Iris Data and Fisher’s Assumption

Shuichi Shinmura ()
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Shuichi Shinmura: Seikei University, Faculty of Economics

Chapter Chapter 2 in New Theory of Discriminant Analysis After R. Fisher, 2016, pp 37-55 from Springer

Abstract: Abstract Anderson collects Iris data. That consists of three species as follows: setosa, versicolor, and virginica. Each species has four variables and 50 cases. Because Fisher evaluates Fisher’s LDF with these data, such data are very popular for the evaluation of discriminant functions. Therefore, we call these data, “Fisher’s Iris data.” Because we can easily separate setosa from virginica and vercicolor through a scatter plot, we usually discriminate two classes, such as the virginica and vercicolor. In this book, our main policy of discrimination consists of two parts: (1) Discriminate the original data by six MP-based LDFs, QDF, and RDA in addition to two statistical LDFs. LINGO solves six MP-based LDFs, such as Revised IP-OLDF, Revised LP-OLDF, Revised IPLP-OLDF, two S-SVMs, and H-SVM explained in Sect. 2.3.3. Downloading a free version of LINGO with manual from LINDO Systems Inc. allows anyone to analyze data. JMP discriminates data by QDF and RDA, in addition to two LDFs, such as Fisher’s LDF and logistic regression. We evaluate nine discriminant functions by NM, except for H-SVM. (2) Generate resampling samples from the original data and discriminate such resampling samples by the 100-fold cross-validation for small sample method (Method 1). We compare five MP-based LDFs and two statistical LDFs by the mean of error rates of the validation sample (M2), and the 95 % CI of discriminant coefficients. We explain the LINGO Program 2 of the Method 1 in Chap. 9 . Because there is a small difference among seven NMs by LINGO Program 1 in Section 2.3.3, with the exception of H-SVM, and we cannot evaluate the ranking of seven LDFs clearly, we should no longer use Iris data to evaluate discriminant functions. Fisher proposed Fisher’s LDF under Fisher’s assumption. However, there are no actual test statistics to determine whether the data satisfy Fisher’s assumption. If the data satisfy Fisher’s assumption, NM of Fisher’s LDF continues to converge on MNM. Although there is no actual test for Fisher’s assumption, we can confirm it by this idea. Section 2.3.3 describes a LINGO Program 1 of six MP-based LDFs that discriminate conventional data.

Keywords: Fisher’s linear discriminant function (Fisher’s LDF); Logistic regression; Soft-margin support vector machine (S-SVM); Hard-margin SVM (H-SVM); Revised IP-OLDF; Revised IPLP-OLDF; Revised LP-OLDF; Best model; 95 % confidence interval (CI) of error rate and discriminant coefficient; LINGO Program 1 of six MP-based LDFs LINGO Program 2 of Method 1 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-2164-0_2

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DOI: 10.1007/978-981-10-2164-0_2

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