LINGO Program 2 of Method 1

Although Fisher established the statistical discriminant analysis based on variance–covariance matrix, he did not define the equation of SE of error rate and discriminant coefficient. Therefore, we proposed the 100-fold cross-validation for small sample method (the Method 1). The Method 1 is the combination of resampling and k-fold cross-validation. We generate large sample as validation sample by resampling and undertake 100-fold cross-validation using large sample. The Method 1 is as follows: (1) We copy 100 times the data from the original data using JMP. (2) We add a uniform random number as a new variable, sort the data in ascending order, and divide it into 100 subsets that are used as 100 training samples. (3) We evaluate eight LDFs by the Method 1Method 1 using these 100 subsets as 100 training samples and large sample as validation sample. I develop LINGO Program 2 of the Method 1 for six MP-based LDFs and JMP script for Fisher’s LDF and logistic regression. In this Chapter, we explain LINGO Program 2. Because we need more pages to explain JMP script, we omit the explanation. LINGO Program 2 supports six MP-based LDFs such as Revised IP-OLDF, Revised LP-OLDF, Revised IPLP-OLDF, H-SVM, SVM4, and SVM1. There is merit in using 100-fold cross-validation because we can easily calculate the 95 % CI of the discriminant coefficients95 % CI of the discriminant coefficient and error rates. Moreover, two error rate means, M1By the mean of error rates of the validation sample and M2, in the training and validation samples\“M1 & M2\” are the mean error rates in the training and validation samples offer direct and powerful model selection procedure such as the best model. We can show the best models of Revised IP-OLDF are better than other LDFs.