The statistical modelling and the analysis of multivariate data typically deal with complex association structures due to various direct and indirect relations among variables. The idea of graphical models is to represent the independence structure of a multivariate random vector by a graph where the vertices correspond to the variables and the absence of an edge between vertices stands for conditional or marginal independences. In many applications some dependency structure between observed variables can be explained by supposing that their distribution arises after marginalizing over, and/or conditioning on, hidden or latent variables. This approach is reasonable if something is known about the generating process. In this work is shown the mathematical structure of a directed acyclic graph with one latent variable for Gaussian systems or quasi linear systems with continuous variables. Such models can be interpreted as a set of recursive univariate regressions and, for identifiable models, it is shown how the likelihood can be maximized using the EM algorithm.

Pennoni, F. (2003). Research hypothesis on the latent structure of data in the social sciences through conditional independence models. In Conference Proceedings 2003 Annual Research Students’ Conference in Probability and Statistics (pp.46-46).

### Research hypothesis on the latent structure of data in the social sciences through conditional independence models

#### Abstract

The statistical modelling and the analysis of multivariate data typically deal with complex association structures due to various direct and indirect relations among variables. The idea of graphical models is to represent the independence structure of a multivariate random vector by a graph where the vertices correspond to the variables and the absence of an edge between vertices stands for conditional or marginal independences. In many applications some dependency structure between observed variables can be explained by supposing that their distribution arises after marginalizing over, and/or conditioning on, hidden or latent variables. This approach is reasonable if something is known about the generating process. In this work is shown the mathematical structure of a directed acyclic graph with one latent variable for Gaussian systems or quasi linear systems with continuous variables. Such models can be interpreted as a set of recursive univariate regressions and, for identifiable models, it is shown how the likelihood can be maximized using the EM algorithm.
##### Scheda breve Scheda completa Scheda completa (DC) abstract + slide
Conditional independence graph models; latent variables; directed acyclic graph models with one latent variable; identifiability; EM algorithm
English
the Annual Research Students’ Conference in Probability and Statistics
2003
Conference Proceedings 2003 Annual Research Students’ Conference in Probability and Statistics
2003
46
46
none
Pennoni, F. (2003). Research hypothesis on the latent structure of data in the social sciences through conditional independence models. In Conference Proceedings 2003 Annual Research Students’ Conference in Probability and Statistics (pp.46-46).
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/53107`
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