Why outer weights change when we add new path ?

[Lanfranchi]

Hello,


could you explain why the outer weights change when we add a new path in the model ?

I have read Tenenhaus, Vinzi et al. (2005) and Chin and Marcolin (1995), but i don't understand when and how a exogenous latent variable and her indicators are affected by a new endogenous variable.

Thank you for your answer.

[jmbecker]

You have an iterative two-step estimation process of the LV scores (outer/inner approximation) till convergence of the weights. Basically the process looks like this:

Step 0: Initial outside approximation

Step 1: Inner weights approximation
Step 2: Inside approximation

Step 3: Outer weights approximation
Step 4: Outside approximation

Repeat from Step 1, until "stop criterion" fulfilled? (i.e. marginal/no change in outer weights)

The inner weights calculation depends on the chosen mode (i.e. the centroid, factor, or path weighting scheme). However, for the inside approximation you use every connected LV. Only in path weighting scheme the way the weights are computed is affected by whether it’s a predecessor or successor, nevertheless you still use every connected LV.
Therefore adding a connecting between LVs affected their inside approximation. The inside approximation is then used to calculate the outer weights, that’s why a new path in the model also effect the outer weights.

Hopefully this will clarify the situation.

[Lanfranchi]

Thanks a lot. After to have tried to calculate the weights on a small example (with Statistica and good SD ! ;)), i have understood the logic of PLS model.