learning Machine (UELM) method to promote orthogonality in the basis function space. These methods are able to model interactions among the input variables, but unfortunately, they are usually considered black boxes. To overcome this limitation, we propose the use of Global Sensitivity Analysis (GSA) techniques, which are able to estimate the importance of each variable by itself and in conjunction with the others. To test the methodology, we have used a sample of 703 Spanish consumers and a multidimensional SRC metric that considers both social and environmental issues. As expected, the non-linear techniques tend to enhance the results provided by the linear techniques.