Abstract factor analysis of data with multiple sources of error and a modified Faber–Kowalski f-test
✍ Scribed by Edmund R. Malinowski
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 82 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0886-9383
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✦ Synopsis
Chemical data gleaned from instrumental measurements, such as spectroscopy and chromatography, are often contaminated by multiple sources of error that vary during data collection. Abstract factor analysis (AFA) of such data invariably leads to an excessive number of factors. Various sources of experimental and instrumental artifacts that cause such errors are discussed. Model data, containing multiple sources of error, are created and factor analyzed. By appropriate truncation of the factor space, the number of chemical factors can be determined in these situations using the factor indicator function (IND), the Malinowski F-test and a modified Faber-Kowalski F-test. Infrared, ultraviolet and visible spectroscopic absorbance data are used to demonstrate the success of the method.
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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 si