Graph Regression Model for Spatial and Temporal Environmental Data-Case of Carbon Dioxide Emissions in the United States

We develop a new model for spatio-temporal data. More specifically, a graph penalty function is incorporated in the cost function in order to estimate the unknown parameters of a spatio-temporal mixed-effect model based on a generalized linear model. This model allows for more flexible and general regression relationships than classical linear ones through the use of generalized linear models (GLMs) and also captures the inherent structural dependencies or relationships of the data through this regularization based on the graph Laplacian. We use a publicly available dataset from the National Centers for Environmental Information (NCEI) in the United States of America and perform statistical inferences of future CO2 emissions in 59 counties. We empirically show how the proposed method outperforms widely used methods, such as the ordinary least squares (OLS) and ridge regression for this challenging problem.