In this work, we studied 28 commercial Virginia and US blends described using various thematic variable groups. Our purpose was to explore the possibility of an explanatory linear model connecting structural dimensions of these groups. A group containing 14 smoke Hoffmann constituents is assumed to depend on 29 chemical tobacco variables, 10 product physical variables, and 4 major smoke compounds (Tar, Nicotine, Carbon monoxide, Water). To solve this problem, we used a multi-array exploration technique: Structural Equation Exploratory Regression (SEER). The purpose of SEER is related to that of more classical methods such as PLS Path Modeling, Multi-block PLS and LISREL (References). But there are fundamental differences in approach and computation. SEER is carried out as described below. First, one must define a thematic partitioning of explanatory variables. This partition is generally based on expert knowledge; yet, in practice, one may start with a basic conceptual model (for example chemical, physical and TCN) and refine it gradually by taking into account the empirical findings provided by former SEER-estimations (we have chosen this latter attitude to illustrate the flexibility of SEER). Second, one uses a multiple covariance criterion extending that of PLS regression to simultaneously extract a small number of structural dimensions in thematic groups (for the sake of robustness) and investigate the linear model linking them. The use of a model that does not compel structural dimensions to be orthogonal between themes allows better use of the conceptual and statistical complementarity of groups, yielding a more realistic and interpretable model than PLSR. A series of graphics help interpret the model, and classical goodness of fit indicators help validate it.