Partial Identification of Latent Correlations with Binary Data

Steffen Grønneberg (), Jonas Moss () and Njål Foldnes ()
Additional contact information
Steffen Grønneberg: BI Norwegian Business School
Jonas Moss: University of Oslo
Njål Foldnes: BI Norwegian Business School

Psychometrika, 2020, vol. 85, issue 4, No 12, 1028-1051

Abstract: Abstract The tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector. However, when the underlying vector is not normal, the tetrachoric correlation will be different from the underlying correlation. Since assuming underlying normality is often done on pragmatic and not substantial grounds, the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling. This motivates studying the range of latent correlations that are compatible with given binary data, when the distribution of the latent vector is partly or completely unknown. We show that nothing can be said about the latent correlations unless we know more than what can be derived from the data. We identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known. Also, we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations. Implications for tests of underlying normality are briefly discussed.

Keywords: tetrachoric correlation; partial identification; model formulation; factor analysis (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11336-020-09737-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:85:y:2020:i:4:d:10.1007_s11336-020-09737-y

Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2

DOI: 10.1007/s11336-020-09737-y

Access Statistics for this article

Psychometrika is currently edited by Irini Moustaki

More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().