Shiers, N. L., Zwiernik, Piotr, Aston, John A. D. and Smith, J. Q. (2016) The correlation space of Gaussian latent tree models and model selection without fitting. Biometrika, 103 (3). pp. 531-545. doi:10.1093/biomet/asw032

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Abstract

We provide a complete description of possible distributions consistent with any Gaussian latent tree model. This description consists of polynomial equations and inequalities involving covariances between the observed variables. Testing inequality constraints can be done using the inverse Wishart distribution and this leads to simple preliminary assessment of tree-compatibility. To test equality constraints we employ general techniques of tetrad analyses. This approach is effective even for small sample sizes and can be easily adjusted to test either entire models or just particular macrostructures of a tree. Our methods are simple to implement and do not require fitting of the model. The versatility of the techniques is illustrated by performing exploratory and confirmatory tetrad analyses in linguistic and biological settings respectively.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Gaussian distribution, Latent variables
Journal or Publication Title:	Biometrika
Publisher:	Oxford University Press
ISSN:	0006-3444
Official Date:	August 2016
Dates:	Date Event August 2016 Published 24 August 2016 Available 3 June 2016 Accepted
Date of first compliant deposit:	28 July 2016
Volume:	103
Number:	3
Page Range:	pp. 531-545
DOI:	10.1093/biomet/asw032
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID ES/I90427/1 Economic and Social Research Council http://dx.doi.org/10.13039/501100000269 EP/K021672/2 Economic and Social Research Council http://dx.doi.org/10.13039/501100000269 PIOF-GA-2011-300975 Seventh Framework Programme http://dx.doi.org/10.13039/100011102
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