Performance of Multiple Linear Regression and Nonlinear Neural Networks and Fuzzy Logic Techniques in Modelling House Prices

Abstract

House price prediction continues to be important for government agencies insurance companies and real estate industry. This study investigates the performance of house sales price models based on linear and non-linear approaches to study the effects of selected variables. Linear stepwise Multiple Regression (MR) and nonlinear models of Neural Network (NN) and Adaptive Neuro-Fuzzy (ANFIS) are developed and compared. The GIS methods are used to integrate the data for the study area (Bathurst, Australia). While it was expected that the nonlinear methods would be much better the analysis shows NN and ANFIS are only slightly better than MR suggesting questions about high R² often found in the literature. While structural data and macro-finance variables may contribute to higher R² performance comparison was the goal of this study and besides the Australian data lacked structural elements. The results show that MR model could be improved. Also, the land value and location explained at best about 45% of the sale price variation. The analysis of price forecasts (within the 10% range of the actual prediction) on average revealed that the non-linear models performed slightly better (29%) than the linear (26%). The inclusion of social data improves the MR prediction in most of the suburbs. The suburbs analysis shows the importance of socially based locations and also variance due to types of housing dominant. In general terms of R², the NN model (0.45) performed only slightly better than ANFIS 0.39) and better than MR (0.37); but the linear MRsoc performed better (0.42). In suburb level, the NN model (7/15) performed better than ANFIS (3/15) but the linear MR (5/15) was better than ANFIS. The improved linear MR (6/15) performed nearly as well as the non-linear NN. Linear methods appear to just as precise as the more time consuming non linear methods in most cases for accounting for the differences and variation. However, when a much more in depth analysis is required non linear methods may prove to be more valuable. More research is needed in the area of house price modelling including more structural elements, modern buyer beliefs and the nature and type of risks noted in modern times.