Effects of multicollinearity and data granularity on regression models of stream temperature

Abstract

Water temperature is a key factor influencing biota of stream ecosystems. Hence, it is important to comprehend the environmental drivers of stream temperature for robust prediction of conditions and effective management of stream communities. Linear regression models are commonly used for predictive purposes, but their predictive capacity and interpretability can be significantly affected by their complexity and the structure of input data. In some cases, researchers may be obligated to favor prediction power or interpretability while compromising the other. Therefore, insight into relationships between model fit, correlation among predictor variables (i.e., multicollinearity), and level of temporal aggregation of data (i.e., data granularity) may be helpful to reduce such trade-offs. In this paper, we investigated these relationships within a hierarchical set of multiple linear regression (MLR) models examining environmental factors influencing stream temperature dynamics. Our findings showed that as the number of predictor variables (i.e., model complexity) increased, the magnitude of multicollinearity in MLR models increased, but model fit also increased. The results also revealed that using data averaged over longer time frames (i.e., coarser data granularity) yielded high multicollinearity, as indexed by variance inflation factor values (VIF) for all model predictors. This led to higher variance in parameter estimates (i.e., parameter instability) and potential challenges in model interpretation as the sign of parameter estimates changed in many streams examined. Multicollinearity was not the only reason for these changes in the sign of parameter estimates as they were also observed in simple linear regression models across varying levels of data granularity. Based on our findings, we conclude that the selection of data granularity is an important consideration in multiple regression modeling, with profound implications for model interpretability.