1. Insight into apartment attributes and location with factors and principal components applying oblique rotation LET, Transport Economics Laboratory (CNRS, University of Lyon, ENTPE) 17 th Annual ERES conference, 2010, Milano, SDA Bocconi Alain Bonnafous Marko Kryvobokov Pierre-Yves Péguy

2. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 2 1. Introduction Methods not focusing on price as dependent variable – an alternative or a complement to hedonic regression: Factor Analysis (FA) Principal Component Analysis (PCA) Others…

3. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 3 1. Introduction Two ways of PCA application in a hedonic price model: PCA + clustering (submarkets) => hedonic price model Example: Bourassa et al. (2003): - citywide hedonic model with dummies for submarkets - hedonic models in each submarket - the best result: clusters based on the first two components load heavily on locational variables PCA (data reduction) => hedonic price model Des Rosiers et al. (2000): principal components are substitutes for initial variables

4. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 4 1. Introduction Selection of the methodology based on the aim (Fabrigar et al., 1999): FA (explains variability existing due to common factors) – for identification of latent constructs underlying the variables (structure detection) PCA (explains all variability in the variables) – for data reduction

5. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 5 1. Introduction Selection of the rotation method (Fabrigar et al., 1999): Methodological literature suggests little justification for using orthogonal rotation Orthogonal rotation can be reasonable only if the oblique rotation indicates that factors are uncorrelated

6. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 6 1. Introduction Aim 1: identification of latent construct underlying our variables with FA Aim 2: data reduction with PCA Rotation: oblique (non-orthogonal)

7. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 7 2. Data preparation Location of apartments: central part of the Lyon Urban Area

8. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 8 2. Data preparation Lyon

9. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 9 2. Data preparation 4,251 apartment sales 1997-2008 Location data for IRIS (îlots regroupés pour l'information statistique) Count variables as continuous variables Categorical variables as continuous variables (Kolenikov and Angeles, 2004) Skew < 2 Kurtosis < 7 (West et al., 1995)

10. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 10 2. Data preparation DescriptionMeanMinimumMaximum Std. deviation SkewKurtosis Transaction price, Euros122,235.9020,276.00500,000.0069,979.671.452.93 Count for year of transaction6.871122.87-0.10-0.88 Apartment area, square metres68.631819625.980.781.51 Number of rooms3.05181.190.26-0.18 Floor2.840182.251.353.85 Construction period5.12171.75-0.50-0.73 State of apartment2.79130.47-2.143.87 Number of cellars0.69020.50-0.43-0.88 Descriptive statistics of apartment variables

11. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 11 2. Data preparation Descriptive statistics of location variables DescriptionMeanMinimumMaximum Std. deviation SkewKurtosis Percentage of low income households 29.4210.2452.125.78-0.10-0.05 Percentage of high income households 12.584.3428.772.920.510.68 Travel time to Stalingrad11.311.4124.434.850.43-0.25 Travel time to Louis Pradel11.182.2229.365.350.620.01 Travel time to Bellecour-Sala10.990.4531.284.960.890.79 Travel time to Jussieu10.440.4530.365.180.720.01 Travel time to Charles Hernu11.190.4526.175.370.35-0.66 Travel time to Les Belges11.000.4527.485.340.49-0.44 Travel time to Villette Gare10.680.4529.255.350.37-0.81 Travel time to Part-Dieu10.620.4529.365.240.46-0.71 Travel times are calculated with the MOSART transportation model for the a.m. peak period, public transport by Nicolas Ovtracht and Valérie Thiebaut

12. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 12 3. Factor analysis Principal axes factoring – the most widely used method (Warner, 2007) The standard method of non-orthogonal rotation – direct oblimin Of 8 apartment variables, 5 are included Of 15 variables of travel times, 8 are included 4 factors with Eigenvalues > 1 Correlation between Factor 1 and Factor 4 is -0.52 (the choice of non-orthogonal rotation is right) Continuous representation: interpolation of factor scores to raster

13. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 13 3. Factor analysis Communalities and factor loadings VariableCommunality Factors Structure matrixPattern matrix 12341234 Price0.56 -0.180.86-0.08-0.05 -0.120.86-0.12<0.01 Area0.53 0.030.820.07-0.13 0.100.830.040.02 Construction period0.34 0.080.04-0.78-0.13 0.010.06-0.77-0.08 Condition0.14 0.020.08-0.40-0.04 <0.010.09-0.41-0.01 Cellars0.18 0.040.180.37-0.12 0.010.140.36-0.11 % low income households0.85 -0.49-0.120.010.93 -0.01<-0.01-0.040.93 % high income households0.86 0.500.10-0.02-0.94 0.03-0.010.03-0.93 Travel time to Bellecour-Sala0.96 0.68-0.07-0.22-0.60 0.49-0.07-0.18-0.34 Travel time to Les Belges0.98 0.95-0.12-0.15-0.48 0.95-0.05-0.100.01 Travel time to Jussieu0.99 0.94-0.09-0.17-0.63 0.82-0.05-0.12-0.20 Travel time to Part-Dieu0.99 0.95-0.020.04-0.54 0.920.030.09-0.07 Travel time to Louis Pradel0.98 0.87-0.14-0.28-0.55 0.77-0.09-0.23-0.15 Travel time to Charles Hernu0.98 0.93-0.040.06-0.41 >0.990.040.100.11 Travel time to Villette Gare0.99 0.91-0.000.09-0.52 0.900.050.14-0.05 Travel time to Stalingrad0.96 0.88-0.07-0.00-0.37 0.950.010.040.12

14. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 14 3. Factor analysis Raster map of Factor 1: high income households farther from centres

15. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 15 3. Factor analysis Raster map of Factor 4: low income households closer to centres

16. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 16 3. Factor analysis Raster map of Factor 2: big and expensive apartments

17. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 17 3. Factor analysis Raster map of Factor 3: older apartments in bad condition

18. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 18 4. PCA of location attributes Data reduction: - two variables for income groups - 15 variables of travel times to centres Direct oblimin rotation 3 principal components with Eigenvalues > 1 Correlation between Principal Components are 0.54, -0.50 and -0.32 (the choice of non-orthogonal rotation is right) Continuous representation

19. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 19 4. PCA of location attributes Raster map of Principal Component 1: centres of Lyon

20. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 20 4. PCA of location attributes Raster map of Principal Component 2: centres of Villeurbanne

21. 17 th Annual ERES conference, 2010, Milano, SDA Bocconi 21 5. Conclusion and perspective Oblique rotation is found to be applicable for real estate data The results are intuitively easy to interpret Separate factors are formed for apartment attributes and location Factor 4 highlights the existence of a problematic low income area in the central part of Lyon (similarly to the finding of Des Rosier et al. (2000) in the Quebec Urban Community) With PCA a more complex spatial structure is detected Perspective: clusters of factors/principal components as proxies of apartment submarkets?