<p>The objective of this study is to develop a multiple linear regression model that measures the relationship between the church services supply and the attendance to the services in the Uppsala diocese, Church of Sweden. By reviewing previous models and examining the nature of data available, two research questions were introduced, namely, the problem of omitted variables and the problem of spatial autocorrelation. For the first question, two methods were compared, namely, the Y-lag method and the first-differenced equation. Statistical tests then showed that the latter was more preferable for this study. For the second question, geographically weighted regression was used to examine the spatial variations in relationships estimated by above modeling strategies. However, no significant spatial variation was found for them. In conclusion, by using the ordinary least square estimation for the first-differenced equation the most suitable regression model was obtained. The data showed no need to consider the issue of spatial non-stationarity.</p>

The objective of this study is to develop a multiple linear regression model that measures the relationship between the church services supply and the attendance to the services in the Uppsala diocese, Church of Sweden. By reviewing previous models and examining the nature of data available, two research questions were introduced, namely, the problem of omitted variables and the problem of spatial autocorrelation. For the first question, two methods were compared, namely, the Y-lag method and the first-differenced equation. Statistical tests then showed that the latter was more preferable for this study. For the second question, geographically weighted regression was used to examine the spatial variations in relationships estimated by above modeling strategies. However, no significant spatial variation was found for them. In conclusion, by using the ordinary least square estimation for the first-differenced equation the most suitable regression model was obtained. The data showed no need to consider the issue of spatial non-stationarity.

One of the key concerns in spatial analysis and modelling is to study and analyse similarities or dissimilarities between places over geographical space. However, ”global“ spatial models may fail to identify spatial variations of relationships (spatial heterogeneity) by assuming spatial stationarity of relationships. In many real-life situations spatial variation in relationships possibly exists and the assumption of global stationarity might be highly unrealistic leading to ignorance of a large amount of spatial information. In contrast, local spatial models emphasise differences or dissimilarity over space and focus on identifying spatial variations in relationships. These models allow the parameters of models to vary locally and can provide more useful information on the processes generating the data in different parts of the study area. In this study, a framework for localising spatial interaction models, based on geographically weighted (GW) techniques, has been developed. This framework can help in detecting, visualising and analysing spatial heterogeneity in spatial interaction systems. In order to apply the GW concept to spatial interaction models, we investigate several approaches differing mainly in the way calibration points (flows) are defined and spatial separation (distance) between flows is calculated. As a result, a series of localised geographically weighted spatial interaction (GWSI) models are developed. Using custom-built algorithms and computer code, we apply the GWSI models to a journey-to-work dataset in Switzerland for validation and comparison with the related global models. The results of the model calibrations are visualised using a series of conventional and flow maps along with some matrix visualisations. The comparison of the results indicates that in most cases local GWSI models exhibit an improvement over the global models both in providing more useful local information and also in model performance and goodness-of-fit.