Star graphs induce tetrad correlations: for Gaussian as well as for binary variables
Journal article, 2014
Tetrad correlations were obtained historically for Gaussian distributions when tasks are designed to measure an ability or attitude so that a single unobserved variable may generate the observed, linearly increasing dependences among the tasks. We connect such generating processes to a particular type of directed graph, the star graph, and to the notion of traceable regressions. Tetrad correlation conditions for the existence of a single latent variable are derived. These are needed for positive dependences not only in joint Gaussian but also in joint binary distributions. Three applications with binary items are given.
REGRESSIONS
ASSOCIATION
MODELS
item response models
graphical Markov models
SEQUENCES
P157
MPSTER AP
BIOMETRICS
Directed star graph
SYSTEMS
1972
latent class models
factor analysis
traceablereg ression
LIKELIHOOD
IDENTIFICATION
V28
Author
Nanny Wermuth
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Giovanni M. Marchetti
Johannes Gutenberg University Mainz
University of Florence
Chalmers, Mathematical Sciences
Electronic Journal of Statistics
1935-7524 (ISSN)
Vol. 8 1 253-273Subject Categories (SSIF 2011)
Mathematics
Probability Theory and Statistics
DOI
10.1214/14-ejs884