PART 4 ORDINAL-SCALE DATA

Another important feature of mathematical modeling techniques is the nature of the response data that they are capable of handling. Some methods are designed to work with data that are measured on a nominal or ordinal scale this means the results are divided into two or more classes that may bear some relation to one another. Male and female, dead and alive, and aromatic and nonaromatic, are all classifications (dichotomous in this case) based on a nominal scale. Toxic, slightly toxic, and non-toxic are classifications based on an ordinal scale since they can be written as toxic > slightly toxic > non-toxic. The rest of this section is divided into three parts methods that deal with classified responses, methods that handle continuous data, and artificial neural networks that can be used for both. 

An experimental demonstration is depicted in Fig. 8 for the v mode of neat bromochloromethane (45). Part of the data of Fig. 5b are replotted in Fig. 8a with an enlarged ordinate scale. We recall that the anisotropic component (dotted line in Fig. 5b) is negligible for the special case here,... 

Even superficial inspection of the three sets of data reported in Fig. 11 (note that the ordinate scales of parts (a) and (c) of Fig. 11 differ by one order of magnitude) demonstrates the dramatic decrease of the surface coverages of both hydride and hydroxyl groups formed upon H2 adsorption on samples having decreasing surface areas. The reduction of the density of surface defects as the surface area decreases is thus evident. On the smoke MgO sample, only the bands characterizing molecularly... 

Figure 4. Dielectric loss data of I, l -di(4-methoxy-5-methyl phenyl (cyclohexane (BMMPC) at various combinations of temperature and pressure as indicated to demonstrate the invariance of the dispersion of the a-relaxation at constant a-loss peak frequency or equivalently at constant a-relaxation time The dashed line is the imaginary part of the one-sided Fourier transform of the KWW function with Pkww — (I n) — 0.55. The logarithmic ordinate scale makes evident the presence of an excess wing at higher frequencies.

Figure 4.7. Cubic susceptibility, real part. Comparison with the experiment [64] for the frequencies 30 Hz (a), 80 Hz (b), 220 Hz (c), 840 Hz (d). The line drawing convention is the same as in Figure 6. The vertical scale (ordinate) coincides with the one adopted in Refs. 64 and 65 for the experimental data.

Fig. 5.37 Plot of the spin polarization of the tunneling current at bias voltages that correspond to the binding energies of the majority and minority part of the Gd(OOOl) surface state (the ordinate is on a logarithmic scale) as obtained by measuring the same sample in three subsequent scans during a time period of approximately 24 h. The data points marked 1, 2, and 3 denote three different locations of the sample. Apparently, the spin polarization decreases with time eltqtsed from surface preparation (reprinted with permission from [131]. Copyright 1999, American Institute of Physics)...

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