Aggregating the response in time series lag models using Quad weight kernel: Impact of Environmental Factors on Schizophrenia Admissions

Abstract

In time series data where a data point has a delayed impact on dependent variables, distributed lag models (DLM) such as Distributed Lag Non-linear Model (DLNM) and Autoregressive Distributed Lag (ARDL) are applicable. Several articles have shown the impact of air pollutants and atmosphere factors like temperature and relative humidity on health. In this paper, we use environmental data (pollutants & climate variables) and daily hospital admissions of schizophrenia patients, to analyze the impact of pollution and climate factors on the hospital admissions in Bengaluru, India. In this work, we are using Number of Admissions (NoA) to hospitals as a proxy for the incidence of schizophrenia emergence. We have explored the applicability of Non-linear ARDL and aggregating responses in DLNM (DLNM-Ag.R) technique. DLNM-Ag.R using Epanechnikov kernel showed improved performance over DLNM by 25%, 15%, 17% and 72% for performance metrices MSE, MAE, MAPE and R2 respectively. Within aggregation methods, we have introduced a quad-weight kernel that further improved performance over Epanechnikov kernel by 17% in terms of MSE.