Simultaneous Equations and Path Analysis

Within the framework of this short introduction to essential methods it is not possible to present all the basic details of path analysis. The interested reader will find details in the books of KMENTA [1971], MARDIA et al. [1979], or JOHNSON and WICHERN [1982]. GELADI [1988] mentioned early applications of PLS (see Section 5.7.2) as a path modeling device. The principle and the advantages are indicated in the introduction to the Section 5.7. 

The path diagram marks the correlations of all primary independent variables and their assumed causal influence on other independent variables and on dependent variables. In addition, all relationships between dependent variables are indicated. 

There are some mathematical conditions to be met the number of paths leading to each resulting variable must not exceed the number of equations if the numbers are equal the system is exactly determined and computational (numerical ) problems should be minimal. 

This step ensures the comparability of all variables. In the following step the calculation of the correlation matrix is simplified. 

The path coeffcients are standardized regression coefficients and are, therefore, directly comparable. 

---