4. The FFR experiment and results
4.5 Modeling phase – feature-extracting module
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4.5 Modeling phase – feature-extracting module
Without loss of generalization, the clustering result of the GHSOM is used to illustrate the operation of a feature-extraction stage and we demonstrate the features of each leaf node of FT. The leaf node #12-24 is excluded due to having only one sample.
For each leaf node of the GHSOM, values of the eight significant variables regarding all clustered samples are the inputs of PCA. According to Kaiser (1960), only those factors whose variances are greater than 13 are retained as the principle components. Table 15 presents the estimated eigenvalues of eight factors regarding all leaf nodes. According to the factor selection criterion, for instance, #11 has retained the first three factors as its principle components, in which factor 1 explains 44.819% of the total variance of the input variables, factor 2 27.842% and factor 3 15.964%.
Table 15. The estimated eigenvalues of eight factors regarding all FT leaf nodes.
Leaf node Factor Eigenvalue % of Variance
#11 1 3.586 44.819
2 2.227 27.842
3 1.277 15.964
4 0.423 5.292
5 0.253 3.162
6 0.138 1.723
7 0.064 0.800
8 0.032 0.398
#12-21 1 6.468 92.400
2 0.532 7.600
3 0.000 0.000
4 0.000 0.000
5 0.000 0.000
6 0.000 0.000
8 0.000 0.000
#12-22 1 2.691 38.440
2 1.697 24.237
3 1.253 17.905
3 That is its corresponding eigenvalue is large than 1.
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4 0.802 11.458
5 0.495 7.069
6 0.039 0.563
8 0.023 0.329
#12-23 1 3.618 51.689
2 1.885 26.931
3 0.953 13.608
4 0.321 4.593
5 0.151 2.161
6 0.042 0.603
8 0.029 0.415
#13-21 1 3.699 46.242
2 1.923 24.038
3 1.440 17.995
4 0.822 10.271
5 0.116 1.455
6 0.000 0.000
7 0.000 0.000
8 0.000 0.000
#13-22 1 2.845 35.560
2 2.633 32.919
3 1.534 19.178
4 0.629 7.860
5 0.262 3.274
6 0.055 0.684
7 0.030 0.379
8 0.012 0.147
#13-23 1 3.926 49.076
2 3.196 39.949
3 0.878 10.975
4 0.000 0.000
5 0.000 0.000
6 0.000 0.000
7 0.000 0.000
8 0.000 0.000
#13-24 1 3.541 44.257
2 2.883 36.044
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3 1.206 15.070
4 0.257 3.219
5 0.113 1.410
6 0.000 0.000
7 0.000 0.000
8 0.000 0.000
#14-21 1 3.092 38.655
2 2.589 32.361
3 1.244 15.545
4 0.850 10.626
5 0.176 2.204
6 0.049 0.609
7 0.000 0.000
8 0.000 0.000
#14-22 1 3.271 40.887
2 1.846 23.079
3 1.469 18.368
4 0.765 9.562
5 0.443 5.532
6 0.172 2.153
7 0.034 0.419
8 0.000 0.000
#14-23 1 2.879 35.982
2 2.100 26.247
3 1.137 14.214
4 0.766 9.580
5 0.439 5.483
6 0.333 4.166
7 0.221 2.761
8 0.125 1.567
#14-24 1 4.048 50.601
2 2.027 25.336
3 0.931 11.637
4 0.660 8.251
5 0.151 1.886
6 0.114 1.425
7 0.063 0.791
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8 0.006 0.074
Note: The values of the sixth factor (SPR) are the same in leaf nodes #12-21,
#12-22 and #12-23. Therefore, they do not have eigenvalues.
Table 15 presents the estimated eigenvalues of eight factors regarding all leaf nodes of FT. The leaf node #13-21, #13-22, and #13-24 has three factors in which the eigenvalue is greater than 1. The leaf node #13-23 has two factors in which the eigenvalue is greater than 1. The leaf node #14-21, #14-22, and #14-23 has three factors whose eigenvalues are bigger than 1. The leaf node #14-24 has two principle factors whose eigenvalues are bigger than 1. Those factors with eigenvalues bigger than 1 are determined as the principle components of its belonging leaf node.
To enhance the interpretability of the obtained principle components, the varimax factor rotation method is used here. This method minimizes the number of variables that have high loadings of a principle component. To differentiate features in each principle component, variables with the absolute value of corresponding factor loadings less than 0.6 are omitted. Table 16 to Table 18 shows the results of a varimax factor rotation method regarding the leaf nodes of FT.
Table 16 shows the results of a varimax factor rotation method regarding all FT leaf nodes.
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Table 16. The factor loadings of all FT leaf nodes.
Leaf node
Principle
component ROA CR QR DR CFR CFAR SPR Z-score
#11
1 0.911
2 0.786 0.732 0.9
3 0.859 0.908
#12-21 1 0.983 0.95 0.975 0.999 -0.93 -0.94 -0.949
#12-22
1 -0.863 0.797
2 0.898
3 0.941 -0.778
#12-23 1 0.706 -0.967 0.905
2 -0.891 0.87 0.953
#13-21 1 -0.902 0.821 0.95
2 0.886 -0.969
3 0.909 -0.967
#13-22 1 0.873 0.934 -0.892
2 0.947 0.927
3 0.708 0.871
#13-23 1 0.99 0.967 0.935 -0.816
2 -0.728 0.815 0.944 -0.999
#13-24 1 -0.929 -0.86 0.97 0.902
2 0.946 -0.931 0.891
3 0.984
#14-21 1 0.869 0.915 0.729
2 0.961 0.768 0.763
3 0.955
#14-22 1 0.63 0.969 0.995
2 -0.915 0.825
3 0.774 0.648 0.828
#14-23 1 0.668 -0.87 0.73 0.92
2 0.74 0.83
3 0.886
#14-24 1 0.851 0.979 0.968 0.957
2 0.892 0.847 -0.645
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As shown in Table 16, the principle components extracted from different leaf nodes have a heterogeneous composite of variables. For instance, regarding the leaf node #11, its first principle component consists of one debt related ratio (CR); its second principle component consists of three liquidity related ratios (QR, CFR and CFAR); and its third principle component consists of one earning related and one corporate governance ratios (ROA and SPR). Hence, the first principle component represents debt paying ability of a firm; the second principle component represents the liquidity of a firm; and the third principle component represents the profitability and financial pressure of a firm. Regarding the leaf node #12-21, all variables are principle component which represents the profitability, liquidity, cash flow ability and financial difficulty of a firm. Regarding the leaf node #12-22, its first principle components consists of two ratios, DR and Z-score, which represent the debt paying ability of a firm; its second principle component consists of one ratio, CFR, which represents the cash flow ability of a firm; its third principle component consists of two ratio, ROA and CFAR, which represents the profitability and the cash flow ability of a firm.
Regarding leaf node #12-23, its first principle component consists of three ratios (ROA, DR and Z-score), which represent the profitability, debt paying ability and financial health of a firm; and its second principle component consists of three liquidity related ratios (CR, CFR and CFAR) which represent the liquidity of a firm.
Regarding the leaf node #13-21, its first principle component consists of three liquidity related ratios (CR, QR and CFAR); its second principle component consists of one earning related and one debt related ratios (ROA and DR); and its third principle component consists of one corporate governance related and one financial healthy related ratios (SPR and Z-score). Hence, the first principle component represents liquidity of a firm; the second principle component represents the profitability and debt paying ability of a firm; and the third principle component represents the financial pressure and financial health of a firm. Regarding the leaf node #13-22, it has three principle components. The fist principle component consists of two ratios (QR and DR) which represent the debt paying ability of a firm. The second principle component consists of one ratio, CFAR, which represents the cash flow ability of a firm. The third principle component consists of two ratios (CR and SPR), which represents the liquidity and corporate governance health of a firm. Regarding the leaf node #13-23, it has two principle components. The first principle component consists of four ratios
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((ROA, CR, QR, SPR)), which represents the profitability, liquidity and financial pressure of a firm; its second principle component consists of four ratios (DR, CFR, CFAR, Z-score), which represents the debt paying ability, cash flow ability and financial health of a firm. Regarding the leaf node #13-24, its first principle component consists of four ratios (CR, QR, CFR and CFAR), which represents the liquidity of a firm; and its second principle components consists of three ratios (ROA, DR, and Z-score) which represent the profitability, debt paying ability and the financial health of a firm. The third principle component consists of one ratio, SPR, which represents the corporate governance health of a firm.
Regarding the leaf node #14-21, its first principle component consists of two liquidity related ratios and one corporate governance related ratios (CFR, CFAR and SPR); its second principle component consists of the debt related ratios (CR, QR and DR); and its third principle component consists of one financial healthy related ratios (Z-score). Hence, the first principle component represents the liquidity of a firm; the second principle component represents the debt paying ability of a firm; and the third principle component represents the financial health of a firm. Regarding the leaf node
#14-22, it has three principle components. The fist principle component consists of three ratios (QR, CFR and CFAR), which represent the liquidity of a firm. The second principle component consists of two ratios (DR and Z-score), which represent the debt paying ability and the financial health of a firm. The third principle component consists of three ratios (ROA, CR, and SPR), which represent the profitability, the liquidity and the corporate governance health of a firm. Regarding the leaf node #14-23, its first principle component consists of four ratios (CR, DR, CFAR and Z-score), which represent the liquidity, debt paying ability and the financial health of a firm; its second principle component consists of two ratios (ROA and QR), which represent the profitability and debt paying ability of a firm; its third principle component consists of one ratios (CFR), which represent the cash flow ability of a firm. Regarding the leaf node #14-24, its first principle component consists of four ratios (ROA, CFR, CFAR and Z-score), which represents the profitability, cash flow ability and financial health of a firm; and its second principle component consists of three ratios (CR, QR and DR), which represent the debt paying ability of a firm.
We can efficiently exploit one single group or compare different groups from comparing the similarity of each extracted features provided by PCA. As Canbas et al.
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(2005) had done, an early warning model for the observations can be estimated according to these major factor loadings, such as discriminant, logit, probit, and ANN.
By applying PCA to the financial data, the important financial factors can be used to explain the FFR patterns under a certain financial conditions of a firm. In sum, the experimental results show that the proposed quantitative approach with the GHSOM and PCA is helpful in obtaining useful features and can be used to help detect deception regarding FFR or other financial distress scenarios.