Pierre Cazes

THEME-SEER: a multidimensional exploratory technique to analyze a structural model using an extended covariance criterion

In this work, we present a new approach to path modeling based on an extended multiple covariance criterion: system extended multiple covariance (SEMC). SEMC is suitable to measure the quality of any structural equations system. We show why SEMC may be preferred to criteria based on usual covariance of components and also to criteria based on residual sums of squares. We give a pursuit algorithm ensuring that SEMC increases and converges. When one wishes to extract more than one component per variable group, a problem arises of component hierarchy. To solve it, we define a local nesting principle of component models that makes the role of each component statistically clear. We then embed the pursuit algorithm in a more general algorithm that extracts sequences of locally nested models. We finally provide a component backward selection strategy. The technique is applied to cigarette data to model the generation of chemical compounds in smoke through tobacco combustion. Copyright

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 experts 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.