Path Analysis: Tracing Rules and Re-Deriving Correlation Coefficients

Below are two photos from the recent lectures on path analysis (thanks again to Sothy). The first photo is more conceptual, on how to identify the relevant sequences for multiplying path coefficients.

One of our 2015 students (BL), came up with a great analogy to understand correlated cause (lower-right corner of photo). W and Y can be thought of as the two parents in a family, and X and Z as the two children. If parent W influences child X, and parent Y influences child Z, then X and Z will receive some of the same influence because the two parents' childrearing practices are likely correlated (path q).

The second photo shows an actual example.

Because the model was saturated (every possible linkage that could have been included, was included), the correlation between Age and Income implied by the tracings in the model is identical (within rounding) to the known, input correlation between Age and Income.

MARCH 2013 UPDATE: This manuscript provides an overview of tracing rules (see Section 2.4).

MAY 2009 UPDATE: A newly released Australian study indeed shows a positive relationship between height and earnings.