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.

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

Författare

Nanny Wermuth

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Giovanni M. Marchetti

Johannes Gutenberg-Universität Mainz

Universita degli Studi di Firenze

Chalmers, Matematiska vetenskaper

Electronic Journal of Statistics

1935-7524 (ISSN)

Vol. 8 1 253-273

Ämneskategorier

Matematik

Sannolikhetsteori och statistik

DOI

10.1214/14-ejs884

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Senast uppdaterat

2018-12-06