Multivariate Modeling of Causal Dependencies

In the following we will meet causal models of increasing integration or complexity. In multiple regression we try to model the dependence of one variable, y, on several influencing variables, x. There are mathematical conditions for reliable estimation of the weights of the independent variables (estimation of regression coefficients)  

If the variables are correlated, the occurring problem of multicollinearity may be circumvented by performing a principal components calculation with the variables x. This will create independent ( orthogonal ) variables and one can continue the regression analysis using the scores (see Section 5.4) instead of the original x values. This method is known as principal components regression. 

on the other hand, the condition of error-free variables x is violated, one can use orthogonal estimation of the regression coefficients. 

If we extend the set of the dependent y variables from one to a number, variables de- 

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