# Linear and Nonlinear Modelling of the Usable Area of Buildings with Multi-Pitched Roofs
## 4 Discussion
Still, the article provides only an illustration of how the modelling process can be organized in order to fill in the specific gaps in data. Every single analysis may be slightly different and there is a possibility that nonlinear models would prove to outperform their linear counterparts given certain circumstances. The computational complexity of such modelling is not a problem these days and practitioners do often consider multiple models before choosing one of them for use. We have proven that modelling usable area with a reasonable accuracy is possible using only a few characteristics of a building. As buildings with multi-pitched roofs are a very heterogeneous group, special attention should be paid to data preparation for modelling purposes. The obtained models are prone to the occurrence of disparities in those areas of the domain in which the representation of objects in the training set is relatively scarce. It should also be noted that regression models can be used as an interpolation tool, understood as searching for the value of an endogenous variable for points that lie within the domain determined by the ranges of the exogenous variables, not outside of it. An attempt to estimate based on such models for atypical data will therefore be often unsuccessful. This occurred in the model validation process when some validation set elements came with strongly underrepresented feature combinations. We have shown that the lacking data on usable area--a problem that concerns up to around 70% of the REPR data (according to previous research [15])--can be successfully addressed by means of relatively easy to use models that predict the usable area based on other characteristics of a building with a reasonable accuracy. Even if the models do not provide the same accuracy for all varying designs, for a majority of the typical houses, the estimation errors are acceptable. In the case of objects described by atypical sets of feature values, the errors are larger and that is natural, but we treat such cases as outliers and treat them separately. The estimated usable area in these cases has to be verified by an expert. And the more such verified cases there are in the database, the more accurately the model will behave during further use. The final choice of the model depends on the nature of the available data and the purpose of the analysis. In this study, the linear model or the regularized linear model was a better tool for forecasting the usable area of a building from the perspective of property appraisers. The results are quite promising in terms of the accuracy of estimating the usable area in the context of their suitability for property valuation. The method is expected to be replicable in other regions of the country where the same legal framework and definition of usable area occurs; however, the model is fitted to the local data. A limitation of these studies is the lack of access to the interiors of existing buildings in Koszalin. This would have enabled identification of atypical building structures, such as the presence of high rooms in residential buildings, which is often associated with mezzanines. Such structures present challenges that are not easily addressed by regression models. Therefore, the next step in estimating the usable area in detached residential buildings with a multi-pitched roof will be the use of neural networks and machine learning methods. Further plans include reaching a larger database of properties and conducting an in-depth analysis, distinguishing more specific groups of buildings, measuring whether clustering can be used, i.e., automatic algorithms that divide objects into coherent, homogeneous classes, or whether it is an issue in which only expert knowledge will bring the desired results. The results from this, past, and future studies may find a practical implementation in form of an end-user friendly application. The LiDAR-based data are accessible for many countries in the EU, thus the national sources can serve as a basis for similar analysis.