Multinomial Logistic Regression with Iris Data
Ugi
August 2, 2015
Present Iris Data
First, present the iris data.
iris #Present iris data## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginicaNote that Sepal.Length, Sepal.Width, Petal.Length, and Petal.Width are metric independent variables, whereas Species is nonmetric (category) dependent variable.
Descriptive Statistics
x1 = iris$Sepal.Length #Sepal.Length will be treated as independent variable
x2 = iris$Sepal.Width #Sepal.Width will be treated as independent variable
x3 = iris$Petal.Length #Petal.Length will be treated as independent variable
x4 = iris$Petal.Width #Petal.Width will be treated as dependent variable
x1## [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4
## [18] 5.1 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5
## [35] 4.9 5.0 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8 5.1 4.6 5.3 5.0 7.0
## [52] 6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8
## [69] 6.2 5.6 5.9 6.1 6.3 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4
## [86] 6.0 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.0 5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8
## [103] 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7
## [120] 6.0 6.9 5.6 7.7 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7
## [137] 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8 6.7 6.7 6.3 6.5 6.2 5.9x2## [1] 3.5 3.0 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 3.7 3.4 3.0 3.0 4.0 4.4 3.9
## [18] 3.5 3.8 3.8 3.4 3.7 3.6 3.3 3.4 3.0 3.4 3.5 3.4 3.2 3.1 3.4 4.1 4.2
## [35] 3.1 3.2 3.5 3.6 3.0 3.4 3.5 2.3 3.2 3.5 3.8 3.0 3.8 3.2 3.7 3.3 3.2
## [52] 3.2 3.1 2.3 2.8 2.8 3.3 2.4 2.9 2.7 2.0 3.0 2.2 2.9 2.9 3.1 3.0 2.7
## [69] 2.2 2.5 3.2 2.8 2.5 2.8 2.9 3.0 2.8 3.0 2.9 2.6 2.4 2.4 2.7 2.7 3.0
## [86] 3.4 3.1 2.3 3.0 2.5 2.6 3.0 2.6 2.3 2.7 3.0 2.9 2.9 2.5 2.8 3.3 2.7
## [103] 3.0 2.9 3.0 3.0 2.5 2.9 2.5 3.6 3.2 2.7 3.0 2.5 2.8 3.2 3.0 3.8 2.6
## [120] 2.2 3.2 2.8 2.8 2.7 3.3 3.2 2.8 3.0 2.8 3.0 2.8 3.8 2.8 2.8 2.6 3.0
## [137] 3.4 3.1 3.0 3.1 3.1 3.1 2.7 3.2 3.3 3.0 2.5 3.0 3.4 3.0x3## [1] 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.5 1.3
## [18] 1.4 1.7 1.5 1.7 1.5 1.0 1.7 1.9 1.6 1.6 1.5 1.4 1.6 1.6 1.5 1.5 1.4
## [35] 1.5 1.2 1.3 1.4 1.3 1.5 1.3 1.3 1.3 1.6 1.9 1.4 1.6 1.4 1.5 1.4 4.7
## [52] 4.5 4.9 4.0 4.6 4.5 4.7 3.3 4.6 3.9 3.5 4.2 4.0 4.7 3.6 4.4 4.5 4.1
## [69] 4.5 3.9 4.8 4.0 4.9 4.7 4.3 4.4 4.8 5.0 4.5 3.5 3.8 3.7 3.9 5.1 4.5
## [86] 4.5 4.7 4.4 4.1 4.0 4.4 4.6 4.0 3.3 4.2 4.2 4.2 4.3 3.0 4.1 6.0 5.1
## [103] 5.9 5.6 5.8 6.6 4.5 6.3 5.8 6.1 5.1 5.3 5.5 5.0 5.1 5.3 5.5 6.7 6.9
## [120] 5.0 5.7 4.9 6.7 4.9 5.7 6.0 4.8 4.9 5.6 5.8 6.1 6.4 5.6 5.1 5.6 6.1
## [137] 5.6 5.5 4.8 5.4 5.6 5.1 5.1 5.9 5.7 5.2 5.0 5.2 5.4 5.1x4## [1] 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 0.2 0.2 0.1 0.1 0.2 0.4 0.4
## [18] 0.3 0.3 0.3 0.2 0.4 0.2 0.5 0.2 0.2 0.4 0.2 0.2 0.2 0.2 0.4 0.1 0.2
## [35] 0.2 0.2 0.2 0.1 0.2 0.2 0.3 0.3 0.2 0.6 0.4 0.3 0.2 0.2 0.2 0.2 1.4
## [52] 1.5 1.5 1.3 1.5 1.3 1.6 1.0 1.3 1.4 1.0 1.5 1.0 1.4 1.3 1.4 1.5 1.0
## [69] 1.5 1.1 1.8 1.3 1.5 1.2 1.3 1.4 1.4 1.7 1.5 1.0 1.1 1.0 1.2 1.6 1.5
## [86] 1.6 1.5 1.3 1.3 1.3 1.2 1.4 1.2 1.0 1.3 1.2 1.3 1.3 1.1 1.3 2.5 1.9
## [103] 2.1 1.8 2.2 2.1 1.7 1.8 1.8 2.5 2.0 1.9 2.1 2.0 2.4 2.3 1.8 2.2 2.3
## [120] 1.5 2.3 2.0 2.0 1.8 2.1 1.8 1.8 1.8 2.1 1.6 1.9 2.0 2.2 1.5 1.4 2.3
## [137] 2.4 1.8 1.8 2.1 2.4 2.3 1.9 2.3 2.5 2.3 1.9 2.0 2.3 1.8summary(x1)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.300 5.100 5.800 5.843 6.400 7.900summary(x2)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.000 2.800 3.000 3.057 3.300 4.400summary(x3)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 1.600 4.350 3.758 5.100 6.900summary(x4)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.100 0.300 1.300 1.199 1.800 2.500The result below based on SPSS.
library(psych) #Load package psych to use function describeBy
describeBy(iris$Sepal.Length, iris$Species) ## group: setosa
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 5.01 0.35 5 5 0.3 4.3 5.8 1.5 0.11 -0.45 0.05
## --------------------------------------------------------
## group: versicolor
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 5.94 0.52 5.9 5.94 0.52 4.9 7 2.1 0.1 -0.69 0.07
## --------------------------------------------------------
## group: virginica
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 6.59 0.64 6.5 6.57 0.59 4.9 7.9 3 0.11 -0.2 0.09describeBy(iris$Sepal.Width, iris$Species)## group: setosa
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 3.43 0.38 3.4 3.42 0.37 2.3 4.4 2.1 0.04 0.6 0.05
## --------------------------------------------------------
## group: versicolor
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 2.77 0.31 2.8 2.78 0.3 2 3.4 1.4 -0.34 -0.55 0.04
## --------------------------------------------------------
## group: virginica
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 2.97 0.32 3 2.96 0.3 2.2 3.8 1.6 0.34 0.38 0.05describeBy(iris$Petal.Length, iris$Species)## group: setosa
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 1.46 0.17 1.5 1.46 0.15 1 1.9 0.9 0.1 0.65 0.02
## --------------------------------------------------------
## group: versicolor
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 4.26 0.47 4.35 4.29 0.52 3 5.1 2.1 -0.57 -0.19 0.07
## --------------------------------------------------------
## group: virginica
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 5.55 0.55 5.55 5.51 0.67 4.5 6.9 2.4 0.52 -0.37 0.08describeBy(iris$Petal.Width, iris$Species)## group: setosa
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 0.25 0.11 0.2 0.24 0 0.1 0.6 0.5 1.18 1.26 0.01
## --------------------------------------------------------
## group: versicolor
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 1.33 0.2 1.3 1.32 0.22 1 1.8 0.8 -0.03 -0.59 0.03
## --------------------------------------------------------
## group: virginica
## vars n mean sd median trimmed mad min max range skew kurtosis se
## 1 1 50 2.03 0.27 2 2.03 0.3 1.4 2.5 1.1 -0.12 -0.75 0.04This result below based on SPSS.
Perform Multinomial Logistic Regression (MLR) Using Iris Data
library(stats4) #Load package stats
library(splines) #Load package splines
#To load package VGAM, need to load package stats4 and splines.
library(VGAM) #Load package VGAM##
## Attaching package: 'VGAM'
##
## The following objects are masked from 'package:psych':
##
## fisherz, logistic, logit#Perform MLR
fit.MLR <- vglm( Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, family=multinomial, iris)## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 2 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 13 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 22 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 34 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 39 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 41 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 47 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 50 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 54 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 59 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 63 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 78 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 91 elements replaced by 1.819e-12## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 101 elements replaced by 1.819e-12## Warning in slot(family, "linkinv")(eta, extra): fitted probabilities
## numerically 0 or 1 occurred## Warning in tfun(mu = mu, y = y, w = w, res = FALSE, eta = eta, extra):
## fitted values close to 0 or 1## Warning in checkwz(wz, M = M, trace = trace, wzepsilon = control
## $wzepsilon): 121 elements replaced by 1.819e-12## Warning in slot(family, "linkinv")(eta, extra): fitted probabilities
## numerically 0 or 1 occurred## Warning in tfun(mu = mu, y = y, w = w, res = FALSE, eta = eta, extra):
## fitted values close to 0 or 1## Warning in vglm.fitter(x = x, y = y, w = w, offset = offset, Xm2 = Xm2, :
## convergence not obtained in 21 iterationssummary(fit.MLR)##
## Call:
## vglm(formula = Species ~ Sepal.Length + Sepal.Width + Petal.Length +
## Petal.Width, family = multinomial, data = iris)
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## log(mu[,1]/mu[,3]) -2.09e-06 -1.787e-07 4.586e-08 6.329e-08 1.327e-05
## log(mu[,2]/mu[,3]) -1.97e+00 -3.382e-04 3.159e-07 4.569e-04 2.560e+00
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept):1 34.243 42494.920 0.001 0.9994
## (Intercept):2 42.638 25.708 1.659 0.0972 .
## Sepal.Length:1 10.747 12615.952 0.001 0.9993
## Sepal.Length:2 2.465 2.394 1.030 0.3032
## Sepal.Width:1 12.815 5841.307 0.002 0.9982
## Sepal.Width:2 6.681 4.480 1.491 0.1359
## Petal.Length:1 -25.043 8946.662 -0.003 0.9978
## Petal.Length:2 -9.429 4.737 -1.990 0.0465 *
## Petal.Width:1 -36.060 14050.767 -0.003 0.9980
## Petal.Width:2 -18.286 9.743 -1.877 0.0605 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of linear predictors: 2
##
## Names of linear predictors: log(mu[,1]/mu[,3]), log(mu[,2]/mu[,3])
##
## Dispersion Parameter for multinomial family: 1
##
## Residual deviance: 11.8985 on 290 degrees of freedom
##
## Log-likelihood: -5.9493 on 290 degrees of freedom
##
## Number of iterations: 21Note that the reference/base category is “Virginica.
The following result based on SPSS.
Based on result in SPSS (below) until 23 iterations, whereas using R until 21 iterations.
Now, we set iteration until 21 iterations in SPSS. So the results as follows.
Perform Classification
#Perform classification
probabilities.MLR <- predict(fit.MLR, iris[,1:4], type="response")## Warning in object@family@linkinv(predictor, extra): fitted probabilities
## numerically 0 or 1 occurredpredictions <- apply(probabilities.MLR, 1, which.max)
predictions[which(predictions=="1")] <- levels(iris$Species)[1]
predictions[which(predictions=="2")] <- levels(iris$Species)[2]
predictions[which(predictions=="3")] <- levels(iris$Species)[3]
# Summarize accuracy
table(iris$Species, predictions) ## predictions
## setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 49 1
## virginica 0 1 49The classification table below based on MLR using SPSS.
#  is command to present SPSS picture