## 5 Discussion  
The discussion and testing of model performance has tended to examine superiority comparing the differing geo-statistical, traditional regression and ML approaches, all of which show advantages and disadvantages for each, and different magnitudes of prediction accuracy, which are all very much data and study area dependent. Of late, the scrutiny of these different approaches has centered more on their amalgamation within a mixed or hybrid framework, and specifically how to optimise model specifications to account for the spatial variation of house prices. For mass appraisal, the alleviation of horizontal and vertical inequity and uniformity is of paramount importance. The results emerging from this study demonstrate that the inclusion of ESFs accounting for SA enhance model explainability and predictive accuracy compared to classic MRA and ML Elastic-net models which use delineated postcode proxies to account for spatial heterogeneity. This finding is in accord with existing research studies employing mixed-based approaches [5, 17, 41, 61] who also found that the inclusion of spatial eigenvectors derived from geographic coordinates improved model performance relative to other ML or regression-based models applying other types of spatial information as proxies. Pertinently, the findings also revealed reduced spatial error and more stable residuals when including spatial filters, again in keeping with extant research [5, 17, 60, 62]. The alleviation of spatial residual error also improves the out-of-sample tests for accuracy, a finding in keeping with [PERSON] et al. [38] who identified that the failure to adequately mitigate SA reduces model reliability and test accuracy. This finding is an important issue when undertaking mass appraisal exercises. The in-sample versus out-of-sample performance is of primary concern when using the model to subsequently value the unsold housing stock and for improving both horizonal and vertical inequity and uniformity within mass appraisal assessment. Indeed, as identified in the study of [PERSON] et al. [5], the superior model performance and prediction accuracy resulted from the addition of coordinate variables are likely to be attributable to the well-matched spatial patterns observed in coordinate variables and house sale price data, and the results do from both a visual and inferential perspective show the spatial eigenvectors to mirror market structure, topography and submarkets which leads to model improvement through the capture of spatial patterns or processes. In contrast, the application of delineated boundaries within ML and other classical regression approaches result in not only the confounding issues of SA, but also lack of explanation relative to house prices as they rarely match housing sub-markets, and further open to scrutiny when considering omitted variable bias. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & & **RMSE** & **MAE** & **MAPE** & **PRD** & **COD** & **N** \\ \hline \multirow{3}{*}{MRA} & Train & 0.2298 & 0.1807 & 1.5172 & 1.057 & 0.194 & 2841 \\  & Test & 0.2351 & 0.1864 & 1.5659 & 1.074 & 0.211 & 602 \\  & Train & 0.2151 & 0.1787 & 1.5099 & 1.053 & 0.185 & 2841 \\  & Test & 0.2268 & 0.1823 & 1.5358 & 1.061 & 0.190 & 602 \\  & Train & 0.2108 & 0.1639 & 1.3777 & 1.044 & 0.171 & 2841 \\  & Test & 0.2194 & 0.1687 & 1.3905 & 1.049 & 0.179 & 602 \\  & Train & 0.2076 & 0.1593 & 1.3682 & 1.032 & 0.159 & 2841 \\  & Test & 0.2134 & 0.1638 & 1.3811 & 1.038 & 0.167 & 602 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model prediction accuracy and ratio statistics.