This study is a comprehensive and modern approach to predict customer churn in the example of an e-commerce retail store operating in Brazil. Our approach consists of three stages in which we combine and use three different datasets: numerical data on orders, textual after-purchase reviews and socio-geo-demographic data from the census. At the pre-processing stage, we find topics from text reviews using Latent Dirichlet Allocation, Dirichlet Multinomial Mixture and Gibbs sampling. In the spatial analysis, we apply DBSCAN to get rural/urban locations and analyse neighbourhoods of customers located with zip codes. At the modelling stage, we apply machine learning extreme gradient boosting and logistic regression. The quality of models is verified with area-under-curve and lift metrics. Explainable artificial intelligence represented with a permutation-based variable importance and a partial dependence profile help to discover the determinants of churn. We show that customers’ propensity to churn depends on: (i) payment value for the first order, number of items bought and shipping cost; (ii) categories of the products bought; (iii) demographic environment of the customer; and (iv) customer location. At the same time, customers’ propensity to churn is not influenced by: (i) population density in the customer’s area and division into rural and urban areas; (ii) quantitative review of the first purchase; and (iii) qualitative review summarised as a topic.

This paper is a methodological guide to using machine learning in the spatial context. It provides an overview of the existing spatial toolbox proposed in the literature: unsupervised learning, which deals with clustering of spatial data, and supervised learning, which displaces classical spatial econometrics. It shows the potential of using this developing methodology, as well as its pitfalls. It catalogues and comments on the usage of spatial clustering methods (for locations and values, both separately and jointly) for mapping, bootstrapping, cross-validation, GWR modelling and density indicators. It provides details of spatial machine learning models, which are combined with spatial data integration, modelling, model fine-tuning and predictions to deal with spatial autocorrelation and big data. The paper delineates “already available” and “forthcoming” methods and gives inspiration for transplanting modern quantitative methods from other thematic areas to research in regional science.

Spatial panels are a powerful econometric tool for the estimation of space-dependent cross-sectional time-series models of economic phenomena. A plethora of parameters and possible specifications require a systematic approach to estimation. This paper presents a strategy of estimation to be considered in applied research on economic policy, including the concept of spatial spillovers and its local and global effects, direct and indirect impacts, as well as the role of different spatial weighting schemes. The paper presents fiscal factors affecting GDP between the years 2002–2015 in a number of European economies.

We use the Akaike information criterion (AIC) to assess the quality of non-nested spatial econometric models with a different number of nearest neighbours (knn) included in the spatial weight matrix W. This is of particular importance in two cases: when estimating the model on geolocated point data without explicit guidance on the optimal value of knn; and when dealing with different spatial patterns and a unique W generalizes diverse spatial structures. By minimizing AIC for a set of competing models, one can find the optimal knn that guarantees the best fit. We show through simulation and empirical analysis that AIC is a non-linear function of knn and reaches its minimum for a given knn. We provide practical evidence that misspecified W may result in a 20% bias of model parameters.

Firm location studies traditionally assume that this is business that attracts other business to a given location. They focus on knowledge transfers between the most productive and innovative firms and analyse agglomeration economies arising from matching, learning and sharing mechanisms. We argue that the population density also attracts firms to the place. Therefore, we extend this stream of research by using the concept of economies of density to discuss the effects of the attraction of firms by population. Our study explores the existence of the hierarchical causal mechanism that occurs when 2nd line firms understood as non-innovative, less productive retail and service businesses together with human settlement create an environment that attracts 1st line firms - the most innovative and productive businesses. We show that population density and business agglomeration jointly affect the location of firms in different sectors and should be considered as complementary rather than substitutable attraction factors.