Modification of Malinowski's F-test for abstract factor analysis applied to the Quail Roost II data sets
✍ Scribed by Klaas Faber; Bruce R. Kowalski
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 836 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0886-9383
No coin nor oath required. For personal study only.
✦ Synopsis
Determining the pseudorank of an experimental data matrix, i.e. the mathematical rank in absence of noise, is a fundamental problem in multivariate data analysis. The prime tool for performing this task is abstract factor analysis (AFA). 1 If an estimate of the noise variance is available one may simply estimate the pseudorank by investigating the size of the residuals of subsequent factor models (after correcting for loss of degrees of freedom). A more sophisticated method is to compare the singular values of the test matrix with the singular values of random matrices in a t-test. 2 In situations where a noise variance estimate is lacking chemometricians have primarily resorted to the factor indicator function 3 or cross-validation. 4 A drawback of these methods is that they do not provide a significance level for the resulting factor model. The latter problem is addressed by Malinowski's F-test 5,6 without losing the attractive characteristic of working without a noise variance estimate. This explains the popularity of Malinowski's Ftest and constitutes a definite advantage over, for instance, the t-test on the singular values.