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On the Notion of Latent Structure in the Statistical Reasoning Process

Last modified: 2013-06-14

#### Abstract

Latent variables are considered in the framework of the more general notion of Latent Structures ,which encompasses a wider range of statistical methods including, for instance, loglinear models for contingency tables. A distinction is made between “ontic” and “epistemic” approaches. In the former case, a latent structure is assumed to exist and appropriate statistical set-ups and techniques of analysis are devised for detecting it. This may imply , for instance , the observation of more complex “manifest “ data structures, such as three –way arrays ,allowing us to uniquely single out underlying “factors” .In the “epistemic” perspective, the search for a latent structure constitutes a way for “explaining” some features of the total variation of observed variables. Epistemological and methodological implications of the above distinction are discussed with reference to different observational set-ups, according to the nature of manifest variables and the complexity of data structures. The role of basic assumptions, such as probabilistic formalization of data or adoption of characterizing properties like “local independence”, “simple structure” etc., is also investigated in this context.

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