Description

Geographically weighted regression (GWR) has been used over the past two decades for modeling spatial phenomena while accounting for spatial non-stationarity (Aturinde, Farnaghi, Pilesjö, Sundquist, & Mansourian, 2021; Fang et al., 2021). In contrast to the global methods like spatial autoregressive models (SAR), GWR enables us to explore spatial data patterns resulting from the underlying processes at the local level. 
The classical GWR has some deficiencies. First, it assumes that all of the modeled processes are operating at the same spatial scale, and therefore it calculates a single bandwidth for all of the independent parameters. Second, conventional GWR neglects the temporal aspect of the underlying process and only focus on spatial neighborhoods. 
The two mentioned shortcomings were addressed through two distinct extensions, called MGWR (Multiscale Geographically Weighted Regression) (Fotheringham, Yang, & Kang, 2017) and GTWR (Geographical and Temporal Weighted Regression) (Fotheringham, Crespo, & Yao, 2015; Que, Ma, Ma, & Chen, 2020). MGWR addresses the shortcoming related to the spatial scale via allowing for optimizing different bandwidth parameters for each independent variable. GTWR also accounts for the temporal proximity and the spatial neighbors to better model the underlying spatiotemporal processes. Still, a combination of these two extensions of MGWR and GTWR is lacking.
In this MSc. topic, you will investigate the possibility of proposing a combinatory GWR model that considers both scale and spatiotemporal neighborhood for modeling spatial non-stationarity. The workflow of the MSc thesis will be as follows.

1. A literature review on the GWR algorithm and its extensions
2. Analyzing the two open-source implementations of MGWR in GTWR in python and R programming languages
3. Proposing the combinatory extension to GWR
4. Development of the model
5. Evaluating the library on a selected case-study
6. Comparing the outcomes of the extension to those of GTWR and MGWR

Case study

In addition to the open-source datasets, e.g., related to house prices, a couple of exciting datasets collected by volunteers are available for this MSc topic. We have a time series of tick sampling data across multiple locations in the Netherlands, and we have an extensive collection of volunteered phenological observations that report the timing of recurring biological events like leafing and flowering. For both datasets, we have access to the spatial environmental data (e.g., gridded temperature datasets) as explanatory variables.

Required skill

Good knowledge of the Python programming language will be helpful for this MSc topic.