Determination of Collinearity Developed in the CMB Model with the Concepts of Multi Linear Regression Analysis

Abstract

The Chemical Mass Balance model (CMB) gives an accurate source apportionment for the contribution of the sources with the input data of the source profile and receptor data collected. The source profiles for different sources should have a unique and specific species characterization for getting accurate source apportionment results. But due to the mixing of sources, the species characterization source profile may not have unique and specific species characterization due to the non-availability of the exact representation of particular sources and culminates collinearity of species during the CMB analysis. It leads to negative source apportionment results in the CMB analysis. Multi Linear Regression analysis that addresses in the study can effectively be used to identify the collinearity contributing sources. The Multi Linear Regression parameters such as tolerance, variance inflation factor (VIF), condition index, and variance decomposition proportions developed with the source profile variables (source profiles for soil, paved road dust, biomass, and traffic) are used for identifying the collinear sources. The tolerance value for the soil and paved road dust sources are obtained as 0.001 each and the variance inflation factor (VIF) for both are obtained as 204.2 and 208.8 respectively. It indicates the collinearity between soil and paved road dust. Collinearity diagnostics of the regression equations showed that the condition index and the variance decomposition proportion obtained for the soil and paved road dust were greater than 30 (104.09) and 90% (100%) respectively. Therefore, the presence of strong collinearity between soil and paved road dust can be understood.