DOCUMENT DE TRAVAIL 1999-015 - FSA ULaval

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DOCUMENT DE TRAVAIL 1999-015

SORTING OUT ACCESS AND NEIGHBOURHOOD FACTORS IN

HEDONIC PRICE MODELLING : AN APPLICATION TO THE

QUEBEC CITY METROPOLITAN AREA

François Des RosiersMarius ThériaultPaul-Y. Villeneuve

Version originale :Original manuscript :Version original :

ISBN – 2-89524-087-6ISBN -ISBN -

Série électronique mise à jour :One-line publication updated :Seria electrónica, puesta al dia

10-1999

Sorting out Access and Neighbourhood Factors in Hedonic Price Modelling:An Application to the Quebec City Metropolitan Area

by

François Des Rosiers1, Marius Thériault2 and Paul-Y Villeneuve3

Paper presented

at the Sixth European Real Estate Society Conference

Athens, 23 -25 June 1999

1. Faculty of Business Administration, Planning and Research Centre, Laval University, Québec, Canada, G1K 7P4Phone: 418-656-2131 ext. 5012, e-mail: [email protected]

2. Department of Geography, Planning and Research Centre, Laval University, Québec, Canada, G1K 7P4Phone: 418-656-2131 ext. 5899, Fax: 418-524-6701 e-mail: [email protected]

3. Department of Planning, Director, Planning and Research Centre, Laval University, Québec, Canada, G1K 7P4Phone: 418-656-2131 ext. 3791, e-mail: [email protected]

Summary of paper

This paper investigates the analytical potential of factor analysis for sorting out neighbourhood andaccess factors in hedonic modelling using a simulation procedure that combines GIS technology andspatial statistics. Application to the housing market of the Quebec City Metropolitan Area (more than2 400 cottages sold from 1993 to 1997) illustrates the relevance of this approach. In the first place,accessibility from each home to selected activity places is computed on the basis of minimum travellingtime using the TransCAD transportation-oriented GIS software. The spatial autocorrelation issue is thenaddressed and a general modelling procedure developed. Following a five-step approach, propertyspecifics are first introduced in the model; proximity and neighbourhood attributes are then successivelyadded on. Finally, factor analyses are performed on each set of access and census variables, therebyreducing to six principal components an array of 49 individual attributes. Substituting the resulting factorsfor the initial descriptors leads to high model performances, controlled collinearity and stable hedonicprices, although remaining spatial autocorrelation is still detected in the residuals.

Key Words: GIS, Hedonic modelling, Accessibility, Travelling time, Urban externalities, Housingmarkets, Spatial analysis

1. Introduction : Context and Objective ofResearch

This paper deals with the integration ofneighbourhood and access attributes to hedonicmodelling, with a focus on how to sort out cross-influences between both series of factors so as toachieve an optimal model design while minimizinginformation loss. The hedonic approach aims atexplaining property prices on the basis of theirphysical and neighbourhood-related characteristics.Its purpose is to evaluate the respective contributionof each attribute of the residential bundle to market

value (Can 1990 & 1993, Dubin 1998), usingmultiple regression analysis. While hedonic modelshave long proved their usefulness as an analyticaldevice, previous research has shown that substantialportion of price variability remains unexplained(Anselin and Can 1986, Dubin and Sung 1987, Can1993, Dubin 1998). Moreover, the appropriateneighbourhood factors needed to improve hedonicmodels may change among locations and marketsegments, making it difficult to integrate allsignificant factors. Finally, multicollinearity ofmodel attributes, as well as structural


Sixth European Real Estate Conference, Athens, June 23-25, 1999 Des Rosiers, Thériault and Villeneuve

- No reproduction, in part or in full, is allowed without the authors’ consent -

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heteroskedasticity and spatial autocorrelation amongresiduals is detrimental to the stability of regressioncoefficients (Dubin 1988, Anselin and Rey 1991, Canand Megbolugbe 1997, Basu and Thibodeau 1998,Pace et al. 1998, Des Rosiers and Thériault 1999).These are issues that need be addressed and thatdeserve substantial research efforts.

Geographic Information Systems (GIS) provideresources to enhance real estate analysis and hedonicmodelling (Can 1992, Des Rosiers and Thériault1992, Thrall 1993, Thrall and Marks 1993, Rodriguezet al. 1995). While GIS can improve the measurementof location and access variables - namely by resortingto time, rather than mere Euclidean distances -, theiranalytical capabilities are greatly enhanced wherespatial statistics methods are integrated (Anselin andGetis 1992, Griffith 1993, Zhang and Griffith 1993,Thériault and Des Rosiers 1995, Levine 1996).Indeed, procedures such as centrographic analysis,trend surface analysis, spatial pattern analysis andautocorrelation analysis (Odland 1988, Cressie 1993,Ord and Getis 1995, Tiefelsdorf and Boots 1997) aswell as variography and Kriging techniques (Dubin1992, Panatier 1996) can help detecting additionalneighbourhood factors that must be considered toexplain market variability.

All these methods greatly improve the analysis andmodelling of the geographical structure of housingmarkets. However, they don’t overcome the problemof sorting out adequately access and neighbourhoodattributes in the first place. Depending on dataavailability, these can be quite numerous and inducesevere collinearity in the model. To reduce its extent,one may limit the number of descriptors to aminimum, thereby causing a partial loss ofinformation. Another option – developed here - is toresort to factor analysis (Thurstone 1947; Rummel1970) in order to generate independent complexvariables used as substitutes for initial attributes.While cross-influences could possibly be detectedbetween access and neighbourhood attributes, the twoseries of house price determinants are consideredseparately in this paper due to the data aggregationissue they raise: whereas accessibility may becomputed at the level of individual properties, censusdata used to define neighbourhood attributes are

aggregated at the level of enumeration areas. In spiteof their usefulness for modelling purposes, theyprovide an averaged out, and therefore less acutepicture of local characteristics.

2. Measuring Accessibility : Time vs. Distance

The accessibility and mobility issues have beenaddressed in a recent paper by Thériault, DesRosiers and Vandersmissen (1999). Accessibilityrelates to the ability of individuals to travel and toparticipate in activities at different locations in anenvironment. GIS could provide sophisticated andpragmatic representations of individual accessibilitywhich may be of significant use in location analysisand transportation planning (Miller 1991). Traveltime is the most common measure of accessibility –or the lack of it -, since it evaluates the perceivedinconvenience of a trip and its impact on the dailyactivity schedule of the commuter as well as of theentire household (Landau et al. 1981). In the currentpaper, the above definition of accessibility isrestricted to the specific case of travelling from anindividual's home location in order to attendactivities at specific locations in the metropolitanarea.

Analysing accessibility requires a spatio-temporalframework that encompasses various aspects ofindividual behaviour relative to daily commutingpatterns as well as to home location choices in thelong term (Nijkamp et al. 1993). Such a framework,originally developed by Hägerstrand (1970), focuseson the disaggregate possibilities of individuals.Afterwards, individual decisions should beaggregated among groups of peoples or specificneighbourhoods, in order to model intra-urbantraffic and transportation mode choices(Timmermans and Golledge 1990). Using GIS andappropriate geo-relational information aboutcommuters, it is already feasible to model travelchoices and individual behaviour (Golledge et al.1994, Thériault et al. 1998). Being integrated in theCAMA GIS, such a procedure can generate usefuldata to improve hedonic modelling.

Earlier urban models are currently based on thecentrality concept. In the traditional monocentriccity, the price of land is higher at the CBD and




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gradually decreases with distance. In a uniformenvironment, this function can be modelled usinggravity principles and is roughly proportional to theinverse of Euclidean squared distance. Due to thecomplexity of the urban fabric though, using mereEuclidean distances to the CBD falls short ofintegrating all relevant aspects of accessibility(Jackson 1979, Dubin and Sung 1987, Niedercorn andAmmari 1987, Hoch and Waddell 1993). Whilevarious studies have stressed the important role ofproximity to services and to environmentaldisturbances in the variation of market values(Guntermann and Colwell 1983, Colwell 1985 &1990, Grieson and White 1989, Sirpal 1994, DesRosiers et al. 1996), most of these studies actuallyresort to Euclidean distances (or their numericaltransforms) to measure the externalities related toaccessibility.

Following behavioural principles, we have shown thatmore sensitive measurements of actual road distancesand travel times could significantly improve hedonicmodelling (Thériault, Des Rosiers and Vandersmissen1999). Applying a GIS distance and trip durationmodelling procedure to more than 2 400 cottages soldin the Quebec region from January 1993 to January1997 provides us with a useful insight into themechanics of household behaviour. For that purpose,service poles are deliberately limited to those oftenreported in the literature: CBD, important workingplaces, schools, shopping centers (Guntermann andColwell 1983, Hickman et al., 1984, Colwell et al.1985, Des Rosiers et al. 1996, Colwell 1998). Also,only the nearest location from home in terms ofshortest route distance (kilometres) or trip duration(minutes) are retained. Finally, in order to compensatefor this drawback and portray the actual mobilitypatterns of individuals, an origin-destination (OD)survey carried out by the Quebec Urban Community’sPublic Transit Corporation in 1991 and based on asample of 50 800 commuters (111 000 daily trips,20 800 households) is integrated in the GIS.

Thus, using the same GIS procedure as above, thebest route followed by each person during each trip isdetermined in order to evaluate road distance andtravel time. This complex task is implemented usingthe TransCAD (Caliper Corporation) transportation-

oriented GIS which provides an efficient bi-directional data exchange link with MapInfo. Foreach travel goal (working, studying, shopping andothers), trips and stays are located in the GIS usingthe activity-event data structure described byGoodchild (1998). Through aggregation of thishighly detailed information, estimates ofaccessibility to various kinds of services in theimmediate neighbourhood is computed for eachproperty, providing both typical trip duration anddistance. Considering the technical requirements forroute modelling, a custom application (Korem 1998)to handle network structuring tasks was developedusing the MapBasic language. This resulted in aregional road network having 52 500 street segments(acting as directional links) and 19 250 nodes(acting as street intersections). Nearest servicelocations and access times are computed for everystreet node using the network partitioningprocedure. Thereafter, since each property is linkedto the appropriate street node, this foreign key canbe used to merge accessibility results to theappropriate homes.

3. Searching for Spatial Autocorrelation

From an analytic point of view, land prices are acombination of externality effects and location rents(Krantz et al. 1982, Hickman et al. 1984, Shefer1986, Yinger et al. 1987, Strange 1992, Can 1993,Dubin 1998). Hoch and Waddell (1993) point outthat the overlapping of access and neighbourhoodcharacteristics leads to highly complex influenceson rent levels and values. As shown by Des Rosierset al. (1996), specific transformation may be appliedto the hedonic equation so as to account for the non-monotonicity of some of the distance functions.

Although quite useful from an explanatoryperspective, integrating large sets of variables into asingle regression model may be highly problematic.Multicollinearity, heteroskedasticity and spatialautocorrelation problems (Anselin and Can 1986,Anselin and Rey 1991, Goodman and Thibodeau1995) should be avoided. In particular, sorting outaccess and neighbourhood attributes can prove quitetricky considering the cross-influences betweenthese two sets of factors. The general procedure to




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be followed - described in more details in Des Rosiersand Thériault (1999) - involves a succession of checksand counterchecks designed to achieve optimal modelperformances, subject to coefficient stability in theregression model (Figure 1).

As is known, the presence of spatial autocorrelation,whereby close properties are assigned similarresiduals (Anselin and Rey 1992, Getis and Ord1992), will cause hedonic model coefficients to beunstable and unreliable. While neither SPSS nor mostGIS softwares provide any mechanism to computespatial autocorrelation, some extensions tocommercial GIS are available in order to overcomethat problem (Zhang and Griffith 1993, Thériault andDes Rosiers 1995). The MapStat package (developedby Thériault) implements a method developed byMoran (1950). Moran's I coefficient is used to carryinferential hypothesis tests about the existence ofsignificant autocorrelation among values atneighbouring points. Thus, pairs of neighbouringhomes are formed, each pair being weighted by theinverse of the squared distance between the twoproperties. The sampling distribution of the mean andvariance expectations of Moran's I are known (Odland1988). They form the basis of a parametric test forassessing the significance of experimental results.Where spatial dependence is found to affect theresiduals, more geographical variables must be addedto the model to capture the appropriate spatial effect.As an alternate solution, trend surface analysis (TSA)or Kriging may be used to implicitly remove thatspace-related bias (Dubin 1992, Des Rosiers andThériault 1999). While spatial autocorrelation is notthe focus of the current paper, Moran’s I values arecomputed for each model displayed thereafter in orderto asses the extent of the problem.

4. Data Bank and Modelling Strategy

The current hedonic model is built upon a global databank of some 31 162 owner-occupied residentialproperties sold within the territory of the QuebecUrban Community (QUC), between January 1986 andJanuary 1997. The property-related informationcomes from the computerised files of the valuationroll of the QUC for the period considered. Theseproperties are located using geodetic co-ordinates.

They are integrated into the MapInfo GIS (DesRosiers and Thériault 1992). In addition, the GISintegrates other data banks such as the 1986, 1991and 1996 federal censuses (by Enumeration Areas),the 1:20,000 topographical maps, the 1986, 1991and 1996 OD surveys for the Quebec MetropolitanArea, lists of primary schools, high schools,colleges, universities, shopping centers, remotesensing images, street grids, road and highwaynetworks, powerlines, etc.. All these multi-sourcesdata are located using appropriate reference systems.They can be linked in the GIS using geo-relationaljoins.

In the current paper, hedonic modelling is performedon some 2 405 cottages sold in the QUC fromJanuary 1993 to January 1997. Prices range from50 000$ to 250 000$, with mean price standing at123 183$. Many attributes are available to describethese transactions. They can be grouped as follows(Table 1):

• Transaction attributes (mainly Sale Price, thedependent variable);

• Property specifics (66 attributes in the initialdata set; 22 selected during stepwise regressionanalysis – Models A to D);

• Local taxation attributes (2 available; 2 selectedby the model – Models A to D);

• Neighbourhood attributes (34 relative attributesextracted from the 1991 Canadian census byenumeration areas – Models C and D);

• Proximity attributes designed at capturingexternalities which operate at a very local leveland consisting of Euclidean distances and bufferzones generated via MapInfo (19 initialvariables – Models B to D);

• Travel accessibility measured on the streetnetwork using TransCAD (15 provided –Model D);

The operational definition of transaction, property-specific, local taxation and proximity attributes isdisplayed in Table 1, together with their descriptivestatistics. Census and access variables are defined inTables 6 and 7. Calibrating a model with stepwise




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regression using 136 potential independent variablesleads to severe multicollinearity problems.Consequently, a multi-step strategy is followedinvolving five steps (Models A to D):

• Most significant property specifics are firstidentified using a stepwise regression on the 68property-related and taxation attributes. Afterwithdrawal of multicollinear variables, Step 1(Table 3 - Model A) retains 24 significantattributes, with heteroskedasticity remainingunder control. Only these significant attributeswere used for later steps.

• In Step 2, proximity attributes (Euclideandistances and buffer zones) are added to Model Adescriptors. This is typical of applications usingall-purpose GIS without transportation modellingcapabilities. Only a few of the 19 initial variablesare actually retained by the stepwise procedure(Table 4 – Model B).

• Neighbourhood attributes (census data) areintroduced in the model in Step 3, with only 9 ofthe 34 available ones emerging as significant. isbuilt by combining census variables with findingsof the previous model. Using street addresses, onecan build a reliable model without the help of aGIS and with no consideration of distance andaccessibility. It is a fair standard that could beused to account for access and, to some extent,proximity effects (Table 5 – Model C).

• The main contribution of this paper rests withStep 4, where a factor analysis is performed onboth neighbourhood and access variables. Theprincipal components method, with a Varimaxrotation, is applied to each set of attributes.Outlined by Hotelling (1933), this methodessentially involves an orthogonal transformationof a set of variables (x1, x2, ..., xm) into a new setof mutually independent components, or factors(y1, y2, ..., ym) (King 1969). Each component thusobtained consists of a linear combination of allinitial variables (Tabachnick and Fidell 1996)which are assigned a specific weight that varyamong components. The first component is tohave the highest variance among the “m” set ofcomponents, that is it accounts for a dominant

portion of the variance observed in the data. TheVarimax saturation obtained in the process foreach variable and within each factor alsoindicates to what extent a given attributecontributes to the phenomenon captured by thefactor. Only the most significant componentswill be retained by the analyst on the grounds ofeither their eigenvalue or percentage of varianceexplained after rotation. The factor analysesperformed on access and neighbourhoodattributes yield most convincing results whichare summarised in Tables 6 and 7. In the formercase (2 components retained), computations arebased on 10 472 travel times while in the latter(4 components retained), 604 enumeration areasare used. Derived factor scores are then assignedto each transacted property via the GIS. Thus,49 initial variables could be reduced to only 6significant factors, without any information loss.

• Finally, Step 5 consists in integrating in thehedonic equation property-related, local taxationand proximity attributes with principalcomponents used as complex independentvariables (Table 8 – Model D).

5. Major Findings

Summary regression results are displayed inTable 2. They indicate that model performances arequite good, with R-squares ranging from 0.831 to0.894 and standard errors of estimate varyingbetween 14.09% to 11.16%. While multicollinearityis generally low – maximum VIF below 5, exceptfor Model C where it reaches 5.6 -, regressionresiduals are significantly autocorrelated (Map 3):indeed, the Moran’s I varies from a low of 0.2964 inModel C to a high of 0.4484 in Model A. Thissuggests a significant spatial trend does operate atthe local level, resulting in potentially unstableregression coefficients.

In spite of a lower performance, Model A (Step 1),with only property-specific attributes and the localtax rate as explanatory variables, still manages toexplain some 83% of price variations with aprediction error of only 14%. All regressioncoefficients are consistent with respect to both signand magnitude. The spatial autocorrelation index,




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though, is highest at 0.46. Adding proximity variablesto the basic model (Model B – Step2) slightlyimproves its global performance (R-square: 0.854 andSEE: 13.07%) while most property-relatedcoefficients remain unchanged. There are a fewexceptions though, among which the lot size(LNLOTSIZ) coefficient whose magnitude more thandoubles. This is no surprise considering the statisticalsignificance of the two descriptors entered (proximityto the nearest college or university and to the nearestregional shopping centre) which tend to capture asignificant proportion of land values in the region.Spatial autocorrelation, however, is hardly improved(0.4365).

Adding census variables to the basic model (Model C– Step 3) clearly improves its strength (R-square:0.894 and SEE: 11.16%). Regression coefficientsshow important differences with the previous one onseveral property specifics (age and apparent age; roofquality) and local tax rate. Distance to the nearestcollege or university is no more significant whileproximity to a major power line is. These changes canbe easily explained by the introduction of majorneighbourhood descriptors which account for thesocio-economic structure of households (educationand tenure profiles) and the quality of the housingstock (proportion of dwellings built before 1960). Byand large, the standard errors are substantially lower,with spatial autocorrelation index dropping from 0.44to 0.30.

Turning to Step 4, factor analysis on access andneighbourhood attributes provides us with aninteresting insight into property value dynamics.Starting with the analysis on accessibility (Table 6), itcan be seen from the right hand side of the upper partof the table (% of variance explained after Varimaxrotation) that two components clearly dominate, with42.1 and 33.6 percent of total variance beingaccounted for by the first and second components,respectively. Looking at Varimax saturations (lowerpart of the table) helps interpreting these results:while the first component is clearly dominated byaccess to regional services (highway entrance,regional shopping centres, colleges and university,Quebec and Ste-foy CBDs), it is the local dimensionthat emerges in component 2 (local and

neighbourhood shopping centres, high schools andprimary schools). In this case then, labellingcomponents is an easy task, as can be visualisedfrom Map 1. This is less so with the second factoranalysis on census data. Here, four principalcomponents are brought out, which explain 66.6percent of total variance. As can be seen fromMap 2, factor 1 (26% of total variance)discriminates on the basis of household structure,housing tenure and socio-economic profile whereasfactor 2 (15%) focuses on educational and socio-economic dimensions. Factors 3 and 4 (13% each)offer a less clear-cut picture, with householdcomposition, location patterns and economic profilebeing accounted for in both components.

Step 5 (Table 8 – Model D) incorporates access andneighbourhood factor scores in the hedonic model,with quite conclusive results. While overall modelperformance is slightly reduced (R-square: 0.881and SEE: 11.79%) as opposed to Model C, the Fratio proves to be stronger. Regression coefficientsundergo only minor changes, an indication of themodel stability. Two proximity attributes (distanceto nearest high school and regional shopping centre)accounted for by principal components are expelledfrom the equation while another one (HIGHWEXM)is added on. Most important, all of the six principalcomponents previously defined are retained ashighly significant. Findings suggest that the secondneighbourhood factor (educational profile; t-value:20.07) as well as both access factors (regional andlocal dimensions; t-values: -10.06 and -8.06,respectively) are major determinants of propertyvalues. Spatial autocorrelation of residuals,however, is still higher than in Model C (Moran’s I:0.3657), although much less pronounced than inModels A and B. Model residuals can be visualisedin Map 3. As can be seen, a clear pattern exists withrespect to undervalued properties which tend toconcentrate in the Upper-City neighbourhoods,particularly along the River cliff.

6. Conclusion and Further Research Suggestions

Main findings from this research clearly suggest thatfactor analysis is highly efficient at sorting outaccess and neighbourhood attributes. Once




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substituted for original variables in the hedonicmodel, principal components allow for a betterstructuring of complex influences affecting houseprices while avoiding excessive multicollinearity.While remaining spatial autocorrelation may betackled using sophisticated analytical tools thatoperate on the very local effects, the respectivecontribution of such paramount housing attributes toproperty values could be further investigated usingcanonical correlation. Designed at analysing therelationships between two sets of variables, thismethod will be the focus of our next researchendeavour.

Acknowledgments

We gratefully acknowledge Martin Lee-Gosselin, CorinneThomas, Josée Bouchard, Isabelle Plamondon, PierreLemieux, Raynald Sirois and Yanick Aubé for theirvaluable help at various stages of this research. This projectwas funded by the Quebec Province's FCAR program, theCanadian SSHRC, the Canadian CMHC and the CanadianNSERC. It was realised in close co-operation with theQuebec Urban Community Appraisal Division, the STCUQ(Quebec Urban Community Transit Society) and theQuebec Ministry of Transport.

References

Anselin, L., and A. Can, 1986. Model comparison and modelvalidation issues in empirical work on urban density functions.Geographical Analysis, 18: 179-197.

Anselin, L., and A. Getis, 1992. Spatial statistical analysis andgeographic information systems. The Annals of RegionalScience, 26: 19-33.

Anselin, L., and S. Rey, 1991. Properties of tests for spatialdependence in linear regression models. GeographicalAnalysis, 23(2): 112-131.

Basu, S., and T. G. Thibodeau, 1998. Analysis of spatialautocorrelation in house prices. The Journal of Real EstateFinance and Economics, 17(1): 61-86.

Can, A., 1990. The measurement of neighbourhood dynamics inurban house prices. Economic Geography, 66: 254-272.

Can, A., 1992. Residential quality assessment: Alternativeapproaches using GIS. The Annals of Regional Science, 26:97-110.

Can, A., 1993. Specification and estimation of hedonic housingprice models. Regional Science and Urban Economics, 22:453-474.

Can, A., and I. Megbolugbe, 1997. Spatial dependence and houseprice index construction. Journal of Real Estate Finance andEconomics, 14: 203-222.

Colwell, P. F., S. S. Gujral and C. Coley, 1985. The impact ofshopping center on the value of surrounding properties. RealEstate Issues, 10(1): 35-39.

Colwell, P. F., 1990. Power lines and land values. Journal ofReal Estate Research, 5(1): 117-127.

Colwell, P. F., 1998. A primer on piecewise parabolic multipleregression analysis via estimations of Chicago CBD landprices, The Journal of Real Estate Finance and Economics,17(1): 87-98.

Cressie, N. A. C., 1993. Statistics for Spatial Data, New York,Wiley, 900 p.

Des Rosiers, F., and M. Thériault, 1992. Integrating geographicinformation systems to hedonic price modelling: Anapplication to the Quebec region. Property Tax Journal,11(1): 29-57.

Des Rosiers, F. and M. Thériault, 1999. House Prices andSpatial Dependence: Towards an Integrated Procedure toModel Neighbourhood Dynamics. Laval University, Facultyof Business Admin., Québec, Publ. 1999-002, 23 p.

Des Rosiers, F. A. Lagana, M. Thériault and M. Beaudoin,1996. Shopping centers and house values: An empiricalinvestigation. Journal of Property Valuation andInvestment, 14(4): 41-63.

Dubin, R. A., 1988. Estimation of regression coefficients in thepresence of spatially autocorrelated error terms. Review ofEconomics and Statistics, 70: 466-474.

Dubin, R. A., 1992. Spatial autocorrelation and neighbourhoodquality. Regional Science and Urban Economics, 22: 433-452.

Dubin, R. A., 1998. Predicting house prices using multiplelistings data. The Journal of Real Estate Finance andEconomics, 17(1): 35-60.

Dubin, R. A., and C. H. Sung, 1987. Spatial variation in theprice of housing: Rent gradients in non-monocentric cities.Urban Studies, 24: 193-204.

Getis, A., and J. K. Ord, 1992. The analysis of spatialassociation by use of distance statistics. GeographicalAnalysis, 24(3): 189-206.

Golledge, R.G., M. P. Kwan and T. Gärling, 1994.Computational process modelling of household traveldecision using a geographical information system. Papers inRegional Science, 73(2): 99-117.

Goodchild, M. F., 1998. GIS and disaggregate transportationmodelling. Geographical Systems, 5(1): 19-44.

Goodman, A. C., and T. G. Thibodeau, 1995. Age-relatedheteroskedasticity in hedonic house price equations. Journalof Housing Research, 6: 25-42.

Grieson, R. E., and J. R. White, 1989. The existence andcapitalization of neighbourhood externalities: Areassessment. Journal of Urban Economics, 25(1): 68-76.

Griffith, D. A., 1993. Advanced spatial statistics for analyzingand visualizing geo-references data. International Journal ofGeographical Information Systems. 7(2): 107-124.

Guntermann, K. L., and P. F. Colwell, 1983. Property valuesand accessibility to primary schools. Real Estate Appraiserand Analyst, 49(1): 62-68.

Hägerstrand, T., 1970. What about people in regional science?Papers of the Regional Science Association, 14: 7-16.




8

Hickman, E. P., J. P. Gaines and F. J. Ingram, 1984. The influenceof neighbourhood quality on residential values. The RealEstate Appraiser and Analyst, 50(2): 36-42.

Hoch, I., and P. Waddell, 1993. Apartment rents: Anotherchallenge to the monocentric model. Geographical Analysis,25(1): 20-34.

Hotelling, H., 1933. Analysis of a Complex of StatisticalVariables into Principal Components. Journal of EducationalPsychology, 24: 417-441; 498-520.

Jackson, J. R., 1979. Intraurban variation in the price of housing.Journal of Urban Economics, 6: 464-479.

King, Leslie J., 1969. Statistical Analysis in Geography, Prentice-Hall, Englewood Cliffs, N.J.

Korem, 1998. MapLogix Version 2.0. Topological Map EditingUtility for MapInfo Professional.HTTP://www.korem.com/maplogix/index.html

Krantz, D. P., R. D. Waever and T. R. Alter, 1982. Residential taxcapitalization: Consistent estimates using micro-level data.Land Economics, 58(4): 488-496.

Landau, U., J. N. Prashker and M. Hirsh, 1981. The effect oftemporal constraints in household travel behaviour.Environment and Planning A, 13: 435-444.

Levine, N., 1996. Spatial statistics and GIS. Software tools toquantify spatial patterns. Journal of the American PlanningAssociation, 62(3): 381-390.

Miller, H. J., 1991. Modelling accessibility using space-timeprism concepts within geographical information systems.International Journal of Geographical Information Systems,5(3): 287-301.

Moran, P. A. P., 1950. Notes on continuous stochasticphenomena. Biometrika, 37: 17-23.

Niedercorn, J. H., and N. S. Ammari, 1987. New evidence on thespecification and performance of neoclassical gravity modelsin the study of urban transportation. The Annals of RegionalSciences, 21(1): 56-64.

Nijkamp, P., L. Van Wissen and A. M. Rima, 1993. A householdlife cycle model for residential relocation behaviour. Socio-Economic Planning Science, 27(1): 35-53.

Odland, J., 1988. Spatial Autocorrelation. Scientific Geography,vol. 9, Newbury Park, Sage, 85 p.

Ord, J. K., and A. Getis, 1995. Spatial autocorrelation statistics:Distribution issues and an application. Geographical Analysis,27(4): 286-306.

Pace, R. K., R. Barry and C. F. Sirmans, 1998. Spatial statisticsand real estate. The Journal of Real Estate Finance andEconomics, 17(1): 5-14.

Panatier, Y., 1996. Variowin: Software for Spatial Data Analysisin 2D. Statistics and Computing, Springer-Verlag, New York,91 p.

Rodriguez, M., C. F. Sirmans and A. P. Marks, 1995. Usinggeographic information systems to improve real estateanalysis. The Journal of Real Estate, 10(2): 163-173.

Rummel, R.J., 1970. Applied Factor Analysis. Evanston,Northwestern University Press.

Shefer, D., 1986. Utility changes in housing and neighbourhoodservices for households moving into and out of distressedneighbourhoods, Journal of Urban Economics, 19: 107-124.

Sirpal, R., 1994. Empirical modelling of the relative impacts ofvarious sizes of shopping centers on the values ofsurrounding residential properties. Journal of Real EstateResearch, 9(4): 487-505.

Strange, W., 1992. Overlapping neighbourhoods and housingexternalities. Journal of Urban Economics, 32: 17-39.

Tabachnick, Barbara G. and L.S. Fidell, 1996. UsingMultivariate Statistics. HarperCollins College Publishers,New York, p. 636.

Tiefelsdorf, M., and B. Boots, 1997. A note on the extremitiesof local Moran’s Its and their impact on global Moran’s I.Geographical Analysis, 29(3): 248-257.

Thériault, M., and F. Des Rosiers, 1995. Combining hedonicmodelling, GIS and spatial statistics to analyze residentialmarkets in the Quebec Urban Community. In Proceedings ofthe Joints European Conference on GeographicalInformation, EGIS Foundation, March 26-31, The Hague,The Netherlands, 2: 131-136.

Thériault, M., D. Leroux and M. H. Vandersmissen, 1998.Modelling travel route and time within GIS: Its use forplanning. In Simulation Technology: Science and Art.Proceedings of the 10th European Simulation Symposium.A. Bargiela and E. Kerckhoffs Eds., The Nottingham-TrentUniversity and Society for Computer SimulationInternational, October 26-28, 402-407.

Thérault, M., F. Des Rosiers and H. Vandermissen, 1999. GIS-Based Simulation of Accessibility to Enhance HedonicModelling and Property Value Appraisal. Joint IAAO-URISA 1999 Conference, New Orleans, April 11-14, 10pages.

Thrall, G. I., 1993. Using GIS to rate the quality of property taxappraisal. Geo Info Systems, 3(3): 56-62.

Thrall, G. I., and A. P. Marks, 1993. Functional requirements ofa geographic information system for performing real estateresearch and analysis. Journal of Real Estate Literature,1(1): 49-61.

Thurstone, L.L., 1947. Multiple Factor Analysis. Chicago,University of Chicago Press.

Timmermans, H., and R. G. Golledge, 1990. Applications ofbehavioural research on spatial problems: preferences andchoice. Progress in Human Geography, 14: 311-354.

Yinger, J. H., H. S. Bloom, A. Borsch-Supan and H. F. Ladd,1987. Property Taxes and House Values: The Theory andEstimation of Intrajurisdictional Property TaxCapitalization. Studies in Urban Economics, AcademicPress, Princeton Univ., 218 p.

Zhang, Z., and D. Griffith, 1993. Developing user-friendlyspatial statistical analysis modules for GIS: An exampleusing ArcView. Computer, Environment and UrbanSystems, 21(1): 5-29.



Table 1 : Operational Definition of Variables and Descriptive StatisticsCottages sold from January 1993 to January 1997(50,000$ to 250,000$ market segment -- N = 2405)

Variable Definition Minimum Maximum

Average Std. Dev.

Transaction AttributesSPRICE Sale price of the property ($) 50 000 250 000 123 183 42 158

Property AttributesLIVAREA Living area of the property (square meters) 38.28 391.87 147.73 35.67APPAGE Apparent age of the property (years) 0 79 15.26 14.65QUALITY House quality index (number of attributes - below / + above average) -2 2 -0.0158 0.3142STONBR51 Presence of stone or brick to cover at least 51% of the exterior walls 0 1 0.3617 0.4806ATTGARAG Presence of an attached garage 0 1 0.1863 0.3894DETGARAG Presence of a detached garage 0 1 0.1983 0.3988FIREPLCE Number of fireplaces 0 6 0.3925 0.5371FINBASMT Presence of a finished basement 0 1 0.3580 0.4795STOREY Number of stories 1.5 3 1.8403 0.2432EXCAPOOL Presence of an excavated pool 0 1 0.0786 0.2691WATRSEWR House linked to the municipal aqueduct and sewer network 0 1 0.9792 0.1427STAIR Presence of an indoor staircase made of hard wood 0 1 0.4728 0.4994LNLOTSIZ Natural logarithm of the lot size (square meters) 4.2572 12.4391 6.4475 0.4652SUPROOFQ Presence of a superior roof quality 0 1 0.0058 0.0761SEMFBSMT Presence of a semi-finished basement 0 1 0.0940 0.2918INFCEILQ Presence of an inferior ceiling quality 0 1 0.0682 0.2521SUPFLOOR Presence of a superior flooring quality 0 1 0.6595 0.4740TOILET Number of toilets (washroom without bath) 0 4 0.9613 0.5620AGE Effective age of the property (years) 0 311 21.12 27.22DISHWASH Presence of a permanent dishwasher 0 1 0.6890 0.4630TERRACE Presence of a terrace 0 1 0.0399 0.1958INFLUMIN Below average luminosity 0 1 0.2686 0.4433

Local Taxation AttributesLTAXRATE Local tax rate ($ per 100$ of appraised value) 1.1991 2.7250 2.1948 0.4047RELTXDIF Relative tax differential; adjusted tax using sale price – effective local tax

(% of sale price)-4.1213 1.3908 -0.0342 0.3144

Census Attributes (Enumeration areas; 1991 Census)UNIVDEGR Proportion of adults with a university degree (%) 0 68.5 26.3 15.7DW46_60 Proportion of dwellings built between 1946 and 1960 (%) 0 75.9 10.9 15.9MOVING5Y Proportion of household that had moved during the last five years (%) 12.9 98.3 47.5 18.4AGE25_44 Proportion of inhabitants aged 25 to 44 (%) 17.3 58.0 39.7 8.4DW_BEF46 Proportion of dwellings built before 1946 (%) 0 95.5 7.0 11.8HIGHSCHL Proportion of adults having a completed high school grade (%) 27.7 98.4 76.9 12.6BUILDING Proportion of dwellings in buildings of 5 stories and more (%) 0 68.6 1.1 5.4TENANT Proportion of tenant (%) 0 100 17.9 18.0CHILDREN Proportion of families with one child or more (%) 33.3 85.3 70.8 8.5

Proximity Attributes (Euclidean distances and Buffer zones)REGSCEDM Euclidean distance to the nearest regional shopping center (>100 shops;

meters)321 15 758 5 346 2 984

POWL300M House within a 300 meters buffer around high voltage power lines 0 1 0.1667 0.3728HISCHEDM Euclidean distance to the nearest high school (meters) 50 8 606 1 847 1 330COLUNEDM Euclidean distance to the nearest college ou university (meters) 138 17 152 5 739 3 462HIGHWEXM Euclidean distance to the nearest highway exit (meters) 88 6 332 1 493 887

Factor scores – Census Attributes(604 Enumeration areas ; 1991 Census)

EA91F1 First factor score -1.9686 1.9467 -0.9013 0.6749EA91F2 Second factor score -1.8600 2.4566 0.3111 0.8485EA91F3 Third factor score -2.4583 2.7797 0.6407 1.1757EA91F3 Fourth factor score -2.1023 1.0220 0.0845 0.3596

Factor scores – Access Attributes(10 472 travelling times ; 1988 network)

AC88F1 First factor score -2.0615 2.5591 0.2105 0.8725AC88F2 Second factor score -1.4233 4.8901 0.2741 0.9250Note: Variables are grouped by categories and ranked according to their general order of entrance in the models using stepwise regression

Table 2 : Model A – Property Attributes Only

Model Summary b

R R Square Adjusted R Square Std. Error of the Estimate0.912 0.832 0.831 17355.13

b. Dependent Variable: SPRICE

Anova b

Sum of Squares df Mean Square F Sig.Regression 3.556E+12 24 1.482E+11 491.893 0.000Residual 7.169E+11 2380 301200411Total 4.273E+12 2404


Coefficients a

Unstandardized Coefficients Collinearity Statistics

B Std. Error t Sig. VIF(Constant) 18208.241 8617.704 2.113 0.035

LIVAREA 521.282 13.051 39.943 0.000 1.729APPAGE -553.213 50.052 -11.053 0.000 4.291

QUALITY 14160.920 1277.579 11.084 0.000 1.286STONBR51 8844.778 822.336 10.756 0.000 1.247ATTGARAG 13916.031 988.286 14.081 0.000 1.182DETGARAG 10584.865 969.329 10.920 0.000 1.193FIREPLCE 6477.797 774.312 8.366 0.000 1.380FINBASMT 6510.161 833.322 7.812 0.000 1.274STOREY 17812.841 1920.830 9.274 0.000 1.742EXCAPOOL 12496.644 1385.452 9.020 0.000 1.110WATRSEWR 19560.960 2703.778 7.235 0.000 1.188STAIR 4164.270 837.188 4.974 0.000 1.395LNLOTSIZ 4205.476 909.071 4.626 0.000 1.427SUPROOFQ 20651.944 4757.189 4.341 0.000 1.046SEMFBSMT 4521.092 1264.761 3.575 0.000 1.087INFCEILQ -6833.108 1612.351 -4.238 0.000 1.319SUPFLOOR 3158.052 858.697 3.678 0.000 1.322TOILET 1803.398 712.986 2.529 0.011 1.282AGE -82.652 24.585 -3.362 0.001 3.575DISHWASH 2354.059 829.325 2.839 0.005 1.177TERRACE 5978.264 1847.199 3.236 0.001 1.044INFLUMIN -2453.533 854.563 -2.871 0.004 1.146LTAXRATE -27492.539 923.458 -29.771 0.000 1.115RELTXDIF 33508.872 1158.418 28.926 0.000 1.058

a. Dependent Variable: SPRICE

Table 3 : Model B – Property and Proximity Attributes

Model Summary b



Anova b



Coefficient a

Unstandardized Coefficients Collinearity Statistics

B Std. Error t Sig. VIF(Constant) -1030.544 8255.329 -0.125 0.901LIVAREA 490.177 12.222 40.107 0.000 1.761APPAGE -776.182 47.820 -16.231 0.000 4.548

QUALITY 11894.608 1191.605 9.982 0.000 1.299STONBR51 6644.759 772.342 8.603 0.000 1.277ATTGARAG 13191.364 920.835 14.325 0.000 1.192DETGARAG 9488.060 902.555 10.512 0.000 1.201FIREPLCE 6098.342 718.863 8.483 0.000 1.381FINBASMT 5633.113 774.652 7.272 0.000 1.279STOREY 17843.144 1783.479 10.005 0.000 1.743EXCAPOOL 11606.363 1286.563 9.021 0.000 1.111WATRSEWR 15834.973 2517.561 6.290 0.000 1.196STAIR 4064.525 777.196 5.230 0.000 1.396LNLOTSIZ 10943.885 915.022 11.960 0.000 1.679SUPROOFQ 21391.876 4426.262 4.833 0.000 1.051SEMFBSMT 2450.430 1178.500 2.079 0.038 1.096INFCEILQ -4306.094 1502.380 -2.866 0.004 1.330SUPFLOOR 2770.037 797.427 3.474 0.001 1.324TOILET 1694.983 662.408 2.559 0.011 1.284AGE -77.754 22.882 -3.398 0.001 3.596DISHWASH 1825.352 770.130 2.370 0.018 1.178TERRACE 5960.015 1716.596 3.472 0.001 1.047INFLUMIN -2126.676 797.343 -2.667 0.008 1.158LTAXRATE -24571.961 1087.158 -22.602 0.000 1.794RELTXDIF 35024.697 1078.259 32.483 0.000 1.065COLUNEDM -1.361 0.145 -9.400 0.000 2.329REGSCEDM -1.668 0.141 -11.809 0.000 1.646


Table 4 : Model C – Property, Proximity and Census Attributes

Model Summary b



Anova b



Coefficients a

Unstandardized Coefficients Collinearity StatisticsB Std. Error t Sig. VIF

(Constant) -73976.545 9318.514 -7.939 0.000LIVAREA 440.194 10.631 41.407 0.000 1.829

APPAGE -1009.662 45.288 -22.294 0.000 5.600QUALITY 11097.603 1019.992 10.880 0.000 1.307STONBR51 5488.769 667.704 8.220 0.000 1.310ATTGARAG 13540.129 787.178 17.201 0.000 1.196DETGARAG 8748.948 778.965 11.232 0.000 1.228FIREPLCE 4558.459 625.375 7.289 0.000 1.435FINBASMT 4162.628 644.685 6.457 0.000 1.216STOREY 14410.099 1547.360 9.313 0.000 1.802EXCAPOOL 10545.679 1105.751 9.537 0.000 1.127WATRSEWR 17616.279 2195.272 8.025 0.000 1.249STAIR 3599.753 667.141 5.396 0.000 1.412LNLOTSIZ 12982.181 813.878 15.951 0.000 1.824SUPROOFQ 14059.193 3919.503 3.587 0.000 1.132SUPFLOOR 2194.427 687.325 3.193 0.001 1.350TOILET 1198.328 568.373 2.108 0.035 1.298AGE -40.729 20.277 -2.009 0.045 3.877DISHWASH 1871.254 657.789 2.845 0.004 1.180TERRACE 2959.517 1470.814 2.012 0.044 1.055INFLUMIN -2473.148 679.977 -3.637 0.000 1.156LTAXRATE -17296.722 941.826 -18.365 0.000 1.849RELTXDIF 35130.557 926.802 37.905 0.000 1.080POWL300M 2563.051 834.035 3.073 0.002 1.230HISCHEDM 0.939 0.313 3.002 0.003 2.204REGSCEDM -1.564 0.146 -10.681 0.000 2.429UNIVDEGR 536.316 37.961 14.128 0.000 4.496DW46_60 333.515 29.345 11.365 0.000 2.763MOVING5Y 256.759 27.045 9.494 0.000 3.160AGE25_44 -420.669 61.282 -6.865 0.000 3.397DW_BEF46 145.202 35.580 4.081 0.000 2.230HIGHSCHL 206.084 49.820 4.137 0.000 4.981BUILDING 247.376 58.899 4.200 0.000 1.304TENANT 68.771 26.820 2.564 0.010 2.975CHILDREN 273.230 54.895 4.977 0.000 2.769


Table 5 : Factor Analysis on Access Attributes

Total Variance ExplainedExtraction Sums of Squared Loadings Rotation Sums of Squared Loadings

Component Total % of Variance Cumulative % Total % of Variance Cumulative %1 9.683 64.556 64.556 6.313 42.086 42.0862 1.668 11.122 75.678 5.039 33.592 75.678

Extraction Method: Principal Component Analysis.

Rotated Component Matrix a

.6466 .3518

.7584 .5554

.5572 .7276

.5455 .6708

.3511 .7967

.9107 .2421

.9156 .2737

.6101 .5335

.8933 .1427

.3198 .7009

.4070 .7762

.0106 .7237

.2733 .8475

.8009 .2968

.8753 .3606

Travel time to nearest highway entrance by car (minutes)

Travel time to nearest regional shopping center by car (minutes)

Travel time to nearest local shopping center by car (minutes)

Travel time to nearest neighbourhood shopping center by car (minutes)

Travel time to nearest highschool by car (minutes)

Travel time to nearest college or university by car (minutes)

Travel time to Laval University by car (minutes)

Travel time to Downtown Quebec by car (minutes)

Travel time to Downtown Ste-Foy by car (minutes)

Travel time to La Capitale shopping center by car (minutes)

Walking time to nearest neighbourhood shopping center (minutes)

Walking time to nearest primary school (minutes)

Walking time to nearest highschool (minutes)

Walking time to nearest college or university (minutes)

Walking time to Laval University (minutes)

1 2

Component

Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.

Rotation converged in 3 iterations.a.

Table 6 : Factor Analysis on Census Attributes

Total Variance ExplainedExtraction Sums of Squared Loadings Rotation Sums of Squared Loadings

Component Total % of Variance Cumulative % Total % of Variance Cumulative %1 11.232 33.035 33.035 8.940 26.296 26.2962 4.909 14.439 47.474 5.066 14.901 41.1963 4.159 12.233 59.707 4.342 12.772 53.9684 2.356 6.929 66.636 4.307 12.668 66.636

Extraction Method: Principal Component Analysis.

Rotated Component Matrix a

Component1 2 3 4

% 0-9 years -0.6708 -0.1424 0.5920 0.2655% 0-14 years -0.7702 -0.1063 0.4719 0.3214% 15-24 years 0.2106 0.2420 -0.1701 0.5721% 25-44 years 0.0993 0.1577 0.8451 0.3082% 45-64 years -0.0366 -0.0400 -0.8284 -0.0092% 65+ years 0.3653 -0.1417 -0.3820 -0.7241% Women 0.2642 0.0100 -0.2173 -0.5744Number of persons per household -0.9118 0.0052 0.0765 0.3590% non-family households 0.9039 0.0232 -0.0680 -0.3289% single-person households 0.8672 -0.0239 -0.0830 -0.3808Children per family -0.7729 -0.1302 0.0534 0.4434% lone-parent families 0.6906 -0.3123 -0.0775 0.0809% families with children -0.6846 -0.2134 0.0595 0.4978% families children 0-6 years 0.0937 -0.0707 0.7486 0.0879% families children 6-14 years -0.3229 0.1468 0.4690 0.2489% detached dwellings -0.8831 0.1276 -0.0218 0.2369% dwellings in large buildings 0.1432 0.0812 -0.1083 -0.7758Persons per room -0.1911 -0.6292 0.3687 0.1963% dwellings built before 1946 0.5776 -0.0605 0.0597 0.0644% dwellings built 1946-60 0.2742 0.0038 -0.4077 0.1458% dwellings built 1961-70 -0.0603 0.0505 -0.6166 0.2247% of tenants 0.8500 -0.2249 0.0563 -0.1705% household with housing cost > 30% of income 0.4703 -0.3276 0.1086 -0.1106% unemployment 15-24 years 0.0800 0.0514 0.0063 -0.0011% unemployment 25+ years 0.4887 -0.4253 -0.0141 0.1586% active labour market 25+ years -0.3907 0.4974 0.4569 0.4492% highschool degree -0.1997 0.9061 0.1286 0.0473% university degree 0.1247 0.9327 0.0004 -0.0456% men college degree -0.1572 0.9067 0.0237 0.0060% women college degree -0.0430 0.9086 0.1784 0.1194Household income ($) -0.7187 0.5941 -0.0577 0.0375% moving during last 5 years 0.5602 0.1777 0.5916 -0.0924Population density (persons / hectare) 0.1865 0.0469 0.0845 -0.6391Dwelling density per hectare 0.2098 0.0508 0.0723 -0.6901Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 8 iterations.

Table 7 : Model D – Property and Proximity Attributeswith Census and Access Factor Scores

Model Summary b



Anova b



Coefficients aUnstandardized Coefficients Collinearity Statistics

B Std. Error t Sig. VIF(Constant) -31380.816 7766.426 -4.041 0.000LIVAREA 454.498 11.046 41.147 0.000 1.769

APPAGE -995.460 35.696 -27.887 0.000 3.117QUALITY 12114.873 1066.527 11.359 0.000 1.280STONBR51 6222.735 695.381 8.949 0.000 1.273ATTGARAG 13637.475 829.399 16.443 0.000 1.189DETGARAG 10211.903 813.587 12.552 0.000 1.200FIREPLCE 4512.810 655.021 6.890 0.000 1.411FINBASMT 4670.160 678.774 6.880 0.000 1.208STOREY 15189.845 1620.905 9.371 0.000 1.771EXCAPOOL 11587.437 1169.367 9.909 0.000 1.129WATRSEWR 16820.082 2358.964 7.130 0.000 1.292STAIR 3905.809 702.009 5.564 0.000 1.401LNLOTSIZ 11399.294 839.263 13.583 0.000 1.737SUPROOFQ 12474.729 4019.148 3.104 0.002 1.066SUPFLOOR 2718.481 720.470 3.773 0.000 1.329TOILET 1260.853 599.155 2.104 0.035 1.293DISHWASH 1877.952 694.166 2.705 0.007 1.177TERRACE 3377.817 1553.892 2.174 0.030 1.055INFLUMIN -1847.760 716.817 -2.578 0.010 1.151LTAXRATE -15092.431 1213.088 -12.441 0.000 2.748RELTXDIF 34998.519 969.331 36.106 0.000 1.058POWL300M 2351.714 854.346 2.753 0.006 1.156HIGHWEXM 3.468 0.440 7.880 0.000 1.739EA91F1 3494.853 732.383 4.772 0.000 2.785EA91F2 11054.938 550.722 20.074 0.000 2.489EA91F3 -1210.282 418.527 -2.892 0.004 2.760EA91F4 -4284.404 1041.385 -4.114 0.000 1.598AC88F1 -7101.018 706.195 -10.055 0.000 4.328AC88F2 -3833.821 475.461 -8.063 0.000 2.205


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Principal Component 1Accessibility to Regional Services

2,641,20,60,2

-0,2-0,6-1,2

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Municipal boundary

Body of water

Stream

Freeway

Regional shopping center

College or university

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Principal Component 2Accessibility to Local Services

9,1591,20,60,2

-0,2-0,6

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Municipal boundary

Body of water

Stream

Freeway

Highschool

Neighbourhood shopping center

Local shopping center

Primary school

Factor 1 (42% of total variance)

Factor 2 (34% of total variance)

Map 1: Factor Analysis on Access Attributes1st Principal Component

2nd Principal Component

Principal Component 11991 Census

1,2 to 2,94 (65)0,6 to 1,2 (129)0,2 to 0,6 (91)

-0,2 to 0,2 (57)-0,6 to -0,2 (59)-1,2 to -0,6 (115)-1,97 to -1,2 (88)


1,2 to 2,59 (81)0,6 to 1,2 (92)0,2 to 0,6 (58)

-0,2 to 0,2 (78)-0,6 to -0,2 (109)-1,2 to -0,6 (124)-2,57 to -1,2 (62)

Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Factor 1 (26% of total variance)Positive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidesmall size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),small size households (lone-persons, non family, lone-parent),few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,few children, very poor, generally tenant, move house frequently,high unemployment rates,high unemployment rates,high unemployment rates,high unemployment rates,high unemployment rates,high unemployment rates,high unemployment rates,high unemployment rates,high unemployment rates,living in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoodsliving in apartment in old neighbourhoods

Negative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sidelarge size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),large size households with many children (0-14 years),high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,high family income, owning single-family detached house,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,living in the same neighbourhood for a long time,low unemployment rates,low unemployment rates,low unemployment rates,low unemployment rates,low unemployment rates,low unemployment rates,low unemployment rates,low unemployment rates,low unemployment rates,living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960living in new suburbs built after 1960

Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Factor 2 (15% of total variance)Positive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidehighly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,highly educated population with generally high family income,low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),low unemployment rates among adults (25-64 years old),large houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent familieslarge houses, few lone-parent families

Negative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sidelow educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,low educated population with generally low family income,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,generally poor living in overpopulated houses,high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),high unemployment rates among adults (25-64 years old),many lone-parent familiesmany lone-parent familiesmany lone-parent familiesmany lone-parent familiesmany lone-parent familiesmany lone-parent familiesmany lone-parent familiesmany lone-parent familiesmany lone-parent families

Map 2: Factor Analysis on Census Attributes1st Principal Component

2nd Principal Component


1,2 to 1,63 (7)0,6 to 1,2 (81)0,2 to 0,6 (214)

-0,2 to 0,2 (175)-0,6 to -0,2 (63)-1,2 to -0,6 (27)-9,07 to -1,2 (37)


1,2 to 2,78 (74)0,6 to 1,2 (86)0,2 to 0,6 (80)

-0,2 to 0,2 (90)-0,6 to -0,2 (107)-1,2 to -0,6 (92)-2,46 to -1,2 (75)

Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)Factor 3 (13% of total variance)

Negative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sidehigh proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),high proportion of adults (more than 45 years old),living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in neighbourhoods built between 1946 and 1970,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,living in that neighbourhoods for a long time,less than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rateless than average gainfully employed rate

Positive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sideYoung family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),Young family with children (less than 14 years old),living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,living in newly created suburbs,relatively small houses,relatively small houses,relatively small houses,relatively small houses,relatively small houses,relatively small houses,relatively small houses,relatively small houses,relatively small houses,high proportion of double income familyhigh proportion of double income familyhigh proportion of double income familyhigh proportion of double income familyhigh proportion of double income familyhigh proportion of double income familyhigh proportion of double income familyhigh proportion of double income familyhigh proportion of double income family

Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)Factor 4 (13% of total variance)

Negative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideNegative sideretired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,retired persons households with many lone-people households,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,no children at home, living in high density neighbourhoods,few gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoplesfew gainfully-employed peoples

Positive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sidePositive sideFamily with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,Family with teenagers living in low density suburbs,many double income householdsmany double income householdsmany double income householdsmany double income householdsmany double income householdsmany double income householdsmany double income householdsmany double income householdsmany double income households

3rd Principal Component

4th Principal Component

Hedonic Model AResidual ($)

60 00040 00025 00010 000

-10 000-25 000-40 000

Hedonic Model BResiduals ($)

64 00040 00025 00010 000

-10 000-25 000-40 000

Map 3: Model ResidualsModel AModel AModel AModel AModel AModel AModel AModel AModel A

Model BModel BModel BModel BModel BModel BModel BModel BModel BHedonic Model BHedonic Model BHedonic Model BHedonic Model BHedonic Model BHedonic Model BHedonic Model BHedonic Model BHedonic Model BSale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Using Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean DistancesUsing Property Specifics & Eclidean Distances

Spatial Autocorrelation of ResidualsAmongs Pairs of Cottages located at less than 1 KmMoran’s I = 0.43648Probability < 0.0001

Hedonic Model AHedonic Model AHedonic Model AHedonic Model AHedonic Model AHedonic Model AHedonic Model AHedonic Model AHedonic Model ASale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Sale Price of Cottages sold between 1993 to 1996Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Prices from $50,000 to $250,000Using Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics OnlyUsing Property Specifics Only

Spatial Autocorrelation of ResidualsAmongs Pairs of Cottages located at less than 1 KmMoran’s I = 0.44838Probability < 0.0001

Negative residual: Model overestimate sale pricePositive residual: Model underestimate sale price

Negative residual: Model overestimate sale pricePositive residual: Model underestimate sale price

Documents

DOCUMENT DE TRAVAIL 1999-015 - FSA ULaval