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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.00716 |
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| _version_ | 1866913565291577344 |
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| author | Liu, Yang Pek, Jolynn Maydeu-Olivares, Alberto |
| author_facet | Liu, Yang Pek, Jolynn Maydeu-Olivares, Alberto |
| contents | Reliability is an essential measure of how closely observed scores represent latent scores (reflecting constructs), assuming some latent variable measurement model. We present a general theoretical framework of reliability, placing emphasis on measuring the association between latent and observed scores. This framework was inspired by McDonald's (2011) regression framework, which highlighted the coefficient of determination as a measure of reliability. We extend McDonald's (2011) framework beyond coefficients of determination and introduce four desiderata for reliability measures (estimability, normalization, symmetry, and invariance). We also present theoretical examples to illustrate distinct measures of reliability and report on a numerical study that demonstrates the behavior of different reliability measures. We conclude with a discussion on the use of reliability coefficients and outline future avenues of research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a General Theoretical Framework of Reliability Liu, Yang Pek, Jolynn Maydeu-Olivares, Alberto Methodology Reliability is an essential measure of how closely observed scores represent latent scores (reflecting constructs), assuming some latent variable measurement model. We present a general theoretical framework of reliability, placing emphasis on measuring the association between latent and observed scores. This framework was inspired by McDonald's (2011) regression framework, which highlighted the coefficient of determination as a measure of reliability. We extend McDonald's (2011) framework beyond coefficients of determination and introduce four desiderata for reliability measures (estimability, normalization, symmetry, and invariance). We also present theoretical examples to illustrate distinct measures of reliability and report on a numerical study that demonstrates the behavior of different reliability measures. We conclude with a discussion on the use of reliability coefficients and outline future avenues of research. |
| title | On a General Theoretical Framework of Reliability |
| topic | Methodology |
| url | https://arxiv.org/abs/2407.00716 |