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Identification of locational influence on real property values using data mining methods

Identifier l'impact local sur la valeur immobilière en utilisant la méthode d'exploration des données
Edson Melanda, Andrew Hunter et Michael Barry

Résumés

La valeur de l'immobilier est une question importante pour les autorités municipales, puisque l'impôt foncier est une de leurs principales sources budgétaires. Son estimation est un processus complexe, en raison de la diversité des facteurs qui l'affectent. Un de ces facteurs est l'emplacement de la propriété, qui englobe la relation géographique entre l'établissement et les commodités environnantes. La modélisation hédonique est fréquemment utilisée pour estimer la valeur d'une propriété, en mesurant l'influence de l'emplacement de la propriété. La région étudiée est habituellement divisée en zones homogènes. Cette division peut introduire un biais (une vision particulière) lié au problème de l'unité territoriale modifiable. Notre intention dans cet article est d'appliquer des techniques d'exploration de données pour répondre à un possible biais expert, (une vision d’expert particulier), dans le modèle actuel d'évaluation de la ville de Calgary. Selon la technique d'arbre de décision, un attribut de localisation (sous-quartier) représenté par les coordonnées (x, y) des propriétés correspond à environ 96% de classifications correctes par rapport à leur désignation parmi les sous-quartiers de Calgary. En adoptant la technique des arbres de régression, nous montrons qu'il est possible d'expliquer environ 73% de variabilité de l'attribut prix de vente, en utilisant uniquement l'attribut sous-quartier ou le (x, y) des coordonnées en entrée. En général, les résultats ont montré une relation cohérente entre la valeur de la propriété et l'emplacement. Cependant, la configuration des prix des propriétés réelles ne correspond pas strictement aux unités politico-administratives adoptées par la ville. Ces structures recoupent parfois les limites des unités administratives ou sont mélangées à l'intérieur d'une unité. Nos résultats suggèrent que l'utilisation des coordonnées d'une propriété spatiale, au lieu des subdivisions politico-administratives, pour rendre compte de son emplacement, conduirait à des résultats plus précis sans encourir le risque de partialité.

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Introduction

1The estimation of real estate property values is a complex process, impacted by diverse factors ranging from the physical characteristics and local amenities to politic-economic factors. Property appraisers tend to use their expert knowledge, subject to critical peer review, to develop regions with similar neighbourhood attributes for the purposes of computer assisted mass appraisal using multiple regression techniques. Appraisers in the City of Calgary approached the research team to examine if the regions that they had developed could be improved, i.e., conflated and therefore produce a more parsimonious modelling system, through mathematical modelling techniques. The application of data mining methods to this problem is described.

2The physical features of a property are typically considered when estimating property values, because they are tangible, understandable, and easily measured.

3Local amenities also strongly influence property value, but this influence is not as readily measurable. For example, it is difficult to calculate how much a buyer will pay for ready access to good schools or recreational facilities, or for the socioeconomic status of living in a particular neighbourhood. To take into account the influence of such amenities on property values, "location" is used as a proxy for unrepresented variables (Pavlov, 2000). Another approach to compute the influence of local amenities on property value is to combine a multilevel modelling and topological relationships of property and local amenities as suggested by Orford (2002).

4The influence of politico-economic factors consists in development incentives, revitalisation projects, real-estate speculation, and even unpredictable events such as the 2008 economic crisis. The effects of these agents on property values are usually long term and do not fall within the scope of this paper.

5Nowadays, appraisers often use hedonic modelling to estimate the value of a property. These models, derived from the utility theory (Rosen, 1974), are used to identify the value of a property from its physical characteristics (e.g., constructed area, lot size, age, and number of rooms), its proximity to various amenities (schools, recreational facilities etc.), and qualitative parameters associated with it (Taylor and Smith 2000). Hedonic price modelling has been used widely because relatively few attributes are necessary for estimation and the resulting models are generally easily comprehensible (Boxall et al, 2005; Mollard et al, 2007; Taylor and Smith, 2000). Also it allows the analyst to identify the underlying preferences for those local amenities or property characteristics included in a model (Taylor, 2008). Key conditions for the modelling paradigm to be valid are that that the real-estate market is competitive, home buyers and sellers are well informed and that there are no discontinuities in either dependent or independent variables across the study area (Taylor, 2008; Wang and Zorn, 1997).

6The key objection to the hedonic methodology that has been raised in the literature concerns the regression step. As with any regression model, to do a good job of estimating the response variable, the correct set of explanatory variables must be specified and the correct mathematical relationships between these variables and the response variable must be presumed. In general both these tasks are challenging. Furthermore, the model is usually fitted to the data by using ordinary least squares (OLS), a relatively unsophisticated method. At the least, then, the potential benefits of more specificity in the index should be weighed against the costs of imposing far more structure, an inherent requirement of hedonic modelling. Focusing on the specificities of each target application should help in this decision (Taylor, 2003; Palmquist, 2006).

7To analyse the effect of a property’s location in hedonic models, the region under analysis is usually divided into homogeneous areas, namely neighbourhoods, which can be defined in various ways. A common way to create neighbourhoods is to adopt the administrative boundaries of quarters, city districts or land divisions. When urban development follows a more organic pattern, the urban area growing by the natural extension of the urban fabric, these municipal limits do not necessarily represent a clear division of neighbourhood. On the other hand, when urban development occurs by great planning projects, such boundaries are more definite and tend to result in well-defined neighbourhoods.

  • 1 GKD is an extension of the Knowledge Discovery from Database (KDD) process (Fayyad et al, 1996) to (...)

8However, the definition of the limits of a neighbourhood is, to some extent, arbitrary, according to Openshaw (1984); Tagashira and Okabe (2002). The authors define this issue as the modifiable areal unit problem (MAUP), and show that different spatial arrangements can lead to distinct results, using the same data and analysis methods. It follows that when a city is subdivided for the purpose of analysis, there is necessarily a bias influencing the results, neither wrong nor right, just a bias. To mitigate this problem, spatial analysis should be done on non-aggregated data, when that is possible and makes sense, or the spatial objects should be constructed from information contained in the actual data, as suggested by the author. Another approach is to utilize Geographic Knowledge Discovery (GKD1) to avoid incurring the MAUP issue, as suggested by Miller (2011).

9For towns and cities, property price estimation is a crucial task, considering that property tax are usually the main source of the municipal budget. For example, in the City of Calgary, Alberta, Canada, property tax generates approximately 50% of the municipal revenue (Calgary, 2009).

10In 2000 the City of Calgary implemented a new assessment system to cope with changes required by Alberta’s Municipal Government Act. Since then, Calgary has to reassess its properties annually to ensure that property assessments and, consequently property taxes stay abreast of changing market conditions. Under this assessment system, the properties are assessed by a mass appraisal approach to determine the most probable market value that a property could realize if it were sold on the open market. To cope with that task, the city was subdivided into 23 valuation areas (single-family market analysis areas-MAA) for modelling property price, taking community boundaries into account. For each MAA, a multiple regression model-using OLS-is built, based on a property sale data set with 214 attributes. The resulting models are then evaluated by statistical tests performed at several aggregation levels: city-wide, regional market area, market analysis area, community, sub-neighbourhood and some other selected attributes.

11This paper is part of a larger project that deals with spatial modelling of property assessment. The overall objective of the project is to improve assessment efficiency by reducing the number of variables that must be collected by city assessors.

12In this paper, we address a possible valuer bias, a particular view coming from the valuers, in the current City of Calgary assessment model, by using spatial data mining. The valuer bias was suggested by the results of a preliminary data analysis, which identified a strong relationship between property prices and administrative subdivisions (communities and sub-neighbourhoods). The bias could have been introduced by the city’s division into valuation areas and has been initially related to MAUP. It will affect the models generated and the modelling assumption of unbiased data is compromised, adding uncertainty to the valuation process.

13Our hypothesis is that there will be a valuer bias in Calgary’s valuation process if (i) the pattern of property price spatial distribution does not conform to the city’s administrative subdivisions, (ii) a sub-neighbourhood can be defined by property attributes or spatial coordinates and (iii) the property price can be modelled either by sub-neighbourhood or by spatial coordinates.

14To accomplish the objectives of this paper we first perform an exploratory spatial data analysis and compare its results against the city’s administrative subdivisions to verify if the spatial distribution pattern of property price conforms to the subdivisions. Secondly, we use a decision tree to verify if sub-neighbourhoods can be determined by property’s attributes or spatial coordinates. Finally, a regression tree is employed to check if property price can be modelled by property attributes (Att), spatial boundaries (MAA, Neighbourhood or Sub-Neighbourhood) or by spatial coordinates with the same level of precision.

15In Section Methods and Data of this paper, we present the methods and the data set used in the analysis. Next, in Section Results and Discussion, we report the findings of the exploratory data analysis and the data mining process and discuss them. Finally, we draw some conclusions in Section Conclusion and Future Work.

Methods and Data

16In this section we describe the property sale data set that was analyzed by exploratory spatial data analysis (ESDA) and data mining techniques, as well the methods, techniques and software utilized.

Data description

17The City of Calgary, located in the Canadian province of Alberta, has over one million inhabitants and is one of the two major cities in the province. Regarding its urban form, two distinct patterns of development can be found: one, a more traditional and organic pattern, with streets following a checkerboard pattern and with no physical barrier between neighbourhoods; the other, in new suburban areas, with precisely defined neighbourhood limits (usually by express roads) and a limited house typology.

18The data employed in this paper is that which the City of Calgary Assessment Business Unit used to calculate property taxes for the year of 2005, comprising six single residential market analysis areas (MAA) in the north-west region of the city, and related to 10,089 house sale transactions over the years of 2002 to 2004. During those years, the housing market in Alberta, as well as in Calgary, could be considered stable with an average percentage change of 2% (year over year) from 1995 to 2005. After 2005, the market became instable, ranging from an increase in prices of over 40% in 2006 to a decrease of more than 10% in the first quarter of 2009, according to Tsounta (2009). Besides sale price and housing characteristics, there is also the information used for taxation (Time-Adjusted-Price, Model for Assessment, Value Assessed), details of transactions (Date, Type of Sale, Validation Code) and property locations (coordinates), totalling 47 attributes. In addition, geographical information related to administrative districts (MAA and neighbourhoods), roads and hydrography was available (Figure 1).

19Considering that the focus of this work is about the relationship between sale price and property features, this kind of relationship is relatively stable over a specific time frame. Due to the information’s sensitive nature, we opted for the latest cycle of property appraisal before the housing market became instable.

20An exploratory statistical analysis was initially performed on all variables to assess their distribution, ranges and the presence of outliers. Properties with data outliers were removed. Variables with low discriminatory power, due to their distribution, were eliminated (Address, Property ID, Sale Validation Code), and only one set of variables with very similar meanings (Sale Price and Time-Adjusted Sale Price; Year of Construction and Age, and so on) was kept. Also, binary variables expressing distinct types of the same feature were merged into one variable. Thus, the attributes were reduced to 27 variables, further referred to as Att. Among these variables, five are related to the property location (MAA, Neighbourhood, Sub-neighbourhood, X and Y), three are related to the sale transaction, 16 are related to structural characteristics, and three are categorical variables related to local amenities: Green (no influence; small park, big park, golf course); Traffic (no influence, collector, main, express); and View (no view, downtown, river, mountain etc.).

Figure 1: Sales transactions, over 2002 and 2004, in the North-West of Calgary, by percentile distribution of Sale Price.

Figure 1: Sales transactions, over 2002 and 2004, in the North-West of Calgary, by percentile distribution of Sale Price.

21The basic tool for data analysis was the computing environment "R" (R Development Core Team, 2009). This allowed a wide variety of statistical analysis routines to be performed, from descriptive analysis and hypothesis testing to linear modelling and spatial analysis, including neighbourhood configuration studies and residual mapping. Operations involving spatial data manipulation, graphical editing, map overlay and some spatial data analysis were performed with the aid of the GIS programs Spring (Camara et al, 1996) and Quantum GIS (Quantum GIS Development Team, 2010). The map presentations were produced with GeoMedia (Intergraph Co.).

Methods

22The data set was initially treated by exploratory spatial data analysis (ESDA), after which the data mining techniques of decision and regression tree were used. The aim of applying the decision tree was to explore the relationship between the attribute Sub-Neighbourhood and the other attributes. The regression tree was used to explore the relationships among the attribute Sale Price, spatial attributes and non-spatial ones.

Exploratory Spatial Data Analysis

23Exploratory data analysis (EDA) is a collection of statistical techniques that can be used to detect data errors, discover patterns, expose unusual or interesting characteristics, differentiate accidental from important features in data and create hypotheses from data (Haining, 2003). When these techniques are applied to geographical data, named exploratory spatial data analysis (ESDA). One technique utilized during the ESDA step was LISA-Local Indicators of Spatial Association (Anselin, 1995). LISA measures the spatial dependence between the value of a variable at one location and its neighbours, indicating the extent of significant spatial clustering of similar values around that location (Longley and Tobon, 2004).

24The ESDA was carried out with GeoDA, a computer program that has the following routines for exploratory spatial data analysis: spatial autocorrelation, spatial regression, LISA calculation, conditional cartograms, maps and graphs (Anselin et al, 2006).

25Through EDA and ESDA, besides detecting some data errors, we identified interesting patterns (clusters of the higher and lower percentiles of the Sale Price) and were able to strengthen the initial hypothesis that the use of administrative subdivisions can introduce a valuer bias in the City of Calgary’s mass appraisal process and that the sale price of a property can be modelled by its sub-neighbourhood or by spatial coordinates.

Data Mining

26Spatial data mining refers to the use of computational tools to discover interesting and useful patterns in objects and events over geographic space. Relationships among objects, events and non-spatial attributes, as well as, the spatial properties of individual objects are examples of patterns that may be revealed (Miller and Han, 2009). Given that we are particularly interested in investigating the relationship among Sale Price, Sub-Neighbourhood and property location, it is possible to apply traditional data-mining algorithms, such as tree-based models, to our experiments.

27Tree-based models are symbolic data-mining techniques used for classification and regression problems. The symbolic data mining techniques represent the extracted knowledge in a comprehensible form that is readily interpreted by a human being for subsequent use. In the tree, each node represents a data set attribute, the branches represent the splitting values at which the attribute is subdivided and the leaves represent classes or regression models. A new case can be classified by following the "top-down" structure, nodes close to the root (top) being more important, in discriminatory terms, than the nodes close to the leaves.

28The construction process of a tree-based model is done by the divide-and-conquer method, selecting an attribute to be the root and creating branches for each of its values. The data set is then divided into subsets, one for each of the branches. Next, for each subset, another attribute is selected and branches created for its values, dividing the data into even small subsets. Assuming that the most desirable tree is the simplest (smallest number of leaves or rules), the best attribute at each node is that which minimizes the tree size in a specific branch. To satisfy this requirement, entropy measures are used to choose the attribute at each node (Witten and Frank, 2005; Quinlan, 1992). In the context of this work, this technique was chosen because of the hierarchization of attributes generated by the algorithm (which puts at the top of the tree the attribute with the highest discriminatory power for the class and so forth) and for the possibility of transposing the tree representation of location attributes into a map form, as shown in Figure 2

Figure 2: Example of transposition of a tree representation into a map form.

Figure 2: Example of transposition of a tree representation into a map form.

29The data mining activities in this project were carried out in the computer environment WEKA, developed for the extraction and analysis of knowledge from databases, by Witten and Frank (2005). In WEKA, diverse algorithms described in the machine-learning literature have been implemented and optimized, providing it with tools for data pre-processing, classification, regression, clustering, visualization and other machine-learning techniques related to data mining and knowledge discovery. Its visual resources were also helpful for EDA, guiding data cleaning and attribute selection.

Results and Discussion

Exploratory Analysis

30To investigate the possibility of occurrence of MAUP related to the administrative subdivisions utilized in the property assessment process, the LISA values for Sale Price were calculated with a weight matrix based on distance decay. To choose the distance decay threshold, it was first evaluated at 250, 500, 750, 1,000 and 2,165 m. The first value (250 m) is the GeoDA recommended default value, and the last (2,165 m) is the range value of an adjusted semi-variogram for the data set by Melanda et. all (2013). The threshold adopted for the weight matrix was 2,165 m, because it generated a weight distribution more similar to a normal distribution, than any of the other distance decay thresholds evaluated.

31In Figure 3 it is possible to identify clusters of properties of high LISA value next to other properties of high LISA value (named high-high or "hot-spots"), as well as high-low, low-high, low-low ("cold-spots") and non-significant ones.

32There are clusters of hot-spots in the south (near downtown), north, west and north-west of the study area (NW Calgary). For cold-spots, the clusters are mainly located to the east and center-west. Some transition areas (high-low and low-high) can be seen between the hot-spots and cold-spots. Non-significant spatial associations are located mainly in areas of transition (high-low; low-high). One of these extends along a line from the SE portion towards the NW and some others are present in the NW area.

33The clusters identified suggest that the distribution of the variable property sale price is spatially dependent. However, they do not match the administrative subdivisions (MAA and Neighbourhood), as the clusters cross the boundaries can be seen in Figure 3. These results are in accordance with those results found by Melanda et. all (2013) using geostatistics to compare the homogeneity of Sale Price spatial distribution against the MMAs.

Figure 3: Local indicators of spatial association and administrative subdivisions in NW Calgary.

Figure 3: Local indicators of spatial association and administrative subdivisions in NW Calgary.

Decision tree models

  • 2 See Figure 1 for location of neighbourhoods

34To test the hypothesis that a sub-neighbourhood can be defined from property attributes and to verify the stability of results across the study area, the algorithm for decision tree (DT) extraction was applied at different levels of spatial complexity2:

  1. the neighbourhoods labelled as CRE and HAW, with intermediate numbers of sub-neighbourhoods;

  2. the neighbourhood ARB, with the largest number of sub-neighbourhoods;

  3. all neighbourhoods in Calgary’s North-West area;

35For each selected region, the DT algorithm was run with and without property coordinates. At level 3, the algorithm was also executed with the attributes MAA and Neighbourhood as input variables. This procedure allowed the intensity level of the spatial component related to the variable Sub-Neighbourhood to be estimated.

36The experiments for decision tree extraction were run in the environment WEKA, using the J.48 algorithm. The default values were adopted for all the parameters required by the algorithm. WEKA’s experimenter module was used to verify the stability of the results, employing a 10-fold cross validation, without tuning the algorithm parameters.

37The data mining results in relation to precision, error level and tree complexity are summarized in Table 1. The results can be considered stable for the set of measures assessed (PCC-percentage correctly classified; RAE-relative absolute error; RRSE-root relative squared error). The trees generated with (x, y) coordinates consistently performed better, with a higher precision (PCC) and a smaller complexity (number of leaves). The performance of these trees was even better in the cases where the property feature attributes (Att, such as age or living area) were not considered. It has to be said that for the data set HAW, this pattern was not so clear (PCC of 94.3% and 90.2% for the trees with and without the (x, y) attributes, respectively), possibly due to the highly unbalanced distribution of classes, with 85% of properties belonging to only one sub-neighbourhood class.

Table 1: Decision tree-summary of experiments

Data set

NoL

PCC

RAE

RRSE

MC

NC

Single Neighbourhood

ARB-Att, (x, y)

26

95.0

6.22

33.03

ARB-Att

138

72.3

38.00

70.67

19.9

13

ARB-(x, y)

24

96.0

5.48

29.79

CRE-Att, (x, y)

8

92.3

11.49

44.49

CRE-Att

54

40.0

90.42

116.13

41.5

7

CRE-(x, y)

9

93.8

9.40

39.86

HAW-Att, (x, y)

16

94.3

28.83

65.21

HAW-Att

44

90.2

44.26

79.50

85.2

5

HAW-(x, y)

11

96.9

14.28

48.31

NW Area

1. Market Area, Att, (x, y)

351

95.22

5.57

30.02

2. Market Area, Att

2,001

53.58

52.78

85.36

3. Market Area, (x, y)

311

96.41

4.24

26.34

4. Neigh, Att, (x, y) *

305

96.44

4.20

25.94

5. Neigh, Att

869

83.91

20.10

51.81

7.0

162

6. Neigh, (x, y)

271

97.11

3.44

23.59

7. Att, (x, y)

355

94.85

5.95

31.17

8. Att

2,347

45.45

61.59

92.52

9. (x, y) *

301

95.86

4.83

28.13

(*) models statistically similar, at 5% significance level in paired Student’s t-test.

NoL-Number of leaves

PCC-Percentage correctly classified

RRSE-Root relative squared error

MC-Percentage in majority Sub-neighbourhood

RAE-Relative absolute error

NC-Number of distinct Sub-neighbourhoods

38Including the attribute Neighbourhood improved performance in all cases. Comparing data set number 4 with 7 and data set 6 with 9, both increase in PCC (of 1.59% and 1.25%, respectively) and a decrease in the number of leaves can be seen. Comparing data set 5 with 8, there was a large increase (38.46%) in PCC and a significant reduction in the tree size when Neighbourhood was included. These findings show how the attribute Neighbourhood contributed to the performance of the tree, slightly when (x, y) coordinates are present and more strongly when they are not. This result was expected, since Neighbourhood represents some kind of spatial location and Sub-Neighbourhood is a subdivision of Neighbourhood. Finally, the inclusion of the attribute MAA did not produce any significant improvements.

39Thus, the decision tree analysis confirms the initial hypothesis that the Sub-Neighbourhood a property belongs to can be determined by the property’s location (either (x, y) coordinates alone or in conjunction with Neighbourhood). The analysis also shows that a property’s attributes (Att) are not useful for determining its sub-neighbourhood, considering that the value of PCC for Att was 45.45%.

40Also, from the data-mining process, it can be said that the initial hypothesis, that the Sub-Neighbourhood attribute possesses a strong spatial component, was confirmed by the consistent results for all data sets, with respect to precision and model complexity.

41To illustrate how closely the Sub-Neighbourhood limits defined by the tree are similar to those defined by administrative designation a branch of intermediate complexity-the Royal Oak (ROY) neighbourhood, which had a PCC of 100%-was selected as a test area. In Figure 4, the decision tree for this neighbourhood is presented. The first node level splits it into two parts, one with X coordinates less than or equal to -15,600 and the other with X coordinates greater than -15,600. The second node level splits, similarly, each part into two others, with respect to the Y coordinate (on the left branch) and X coordinate (on the right branch). This process continues until the leaves are reached.

Figure 4: Royal Oak Neighbourhood, selected decision tree branches - (configuration number 6 of Table 1).

Figure 4: Royal Oak Neighbourhood, selected decision tree branches - (configuration number 6 of Table 1).

42In Figure 5, the ROY tree branches were mapped and overlaid on the sub-neighbourhoods of Royal Oak (red lines). There is a strong correlation between the spatial coordinates of a property and its sub-neighbourhood. This behaviour was also identified in the other 6 trees, suggesting that the attribute Sub-Neighbourhood is very representative of the property’s location. Some discrepancies can be explained by the presence of green areas and parks.

Figure 5: Sub-neighbourhoods of Royal Oak overlaid with decision tree branches.

Figure 5: Sub-neighbourhoods of Royal Oak overlaid with decision tree branches.

Regression trees

43The regression tree technique was employed to determine whether the attribute Sale Price can be modelled by property attributes (Att), spatial boundaries (MAA, Neighbourhood or Sub-Neighbourhood) or by spatial coordinates with the same degree of precision. In composing the subsets, the spatial boundary attributes were not considered simultaneously, as they were correlated by the Cramer’s test, for categorical attributes, and should not be present in the same model.

44Table 2 presents the number of rules in each tree, and the respective error measures for the 15 subsets considered. Some consistent patterns can be observed regarding the trees’ precision. Data sets with (x, y) coordinates showed better results than the data sets with the same attributes but without (x, y) coordinates; this pattern also occurs for data sets with the spatial boundary attributes, MAA, Neighbourhood and Sub-Neighbourhood. These results show that the precision of the trees (R) is improved by incorporating any of the spatial attributes and also suggests that Sale Price has a spatial component.

45The MAA attribute does not influence the precision of the tree when present together with (x, y) coordinates, but does when combined with Att, increasing the value of R from 0.898 to 0.920 (data sets 14 and 2, Table 2). Ideally, we might expect that modelling Sale Price as a function of MAA and property attributes (data set 2) would produce the best results, since this is used in the city assessment process. However, it was only 7th best in performance.

46Both, Neighbourhood and Sub-Neighbourhood improved the tree’s performance in all cases, with a slight difference in favour of Sub-Neighbourhood, as seen in data sets 5 and 9. This was expected, since Sub-Neighbourhood is a subdivision of Neighbourhood.

47It is worth mentioning that either (x, y) coordinates or Sub-Neighbourhood alone explains about 73% of Sale Price variability (R of 0.732 and 0.738, respectively). Those values are particularly interesting when compared with the value R = 0.763 found by Huang et al (2010) for a hedonic global model, involving 11 attributes, to estimate property price in a distinct subset of the same original data set used in the present paper. From this, we can infer a strong correlation between the price of a property and its location. Owing to the similarity between the results of the experiments involving (x,y) coordinates and Sub-Neighbourhood (data sets 11, 12 and 15), it is plausible to say that Sub-Neighbourhood has a strong spatial component, corroborating the results shown in Section Decision tree models and strengthening the hypothesis of the occurrence of MAUP in the property sale data set.

Table 2: Regression tree-summary of experiments

Data set

Rank

NoR

R

RRSE

MAE

 1. Market Area, Att, (x, y)

5

47

0.925

37.98

20,535.26

 2. Market Area, Att

7

25

0.920

39.09

21,174.00

 3. Market Area, (x, y)

12

194

0.736

67.79

35,469.32

 4. Market Area

15

1

0.354

93.51

52,005.43

 5. Neigh, Att, (x, y) *

2

30

0.932

36.33

19,812.50

 6. Neigh, Att

4

26

0.927

37.50

20,466.09

 7. Neigh, (x, y)

11

172

0.737

67.65

35,274.33

 8. Neigh

14

1

0.557

83.03

44,890.87

 9. Sub-Neigh, Att, (x, y) *

1

24

0.936

35.14

19,527.77

10. Sub-Neigh, Att

3

24

0.928

37.21

20,527.23

11. Sub-Neigh, (x, y)

9

1

0.750

66.13

34,987.51

12. Sub-Neigh

10

2

0.738

67.48

35,989.58

13. Att, (x, y)

6

61

0.924

38.27

20,628.82

14. Att

8

70

0.898

44.02

23,922.73

15. (x, y)

13

204

0.732

68.32

35,494.76

(*) models statistically similar, at least 0.25 of significance in paired Student’s t-test.

NoR-Number of rules

RRSE-Root relative squared error

MAE-Mean absolute error

R-Correlation coefficient

Rank-Based on correlation coefficient

Additional information about those measures is available in Witten-Frank(1999).

48To explore the reasoning embedded in the regression tree models, a map was elaborated, shown in Figure. This map shows the spatial distribution of the properties covered by each rule from data set 12, Table 2 (chosen because it is the simplest tree with more than 1 branch). It is worth remembering that this case only considers the property’s Sub-Neighbourhood to determine Sale Price.

49In Figure 6, model 1 can be related to areas of higher prices, and model 2 to areas of lower prices. The identified patterns are consistent with the patterns shown in Figures 1 and 3, which also reveal clusters of high and low priced properties. However, the patterns identified in Figure 6do not match the boundaries of the MMAs (except for the MAA located at the south, near downtown). Once again, we find the possible occurrence of MAUP on the property sale data set, since the valuation division adopted in Calgary does not conform properly to the pattern of spatial distribution for Sale Price.

Figure 6: Mapped regression tree model from data set 12 Table 2.

Figure 6: Mapped regression tree model from data set 12 Table 2.

Conclusion and Future Work

50As previous studies have demonstrated, the use of politico-administrative divisions in spatial analysis can lead to MAUP; thus, it is recommended that locational divisions be based on the data set. This study took the approach of using data mining techniques to model spatial boundaries from the data set and then comparing them with the boundaries currently utilized in Calgary.

51We analysed the Calgary property sale data set by using LISA, decision tree and regression tree. Our findings from LISA indicate some patterns in the spatial variation of sale price, with clusters of "high-high" (high prices surrounded by high prices) and "low-low" (low prices surrounded by low prices) and in-between transitional areas of "high-low", non-significant relation and "low-high". However, these patterns do not agree with Calgary’s municipal valuation areas, which is one of our concerns.

52Relating LISA pattern to its proximity to the city centre, there is an elliptical pattern that extends from downtown to the university, mainly on the south side of the Trans-Canada road. That well-established region is going through a natural process of renovation, which explains the presence of high-low property points. Aside from this region, there is no evidence of a relation between LISA patterns and the distance to the city centre. The hot-spots located in the north and in the west could be related to the new suburban development areas located near very attractive amenities, for instance golf courses, lakes and hilltops.

53Through the decision tree analysis, we confirmed the initial hypothesis that the Sub-Neighbourhood attribute is representative of properties’ locations, since using only the (x, y) coordinates as parameters, the decision tree achieved a PCC of 95.86%. This value is statistically not much better than the one obtained when the Neighbourhood attribute was included (97.11%), even though Sub-Neighbourhood is a subdivision of Neighbourhood. In light of this finding, a modelling process that uses Sub-Neighbourhoods could possibly be modified to use (x, y) coordinates while avoiding incurring the MAUP problem and being able to reflect the changes from one area to another gradually. Furthermore, the presence of the Sub-Neighbourhood attribute can mask the effect of attributes related to the influence of local amenities (Green; Traffic and View), even though these attributes represent the proximity to amenities in a simplified way.

54The aim of the use of the regression tree was to explore how different combinations of attributes, especially the spatial ones, would perform in explaining the Sale Price attribute. The categorical attributes (Att), by themselves, performed quite well (R=0.898 with 70 rules). By including any spatial attribute, the results were improved (R 0.920, 0.924, 0.927 and 0.928, for MAA, (x, y) coordinates, Neighbourhood and Sub-Neighbourhood respectively). The best regression tree was obtained by combining the Sub-Neighbourhood, Att and (x, y) coordinates (R=0.936). It is noteworthy that it was possible to explain about 73% of Sale Price by using only (x, y) coordinates or the Sub-Neighbourhood. These results show that the precision of the trees (R) is improved by incorporating any of the spatial attributes and also suggests that Sale Price has an unmapped spatial component. So, we can conclude that the spatial attributes might be acting as a strong proxy for local amenities, despite the presence of attributes related to them in the Att set.

55As a general conclusion, MAA seems to not conform properly to homogeneous urban areas and a viability study for implementation of a more elaborated modelling process, with the use of GIS and robust statistical models, should be considered by the City of Calgary. However, changing the current methodology is a complex and delicate matter. It is a task that involves, beyond the technical aspects, convincing the many market actors, including policy makers, taxpayers and developers.

56Our future work will concentrate on the following issues. First, the use of tree-based models has embedded knowledge that merits further investigation. Work should be done to enrich the data set by using GIS to evaluate the influence of local amenities and transform them into attributes. Decision tree models can be employed to construct neighbourhood configurations from information contained in the actual data, avoiding the MAUP. Residuals from regression trees should be evaluated and compared with other methodologies, for instance ordinary least squares (OLS), iterative generalized least squares (IGLS) (Orford, 2002), geographic weighted regression (GWR) (Fotheringham et al, 2002) and also the residuals from the procedures utilized by the City of Calgary’s appraisal department. Finally, tests should be done on attribute selection and generalization, as well as tuning of the tree generation algorithms.

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Notes

1 GKD is an extension of the Knowledge Discovery from Database (KDD) process (Fayyad et al, 1996) to deal with georeferenced databases.

2 See Figure 1 for location of neighbourhoods

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Table des illustrations

Titre Figure 1: Sales transactions, over 2002 and 2004, in the North-West of Calgary, by percentile distribution of Sale Price.
URL http://cybergeo.revues.org/docannexe/image/27493/img-1.jpg
Fichier image/jpeg, 1,1M
Titre Figure 2: Example of transposition of a tree representation into a map form.
URL http://cybergeo.revues.org/docannexe/image/27493/img-2.png
Fichier image/png, 42k
Titre Figure 3: Local indicators of spatial association and administrative subdivisions in NW Calgary.
URL http://cybergeo.revues.org/docannexe/image/27493/img-3.jpg
Fichier image/jpeg, 952k
Titre Figure 4: Royal Oak Neighbourhood, selected decision tree branches - (configuration number 6 of Table 1).
URL http://cybergeo.revues.org/docannexe/image/27493/img-4.png
Fichier image/png, 38k
Titre Figure 5: Sub-neighbourhoods of Royal Oak overlaid with decision tree branches.
URL http://cybergeo.revues.org/docannexe/image/27493/img-5.jpg
Fichier image/jpeg, 668k
Titre Figure 6: Mapped regression tree model from data set 12 Table 2.
URL http://cybergeo.revues.org/docannexe/image/27493/img-6.jpg
Fichier image/jpeg, 844k
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Pour citer cet article

Référence électronique

Edson Melanda, Andrew Hunter et Michael Barry, « Identification of locational influence on real property values using data mining methods », Cybergeo : European Journal of Geography [En ligne], Systèmes, Modélisation, Géostatistiques, document 771, mis en ligne le 04 février 2016, consulté le 06 décembre 2016. URL : http://cybergeo.revues.org/27493 ; DOI : 10.4000/cybergeo.27493

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Auteurs

Edson Melanda

Federal University of São Carlos, Brazil, Associate Professor, melanda@ufscar.br

Andrew Hunter

University of Calgary, Canada, Associate Professor, ahunter@ucalgary.ca

Michael Barry

University of Calgary, Canada, Professor, mbarry@ucalgary.ca

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Droits d’auteur

© CNRS-UMR Géographie-cités 8504

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