The SMH Algorithm : An Heuristic for Structural Matrix Computation in the Partial Least Square Path Modeling

The Structural equations modeling with latent's variables (SEMLV) are a class of statistical methods for modeling the relationships between unobservable concepts called latent variables. In this type of model, each latent variable is described by a number of observable variables called manifest variables. The most used version of this category of statistical methods is the partial least square path modeling (PLS Path Modeling). In PLS Path Modeling, the specification of the relashonships between the unobservable concepts, knows as structural relationships, is the most important thing to know for practical purposes. In general, this specification is obtained manually using a lower triangular binary matrix. To obtain this lower triangular matrix, the modeler must put the latent variables in a very precise order, otherwise the matrix obtained will not be triangular inferior. Indeed, the construction of such a matrix only reflects the links of cause and effect between the latent variables. Thus, with each ordering of the latent variables corresponds a precise matrix. The real problem is that, the more the number of studied concepts increases, the more the search for a good order in which it is necessary to put the latent variables to obtain a lower triangular matrix becomes more and more tedious. For five concepts, the modeler must test 5! = 120 possibilities. However, in practice, it is easy to study more than ten variables, so that the manual search for an adequate order to obtain a lower triangular matrix extremely difficult work for the modeler. In this article, we propose an heuristic way to make possible an automatic computation of the structural matrix in order to avoid the usual manual specifications and related subsequent errors.