Abstract
Many multivariate statistical models have dimensional structures. Such models typically require judicious choice of dimensionality. Likelihood ratio tests are often used for dimensionality selection. However, to this day there is still a great deal of confusion about the asymptotic distributional properties of the log-likelihood ratio (LR) statistics in some areas of psychometrics. Although in many cases the asymptotic distribution of the LR statistic representing the difference between the correct model (of specific dimensionality) and the saturated model is guaranteed to be chi-square, that of the LR statistic representing the difference between the correct model and the one with one dimension higher than the correct model is not likely to be chi-square due to a violation of one of regularity conditions. In this paper, we attempt to clarify the misunderstanding that the latter is also assured to be asymptotically chi-square. This common misunderstanding has occurred repeatedly in various fields, although in some areas it has been corrected.
| Original language | English |
|---|---|
| Title of host publication | Facets of Behaviormetrics |
| Subtitle of host publication | The 50th Anniversary of the Behaviormetric Society |
| Editors | Akinori Okada, Kazuo Shigemasu, Ryozo Yoshino, Satoru Yokoyama |
| Place of Publication | Singapore |
| Publisher | Springer |
| Pages | 219-241 |
| Edition | 1 |
| ISBN (Electronic) | 978-981-99-2240-6 |
| ISBN (Print) | 978-981-99-2239-0, 978-981-99-2242-0 |
| DOIs | |
| Publication status | Published - 17 Aug 2023 |
Keywords
- Asymptotic chi-square distribution
- Regularity conditions
- Canonical correlation analysis
- Models of contingency tables
- Multidimensional scaling
- Factor analysis
- Normal mixture models