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The aim of this paper is to recall the foundations of SIA theory and modify these slightly in order to clarify and reinforce them, as well as make them more adaptable to various scientific models. Some issues regarding one of the founding blocks of SIA, the implicative intensity, are discussed and detailed. This paper is composed of two mostly separable sections. The first half of this paper focuses on a generalization of SIA so that known differences between individuals, which we shall refer to as multiple behaviors, can be taken into account in an analysis. The second half focuses on two issues related to the implicative intensity, the second of which being the well-known issue raised by large numbers of individuals in SIA data sets. [ABSTRACT FROM AUTHOR]

In this paper, we use the generalized SIA distributions developed in Delacroix (2013) with the model described in Delacroix and Boubekki (2012). The aim is to develop an analysis based on SIA theory which allows a researcher in social sciences to suppress uninteresting pseudo-implications a priori in the analysis. More precisely, we look at relations between the success of students to the different questions in an exam, while taking into account a notion of student level in a multiple behavior analysis. [ABSTRACT FROM AUTHOR]