Our aim is to explore a structural model: several variable groups describing the same units are assumed to be structured around latent dimensions that are linked together through a linear model that may have several equations. This type of model is commonly dealt with by methods assuming that the latent dimension in each group is unique. However, conceptual models generally link concepts that are multidimensional. We first propose a general class of criteria suitable to measure the quality of a Structural Equation Model. This class contains the covariance criteria used in PLS Regression methods and the Multiple Covariance criterion of the SEER method. All criteria in the class must be maximized under a unit norm constraint. This maximization is used within a general algorithm named THEME (Thematic Equation Model Exploration), which allows us to extend the multiple covariance criterion in two ways:1) The criterion is generalized so as to take into account the structural strength of a component in a more flexible way, including multiple covariance, but also variable-bundle-oriented measures,2) It is also extended to models having any number of dependent / predictor groups.

We have applied THEME to model the production of Hoffmann compounds from 52 physical and chemical variables describing 19 cigarettes. The variables were partitioned into 7 thematic groups, linked through 2 equations structural model. Equation 1 models Hoffmann compounds smoke contents under intense smoking from the characteristics of the cigarette (combustion process), and equation 2 models Hoffmann compounds smoke contents under ISO smoking regime from those under intense smoking regime and characteristics of filter under ISO smoking conditions (Filter ventilation process). THEME allowed us to separate the complementary roles, on Hoffmann compounds, of: tobacco quality, tobacco type, combustion chemical enhancers or inhibitors, filter retention and ventilation powers. It yielded a complete and robust model having accuracy within reproducibility limits.