Analysis of Property Yields for Multi-Family Houses with Spatial Method and ANN

In this work, we compare the results of multiple linear regression analysis (MLR) with spatial analysis method (geographically weighted regressions (GWR)) and an artificial neural network (ANN) approach deriving a state-wide model for property yields. The database consists of approx. 3000 purchase prices in the market of multi-family houses collected in the purchase price database of Lower Saxony (Germany). The purchases occurred between 2014 and 2018. The locational quality as well as the theoretical age (deprecation) of the real estates are the influencing variables in the analysis. In the GWR, different fixed and variable kernels are used. The approaches are evaluated using cross-validation procedure with quality parameters like the root mean square error (RMSE), the mean absolute error (MAE) and the error below 5% (eb5). The first analysis shows that GWR leads to better results in comparison to classical approaches (MLR) because local phenomena can be modelled. Also, the approach of ANN is superior in comparison to the classical regression analysis because of its ability of nonlinear modelling. In this dataset, the ANN cannot reach the accuracy of GWR which leads to the conclusion, that the spatial inhomogeneity has a bigger influence than a data non-linearity. Further investigation shows that the complexity of the data and the amount of available data plays a key role in the performance of ANN.