Target testing, factor analysis

Varimax rotation is a commonly used and widely available factor rotation technique, but other methods have been proposed for interpreting factors from analytical chemistry data. We could rotate the axes in order that they align directly with factors from expected components. These axes, referred to as test vectors, would be physically significant in terms of interpretation and the rotation procedure is referred to as target transformation. Target transformation factor analysis has proved to be a valuable technique in chemo-metrics. The number of components in mixture spectra can be identified and the rotated factor loadings in terms of test data relating to standard, known spectra, can be interpreted. 

Malinowski, E.R., "Statistical F-Tests for Abstract Factor Analysis and Target Testing 1,/. Chemo. 1987 (1) 49-60... 

E.R. Malinowski, Statistical F-tests for abstract factor analysis and target testing. J. Chemom., 3 (1988)49-60. 

The basic idea of Target Factor Analysis is very simple. In order to test whether a certain compound is taking part in the process, whether its spectrum exists in the measurement, we test whether that spectrum lies in V. If such a test spectrum is outside V, there is no doubt that the component does not take part in the process under investigation. If it is in the subspace, we cannot positively conclude that the species is there the test spectrum could be a linear combination of the existing spectra. 

The applicability of Eq. (2.63) was tested for some 180 individual solutes (with up to 10 carbon atoms) and 25 dry solvents by stepwise multivariable Unear regression and for 28 solutes and 9 dry solvents by target factor analysis essentially the same conclusions and universal coefficients were obtained by both methods. As an example of the application of Eq. (2.63), the distribution of succinic acid between water and chloroform (a dry solvent with = 0.0048) and tri-n-butyl phosphate (a wet solvent with Xw = 0.497) may be cited [13]. 

Results For the St. Louis data, the target transformation analysis results for the fine fraction without July Uth and 5th are given in table 6. The presence of a motor vehicle source, a sulfur source, a soil or flyash source, a titanium source, and a zinc source are indicated. The sulfur, titanium and zinc factors were determined from the simple initial test vectors for those elements. The concentration of sulfur was not related to any other elements and represents a secondary sulfate aerosol resulting from the conversion of primary sulfur oxide emissions. Titanium was found to be associated with sulfur, calcium, iron, and barium. Rheingrover ( jt) identified the source of titanium as a paint-pigment factory located to the south of station 112. The zinc factor, associated with the elements chlorine, potassium, iron and lead, is attributed to refuse incinerator emissions. This factor could also represent particles from zinc and/or lead smelters, though a high chlorine concentration is usually associated with particles from refuse incinerators ( ). The sulfur concentration in the refined sulfate factor is consistent with that of ammonium sulfate. The calculated lead concentration in the motor vehicle factor of ten percent and a lead to bromine ratio of about 0.28 are typical of values reported in the literature (25). The concentration of lead in... 

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