Star graphs induce tetrad correlations: for Gaussian as well as for binary variables
Artikel i vetenskaplig tidskrift, 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.

traceablereg ression

V28

P157

MPSTER AP

SYSTEMS

IDENTIFICATION

LIKELIHOOD

graphical Markov models

factor analysis

BIOMETRICS

latent class models

Directed star graph

REGRESSIONS

1972

SEQUENCES

ASSOCIATION

MODELS

item response models

Författare

Nanny Wermuth

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

G. M. Marchetti

Chalmers

Universita degli Studi di Firenze

Johannes Gutenberg-Universität Mainz

Electronic Journal of Statistics

1935-7524 (ISSN)

Vol. 8 1 253-273

Ämneskategorier

Matematik

Sannolikhetsteori och statistik

DOI

10.1214/14-ejs884