Maximum Likelihood Estimation of the Polychoric Correlation Coefficient

Olsson, Ulf

doi:10.1007/bf02296207

Cited by 1,127Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Methods and Applications

Maximum Likelihood Estimation of the Polychoric Correlation Coefficient

Olsson, Ulf·1979·Psychometrika

DOI 10.1007/bf02296207

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Abstract

The polychoric correlation is discussed as a generalization of the tetrachoric correlation coefficient to more than two classes. Two estimation methods are discussed: Maximum likelihood estimation, and what may be called “two-step maximum likelihood” estimation. For the latter method, the thresholds are estimated in the first step. For both methods, asymptotic covariance matrices for estimates are derived, and the methods are illustrated and compared with artificial and real data.

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The two questionnaire variables (MeDown and MeMirror) were combined using Polychoric PCA, which accounts for the ordinal nature of the variables.
“The two questionnaire variables (MeDown and MeMirror) were combined using Polychoric PCA26 which is a method that specifically accounts for the fact that the variables being combined are ordinal.”
From Conversations between self and self as Sigmund Freud—A virtual body ownership paradigm for self counselling (2015) · cites this paper as [26]

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Authors: Olsson, U.
Affiliations: Uppsala University (SE)
Corresponding author: Olsson, Ulf
Venue: Psychometrika
Publisher: Cambridge University Press (CUP)
Published: 1979-12
Volume: 44
Issue: 4
Pages: 443-460
ISSN: 0033-3123 (ISSN-L)
1860-0980
DOI: 10.1007/bf02296207
OpenAlex: W1996467017
Cited by: 1,127
References: 17
Citations by year: 2026: 45 · 2025: 53 · 2024: 33 · 2023: 43 · 2022: 47 · 2021: 58 · 2020: 58 · 2019: 48 · 2018: 41 · 2017: 48 · 2016: 48 · 2015: 54 · 2014: 58 · 2013: 30 · 2012: 45
FWCI: 2.55
Type: journal article
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified, 16468 d)
Locations: Psychometrika (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: polychoric correlation, tetrachoric correlation, maximum likelihood estimation, threshold estimation, asymptotic covariance matrix, categorical data, latent variable models

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Maximum Likelihood Estimation of the Polychoric Correlation Coefficient

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