1# RECORD 0795e1f2569ab3c9b87c0451960aa547390933192# TITLE: PERFORMANCE OF MULTIPLE LINEAR REGRESSION AND NONLINEAR NEURAL NETWORKS AND FUZZY LOGIC TECHNIQUES IN MODELLING HOUSE PRICES3# YEAR: 2012.0 VENUE: nan DOI: 10.3844/jmssp.2012.419.4344# AUTHORS: Siti Amri; Gurudeo Anand Tularam5# PAGES: 16 CANDIDATE TABLE PAGES (1-based): [1]6# ABSTRACT: House price prediction continues to be important fo r government agencies insurance companies and real estate industry. This study investigates the perfor mance of house sales price models based on linear a nd non-linear approaches to study the effects of selec ted variables. Linear stepwise Multivariate Regress ion (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 wo uld be much better the analysis shows NN and ANFIS are only slightly better than MR suggesting q uestions about high R 2 often found in the literature. While structural data and macro-finance variables m ay contribute to higher R 2 performance comparison was the goal of this study and besides the Australi an data lacked structural elements. The results sho w 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 perform ed slightly better (29%) than the linear (26%). Th e 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 R 2 , the NN model (0.45) performed only slightly bette r than ANFIS 0.39) and better than MR (0.37); but the linear MRsoc performed bett er (0.42). In suburb level, the NN model (7/15) performed better than ANFIS (3/15) but the linear M R (5/15) was better than ANFIS. The improved linear MR (6/15) performed nearly as well as the no n-linear NN. Linear methods appear to just as precise as the 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 nee ded 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.789===== PAGE 1 (score 12, numeric-paren 3, table-words 3, var-words 3) =====1011Journal of Mathematics and Statistics 2012, 8 (4), 419-434 12ISSN 1549-3644 13© 2012 Science Publications 14doi:10.3844/jmssp.2012.419.434 Published Online 8 (4) 2012 (http://www.thescipub.com/jmss.toc) 15Corresponding Author: Gurudeo Anand Tularam, Senior Lecturer in Mathematics and Statistics, Science Environment Engineering 16and Technology (ENV) Griffith University Brisbane, Australia 17 18419 19Science Publications 20JMSS 21Performance of Multiple Linear Regression and Nonlinear Neural 22Networks and Fuzzy Logic Techniques in Modelling House Prices 23Siti Amri and Gurudeo Anand Tularam 24 25Centre for Environmental Futures, 26Faculty of Science, Environment, Engineering and Technology (ENV), Griffith University, Australia 27 28Received 2012-06-14, Revised 2012-09-08; Accepted 2012-12-18 29ABSTRACT 30House price prediction continues to be important for government agencies insurance companies and 31real estate industry. This study investigates the performance of house sales price models based on linear 32and non-linear approaches to study the effects of selected variables. Linear stepwise Multiple 33Regression (MR) and nonlinear models of Neural Network (NN) and Adaptive Neuro-Fuzzy (ANFIS) 34are developed and compared. The GIS methods are used to integrate the data for the study area 35(Bathurst, Australia). While it was expected that the nonlinear methods would be much better the 36analysis shows NN and ANFIS are only slightly better than MR suggesting questions about high R2 37often found in the literature. While structural data and macro-finance variables may contribute to 38higher R2 performance comparison was the goal of this study and besides the Australian data lacked 39structural elements. The results show that MR model could be improved. Also, the land value and 40location explained at best about 45% of the sale price variation. The analysis of price forecasts (within 41the 10% range of the actual prediction) on average revealed that the non-linear models performed 42slightly better (29%) than the linear (26%). The inclusion of social data improves the MR prediction in 43most of the suburbs. The suburbs analysis shows the importance of socially based locations and also 44variance due to types of housing dominant. In general terms of R2, the NN model (0.45) performed 45only slightly better than ANFIS 0.39) and better than MR (0.37); but the linear MRsoc performed better 46(0.42). In suburb level, the NN model (7/15) performed better than ANFIS (3/15) but the linear MR 47(5/15) was better than ANFIS. The improved linear MR (6/15) performed nearly as well as the non-48linear NN. Linear methods appear to just as precise as the more time consuming non linear methods 49in most cases for accounting for the differences and variation. However, when a much more in depth 50analysis is required non linear methods may prove to be more valuable. More research is needed in 51the area of house price modelling including more structural elements, modern buyer beliefs and the 52nature and type of risks noted in modern times. 53 54Keywords: Neural Network (NN), Adaptive Neuro-Fuzzy (ANFIS), Multiple Regression (MR), Global 55Financial Crisis (GFC), International Monetray Fund (IMF), Statistics 56 571. INTRODUCTION 58 59Housing investment is an important investment in 60Australia and worldwide and it is the means through which 61many have increased their wealth in the past. It is 62probably not possible for house prices to increase without 63bounds and as such the investment choice has been 64questioned causing a number of commentators (Stapledon, 652009) predicting a price decreases in not too distance 66future if only to stabilize the market. Whatever the market 67place does, it is nonetheless important to study the growth of 68house prices to predict prices for the use of real estate 697071===== PAGE 2 (score 7, numeric-paren 0, table-words 0, var-words 7) =====7273Siti Amri and Gurudeo Anand Tularam / Journal of Mathematics and Statistics 8 (4) (2012) 419-434 74 75420 76Science Publications 77JMSS 78agents, insurance companies and government departments. 79Government agencies and councils can use the predicted 80prices to determine future rates payable amounts and use 81them to conduct forward planning such as budgeting for the 82corridors of growth in cities and so on. 83 84In 2008, the International Monetray Fund (IMF) 85reported that the Australian house price was overpriced by 86around 20% (IMF, 2008). Given that house prices have 87softened in many overseas countries it is not surprising 88then that Australians are debating whether similar 89corrections may occur here. After the Global Financial 90Crisis (GFC) in 2007-8 the Australian government 91provided a number of stimulus measures and one of them 92to the housing industry; namely, the First Home Owners 93Grant that has allowed the Australian housing market to 94remain relatively strong. This has caused some heating of 95the market and the government acted swiftly increasing 96cash rates in order to slow the market and this has indeed 97slowed the growth rate and economy significantly in 98Australia. Since there has been over 70% owners 99occupiers in Australia, there is a vested interest in a strong 100housing market (ABS, 2009). In addition, the market has 101been favourably aided by government policy of negative 102gearing for investors to be active. The capital gains made 103in the past and the above mentioned tax policy have led 104to a significant increase in private investors. Evidence of 105this is noted in the proportion of investors taking out new 106housing loans increasing from 11-27% between 1990-1072008 (ABS, 41020) but this appears to be slowing caused 108by many factors such as the global financial crisis and 109increasing interest rates. Nonetheless, significant 110increase in rental prices continue to lure new investors 111into the market. 112 113As noted there is a need to estimated house prices but 114this is a challenge due to incomplete and “noisy” data of 115the market (Prasad and Richard, 2006). The data used in 116house price estimation is often based on historical sales 117records representing a small percentage of the total 118housing stock in a given area. Newly constructed homes 119also dominate the sales market and often there is lack of 120details regarding improvements or renovations as well as 121those pertaining to structural data. In this regard, the price 122reporting from previous sales records may not represent 123the true value of housing market appreciation. This 124suggests that the price patterns for many areas may be 125inaccurate due to a lack of appropriate sample information. 126 127The housing system is a complex system. Housing 128data is complex and is kept in multiple data bases that is 129subject 130to 131ever 132changing 133financial 134and 135urban 136environment. However, there are some important factors 137impacting on prices such as accessibility, neighbourhood-138quality, environmental, structural and speculation to name 139a few (Yates, 2002). Buyer’s decision to pay above 140average prices for property in a premium location adds to 141the complexity in the development of accurate models. 142The local level factors include population demand, 143migration and other social variables, and the global level 144factors such as government policies and mortgage interest 145rates all have an impact on house price estimation (Fig. 1). 1461.1. Modelling of House Prices 147 148While there has been work done on house price 149modelling much is yet to be understood about house price 150fluctuations, patterns and growth (Farlow, 2004). The 151models can be grouped as those that use urban economics 152perspective focusing mainly on spatial; and those that use 153macroeconomic or financial economics. The latter 154focusing on housing as an asset using optimal methods in 155a consumption type model for example. Authors have 156used models based on heterogeneous assets labelled 157hedonic regression and also time series related models 158(Cannaday et al., 2005; DEWHA, 2008; Nagaraja 159et al., 2011; Shiller, 1993) while others use 160spatiotemporal models (Holly et al., 2010; Yu et al., 1612007); Some have used the Torbin’s Q model when 162others use genetic algorithmic type models (Wilson 163et al., 2004). Amri and Bossomaier (2003) have 164attempted an agent based model but much work is yet 165undone in this area. 166 167 168 169Fig. 1. Complex housing system 170