This is an interesting application of Path Analysis leveraging Richard Florida's findings regarding real estate valuations in different cities. This example serves as an introduction to Path Analysis.

1. Path Analysis Human Capital vs Homeownership Gaetan “Guy” Lion April 2009

3. The Rosetta Stone in Path Analysis With standardized variables within a single relationship the Correlation is equal to the Slope.

5. The Actual Correlations We embedded the correlations within the diagram. We also added a correlation directly from Human Capital to Home ownership. Most correlation signs support the hypothesis except Unemployment.

6. The Path Coefficients Given that the variables are standardized, all bivariate correlations already represent Path coefficients (in white). We’ll calculate the Path coefficients in yellow with a regression model. Dependent variable is Homeownership rate

7. Correlations vs Path Coefficients Correlations reflect the relationship between just two variables. The Path coefficients reflect the effect one variable has on another when controlled for the other three variables. Now the Path coefficient of Unemployment rate is negative.

8. Direct and Indirect Effects The Correlation of the independent variable can be decomposed into its Direct Effect and Indirect Effect on the dependent variable. The Causal Effect is the sum of the mentioned Effects and should equal the Correlation.

9. Human Capital Direct and Indirect Effects Human Capital causal effect (-0.176) on Homeownership equals its correlation.

11. Reconstructing correlations

12. Assessing closeness of fit with RMSE