Penalized local polynomial regression for spatial data

Assessing the spatial structure of the association between attendance at preschool and children's developmental vulnerabilities in Queensland, Australia

Demographic and educational factors are essential, influential factors of early childhood development. This study aimed to investigate spatial patterns in the association between attendance at preschool and children's developmental vulnerabilities in one or more domain(s) in their first year of full-time school at a small area level in Queensland, Australia. This was achieved by applying geographically weighted regression (GWR) followed by K-means clustering of the regression coefficients. Three distinct geographical clusters were found in Queensland using the GWR coefficients. The first cluster covered more than half of the state of Queensland, including the Greater Brisbane region, and displays a strong negative association between developmental vulnerabilities and attendance at preschool. That is, areas with high proportions of preschool attendance tended to have lower proportions of children with at least one developmental vulnerability in the first year of full-time school. Clusters two and three were characterized by stronger negative associations between developmental vulnerabilities, English as the mother language, and geographic remoteness, respectively. This research provides evidence of the need for collaboration between health and education sectors in specific regions of Queensland to update current service provision policies and to ensure holistic and appropriate care is available to support children with developmental vulnerabilities.

Clustered spatio-temporal varying coefficient regression model

In regression analysis for spatio-temporal data, identifying clusters of spatial units over time in a regression coefficient could provide insight into the unique relationship between a response and covariates in certain subdomains of space and time windows relative to the background in other parts of the spatial domain and the time period of interest. In this article, we propose a varying coefficient regression method for spatial data repeatedly sampled over time, with heterogeneity in regression coefficients across both space and over time. In particular, we extend a varying coefficient regression model for spatial-only data to spatio-temporal data with flexible temporal patterns. We consider the detection of a potential cylindrical cluster of regression coefficients based on testing whether the regression coefficient is the same or not over the entire spatial domain for each time point. For multiple clusters, we develop a sequential identification approach. We assess the power and identification of known clusters via a simulation study. Our proposed methodology is illustrated by the analysis of a cancer mortality dataset in the Southeast of the U.S.