The author (P. J. Lewi), who in 1974 had a strong interest in scientific computing, obtained a computer program of Correspondence Analysis (CA) with the help of IBM and a group of French statisticians. The program was written in APL, an interactive mathematical programming language designed by Kenneth Iverson.
After some reverse engineering it appeared that Correspondence Analysis was quite capable of solving the “size and shape” problem and produce a classification of the profiles of the compounds in terms of the various tests performed on them. As an extra bonus it also produced a classification of the profiles of the tests performed in terms of the various compounds submitted to them. The two entities, compounds and tests, could be represented in a biplot spanned by the two most important factors.
The inconvenience of the method was that it could only be applied to the raw ED50 values, and not to their logarithms.
This greatly distorted the patterns of compounds and tests on the biplot. Logarithms are fundamental in the study physical and biological phenomena, as many scales of measurement are defined on ratio scales. This means that computing ratios between measurements is more relevant than determining arithmetic differences. Pharmacologists often say that a given new compound is so many times more potent or less potent than a particular reference compound. Furthermore, many physical and biophysical laws are linear in their terms after taking logarithms, as exemplified by the law of gravitation, the law of perfect gases, and many more.
After some reflection it became evident that after taking logarithms from the data, the size component could be removed by subtracting the corresponding marginal row- and column-means (double-centering of the logarithms). This is equivalent to dividing the data by the corresponding marginal row- and column-totals in Correspondence Analysis (double-closure of the counts).
The approach of log double-centering followed by factorial analysis and biplot mapping was called Spectral Mapping. When weighting by the row-and column-totals of the original table is applied, Spectral Mapping differs only from Correspondence Analysis by the type of preprocessing of the data (log double-centering versus double-closure). It can be proved that when the differences between profiles (contrasts) are not very large, the biplots from both methods are very similar. A formal description of Spectral Mapping is that of a weighted Principal Components Analysis (PCA) of log double-centered data.
The figure shows the spectral map of 45 neuroleptic (antipsychotic) compounds in three selected test in rats. The three tests have been selected on the basis of an analysis of the complete battery of 12 pharmacologic tests, which is discussed further down. The three tests are specific for three important neurotransmitters (messenger substances) in the brain, namely dopamine, norepinephrine (adrenaline) and serotonin. These form the three poles (vertices) of a triangular diagram. (The pharmacological effects of apomorphine and tryptamine in rat are related to those of dopamine and serotonin, respectively.) Each of the three (bipolar) axes that join the poles of the diagram represents a particular ratio between the corresponding pharmacological tests. A triangular spectral map, such as the one shown here, always reproduces 100 % of the information from the three ratios.
The figure was produced by the program Spectramap designed by the author (P. J. Lewi) and Jul Van Hoof from data published by Paul A. J. Janssen et al. (1965). (Spectramap is a trade name owned by Coloritto BV.)
More recently Michael Greenacre has studied the mathematical and statistical properties and has shown that Spectral Map Analysis (SMA) is equivalent to analyzing the log-ratios of the data. For this reason he proposed the term Log-Ratio Analysis (LRA), as an alternative term for Spectral Mapping.
In what follows we discuss the spectral map of the neuroleptic compounds in the complete battery of 12 pharmacological tests in rats.
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