Exploring a physico-chemical multi-array explanatory model with a new multiple covariance-based technique: Structural equation exploratory regression

In this work, we consider chemical and physical variable groups describing a common set of observations (cigarettes). One of the groups, minor smoke compounds (minSC), is assumed to depend on the others (minSC predictors). PLS regression (PLSR) of m inSC on the set of all predictors appears not to lead to a satisfactory analytic model, because it does not take into account the expert's knowledge. PLS path modeling (PLSPM) does not use the multidimensional structure of predictor groups. Indeed, the expert needs to separate the influence of several pre-designed predictor groups on minSC, in order to see what dimensions this influence involves. To meet these needs, we consider a multi-group component-regression model, and propose a method to extract from each group several strong uncorrelated components that fit the model. Estimation is based on a global multiple covariance criterion, used in combination with an appropriate nesting approach. Compared to PLSR and PLSPM, the structural equation exploratory regression (SEER) we propose fully uses predictor group complementarity, both conceptually and statistically, to predict the dependent group.