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LET, Transport Economics Laboratory (CNRS, University of Lyon, ENTPE)

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

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LET, Transport Economics Laboratory (CNRS, University of Lyon, ENTPE)

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

  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. 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. 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. 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. 1. Introduction • Aim 1: identification of latent construct underlying our variables with FA • Aim 2: data reduction with PCA • Rotation: oblique (non-orthogonal)

  7. 2. Data preparation Location of apartments: central part of the Lyon Urban Area

  8. 2. Data preparation Lyon

  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. 2. Data preparation Descriptive statistics of apartment variables

  11. 2. Data preparation Descriptive statistics of location variables Travel times are calculated with the MOSART transportation model for the a.m. peak period, public transport by Nicolas Ovtracht and Valérie Thiebaut

  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. 3. Factor analysis Communalities and factor loadings

  14. 3. Factor analysis Raster map of Factor 1: high income households farther from centres

  15. 3. Factor analysis Raster map of Factor 4: low income households closer to centres

  16. 3. Factor analysis Raster map of Factor 2: big and expensive apartments

  17. 3. Factor analysis Raster map of Factor 3: older apartments in bad condition

  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. 4. PCA of location attributes Raster map of Principal Component 1: centres of Lyon

  20. 4. PCA of location attributes Raster map of Principal Component 2: centres of Villeurbanne

  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?

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