Path Analysis (statistics) - Path Tracing Rules

Path Tracing Rules

In order to validly calculate the relationship between any two boxes in the diagram, Wright (1934) proposed a simple set of path tracing rules, for calculating the correlation between two variables. The correlation is equal to the sum of the contribution of all the pathways through which the two variables are connected. The strength of each of these contributing pathways is calculated as the product of the path-coefficients along that pathway.

The rules for path tracing are:

1. You can trace backward up an arrow and then forward along the next, or forwards from one variable to the other, but never forward and then back.
2. You can pass through each variable only once in a given chain of paths.
3. No more than one bi-directional arrow can be included in each path-chain.

Another way to think of rule one is that you can never pass out of one arrow head and into another arrowhead: heads-tails, or tails-heads, not heads-heads.

Again, the expected correlation due to each chain traced between two variables is the product of the standardized path coefficients, and the total expected correlation between two variables is the sum of these contributing path-chains.

NB: Wright's rules assume a model without feedback loops: the directed graph of the model must contain no cycles.