Non-Linear Visualization and Importance Ratio Analysis of Multivariate Polynomial Regression Ecological Models Based on River Hydromorphology and Water Quality

Abstract

Multivariate polynomial regression (MPR) models were developed for five macrophyte indices. MPR models are able to capture complex interactions in the data while being tractable and transparent for further analysis. The performance of the MPR modeling approach was compared to previous work using artificial neural networks. The data were obtained from hydromorphologically modified Polish rivers with a widely varying water quality. The modeled indices were the Macrophyte Index for Rivers (MIR), the Macrophyte Biological Index for Rivers (IBMR), and the River Macrophyte Nutrient Index (RMNI). These indices measure the trophic and ecological status of the rivers. Additionally, two biological diversity indices, species richness (N) and the Simpson index (D), were modeled. The explanatory variables were physico-chemical properties depicting water quality and river hydromorphological status indices. In comparison to artificial neural networks, the MPR models performed similarly in terms of goodness of fit. However, the MPR models had advantages such as model simplicity and ability to be subject to effective visualization of complex nonlinear input–output relationships, as well as facilitating sensitivity analysis using importance ratios to identify effects of individual input variables.

A mathematical model of catalyst combination design and temperature control in the preparation of C4 olefins through ethanol coupling

“…According to the results of the multiple linear regression, 31 it was necessary to analyse the possible nonlinear relationship including an interaction effect between the reaction conditions. 32 Since the units of temperature, Co loading, Co/SiO 2 , HAP, and ethanol added per minute differ (Table 8), the data for these variables were divided by the corresponding data in the rst row in order to remove the units. From previous analyses, multiple interaction effects are known to exist under charging method I, and multiple nonlinear regression was used.…”

“…According to the results of the multiple linear regression, 31 it was necessary to analyse the possible nonlinear relationship including an interaction effect between the reaction conditions. 32 …”