Star graphs induce tetrad correlations: for Gaussian as well as for binary variables. (English) Zbl 1293.62029
Summary: 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.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 62H17 | Contingency tables |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
Keywords:
directed star graph; factor analysis; graphical Markov models; item response models; latent class models; traceable regressionReferences:
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