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There is 3 classes and 4 variables: min(3-1,4)=2 discriminants can be extracted. Only the extraction (no classification of data points) will be done. Eigenvalues and canonical correlations (Canonical correlation squared is SSbetween/SStotal of ANOVA by that discriminant) Dis1 32.19192920 .98482089 Dis2 .28539104 .47119702 # @Etienne's comment: # In R eigenvalues are expected from # lda(as.factor(Species)~.,data=iris)$svd, but this produces # Dis1 Dis2 # 48.642644 4.579983 # @ttnphns' comment: # The difference might be due to different computational approach # (e.g. me used eigendecomposition and R used svd?) and is of no importance. # Canonical correlations though should be the same. Eigenvectors Dis1 Dis2 SLength -.0684059150 .0019879117 SWidth -.1265612055 .1785267025 PLength .1815528774 -.0768635659 PWidth .2318028594 .2341722673 Eigenvectors (as before, but column-normalized to SS=1: cosines of rotation of variables into discriminants). Dis1 Dis2 SLength -.2087418215 .0065319640 SWidth -.3862036868 .5866105531 PLength .5540117156 -.2525615400 PWidth .7073503964 .7694530921 Unstandardized discriminant coefficients (proportionally related to eigenvectors) Dis1 Dis2 SLength -.829377642 .024102149 SWidth -1.534473068 2.164521235 PLength 2.201211656 -.931921210 PWidth 2.810460309 2.839187853 # @Etienne's comment: # This is obtained in R with # lda(as.factor(Species)~.,data=iris)$scaling # which is described as being standardized discriminant coefficients in the function definition. Standardized discriminant coefficients Dis1 Dis2 SLength -.4269548486 .0124075316 SWidth -.5212416758 .7352613085 PLength .9472572487 -.4010378190 PWidth .5751607719 .5810398645 Pooled within-groups correlations between variables and discriminants Dis1 Dis2 SLength .2225959415 .3108117231 SWidth -.1190115149 .8636809224 PLength .7060653811 .1677013843 PWidth .6331779262 .7372420588 Discriminant scores (Centered 4-variable data multiplied by unstandardized coefficients) Dis1 Dis2 -8.061799783 .300420621 -7.128687721 -.786660426 -7.489827971 -.265384488 -6.813200569 -.670631068 -8.132309326 .514462530 -7.701946744 1.461720967 -7.212617624 .355836209 -7.605293546 -.011633838 -6.560551593 -1.015163624 -7.343059893 -.947319209 ... etc. # @Etienne's comment: # This is obtained in R with # predict(lda(as.factor(Species)~.,data=iris), iris[,-5])$x 

There is 3 classes and 4 variables: min(3-1,4)=2 discriminants can be extracted. Only the extraction (no classification of data points) will be done. The Within scatter matrix 38.95620000 13.63000000 24.62460000 5.64500000 13.63000000 16.96200000 8.12080000 4.80840000 24.62460000 8.12080000 27.22260000 6.27180000 5.64500000 4.80840000 6.27180000 6.15660000 The Between scatter matrix 63.2121333 -19.9526667 165.2484000 71.2793333 -19.9526667 11.3449333 -57.2396000 -22.9326667 165.2484000 -57.2396000 437.1028000 186.7740000 71.2793333 -22.9326667 186.7740000 80.4133333 Eigenvalues and canonical correlations (Canonical correlation squared is SSbetween/SStotal of ANOVA by that discriminant) Dis1 32.19192920 .98482089 Dis2 .28539104 .47119702 # @Etienne's comment: # In R eigenvalues are expected from # lda(as.factor(Species)~.,data=iris)$svd, but this produces # Dis1 Dis2 # 48.642644 4.579983 # @ttnphns' comment: # The difference might be due to different computational approach # (e.g. me used eigendecomposition and R used svd?) and is of no importance. # Canonical correlations though should be the same. Eigenvectors Dis1 Dis2 SLength -.0684059150 .0019879117 SWidth -.1265612055 .1785267025 PLength .1815528774 -.0768635659 PWidth .2318028594 .2341722673 Eigenvectors (as before, but column-normalized to SS=1: cosines of rotation of variables into discriminants). Dis1 Dis2 SLength -.2087418215 .0065319640 SWidth -.3862036868 .5866105531 PLength .5540117156 -.2525615400 PWidth .7073503964 .7694530921 Unstandardized discriminant coefficients (proportionally related to eigenvectors) Dis1 Dis2 SLength -.829377642 .024102149 SWidth -1.534473068 2.164521235 PLength 2.201211656 -.931921210 PWidth 2.810460309 2.839187853 # @Etienne's comment: # This is obtained in R with # lda(as.factor(Species)~.,data=iris)$scaling # which is described as being standardized discriminant coefficients in the function definition. Standardized discriminant coefficients Dis1 Dis2 SLength -.4269548486 .0124075316 SWidth -.5212416758 .7352613085 PLength .9472572487 -.4010378190 PWidth .5751607719 .5810398645 Pooled within-groups correlations between variables and discriminants Dis1 Dis2 SLength .2225959415 .3108117231 SWidth -.1190115149 .8636809224 PLength .7060653811 .1677013843 PWidth .6331779262 .7372420588 Discriminant scores (Centered 4-variable data multiplied by unstandardized coefficients) Dis1 Dis2 -8.061799783 .300420621 -7.128687721 -.786660426 -7.489827971 -.265384488 -6.813200569 -.670631068 -8.132309326 .514462530 -7.701946744 1.461720967 -7.212617624 .355836209 -7.605293546 -.011633838 -6.560551593 -1.015163624 -7.343059893 -.947319209 ... etc. # @Etienne's comment: # This is obtained in R with # predict(lda(as.factor(Species)~.,data=iris), iris[,-5])$x 

There is 3 classes and 4 variables: min(3-1,4)=2 discriminants can be extracted. Only the extraction (no classification of data points) will be done. Eigenvalues and canonical correlations (Canonical correlation squared is SSbetween/SStotal of ANOVA by that discriminant) Dis1 32.19192920 .98482089 Dis2 .28539104 .47119702 # @Etienne's comment: # In R eigenvalues are expected from # lda(as.factor(Species)~.,data=iris)$svd, but this produces # Dis1 Dis2 # 48.642644 4.579983 # @ttnphns' comment: # The difference might be due to different computational approach # (e.g. me used eigendecomposition and R used svd?) and is of no importance. # Canonical correlations though should be the same. Eigenvectors (here, column-normalized to SS=1: cosines of rotation of variables into discriminants) Dis1 Dis2 SLength -.2087418215 .0065319640 SWidth -.3862036868 .5866105531 PLength .5540117156 -.2525615400 PWidth .7073503964 .7694530921 Unstandardized discriminant coefficients (proportionally related to eigenvectors) Dis1 Dis2 SLength -.829377642 .024102149 SWidth -1.534473068 2.164521235 PLength 2.201211656 -.931921210 PWidth 2.810460309 2.839187853 # @Etienne's comment: # This is obtained in R with # lda(as.factor(Species)~.,data=iris)$scaling # which is described as being standardized discriminant coefficients in the function definition. Standardized discriminant coefficients Dis1 Dis2 SLength -.4269548486 .0124075316 SWidth -.5212416758 .7352613085 PLength .9472572487 -.4010378190 PWidth .5751607719 .5810398645 Pooled within-groups correlations between variables and discriminants Dis1 Dis2 SLength .2225959415 .3108117231 SWidth -.1190115149 .8636809224 PLength .7060653811 .1677013843 PWidth .6331779262 .7372420588 Discriminant scores (Centered 4-variable data multiplied by unstandardized coefficients) Dis1 Dis2 -8.061799783 .300420621 -7.128687721 -.786660426 -7.489827971 -.265384488 -6.813200569 -.670631068 -8.132309326 .514462530 -7.701946744 1.461720967 -7.212617624 .355836209 -7.605293546 -.011633838 -6.560551593 -1.015163624 -7.343059893 -.947319209 ... etc. # @Etienne's comment: # This is obtained in R with # predict(lda(as.factor(Species)~.,data=iris), iris[,-5])$x 

There is 3 classes and 4 variables: min(3-1,4)=2 discriminants can be extracted. Only the extraction (no classification of data points) will be done. Eigenvalues and canonical correlations (Canonical correlation squared is SSbetween/SStotal of ANOVA by that discriminant) Dis1 32.19192920 .98482089 Dis2 .28539104 .47119702 # @Etienne's comment: # In R eigenvalues are expected from # lda(as.factor(Species)~.,data=iris)$svd, but this produces # Dis1 Dis2 # 48.642644 4.579983 # @ttnphns' comment: # The difference might be due to different computational approach # (e.g. me used eigendecomposition and R used svd?) and is of no importance. # Canonical correlations though should be the same. Eigenvectors Dis1 Dis2 SLength -.0684059150 .0019879117 SWidth -.1265612055 .1785267025 PLength  .1815528774 -.0768635659 PWidth .2318028594 .2341722673 Eigenvectors (as before, but column-normalized to SS=1: cosines of rotation of variables into discriminants). Dis1 Dis2 SLength -.2087418215 .0065319640 SWidth -.3862036868 .5866105531 PLength .5540117156 -.2525615400 PWidth .7073503964 .7694530921 Unstandardized discriminant coefficients (proportionally related to eigenvectors) Dis1 Dis2 SLength -.829377642 .024102149 SWidth -1.534473068 2.164521235 PLength 2.201211656 -.931921210 PWidth 2.810460309 2.839187853 # @Etienne's comment: # This is obtained in R with # lda(as.factor(Species)~.,data=iris)$scaling # which is described as being standardized discriminant coefficients in the function definition. Standardized discriminant coefficients Dis1 Dis2 SLength -.4269548486 .0124075316 SWidth -.5212416758 .7352613085 PLength .9472572487 -.4010378190 PWidth .5751607719 .5810398645 Pooled within-groups correlations between variables and discriminants Dis1 Dis2 SLength .2225959415 .3108117231 SWidth -.1190115149 .8636809224 PLength .7060653811 .1677013843 PWidth .6331779262 .7372420588 Discriminant scores (Centered 4-variable data multiplied by unstandardized coefficients) Dis1 Dis2 -8.061799783 .300420621 -7.128687721 -.786660426 -7.489827971 -.265384488 -6.813200569 -.670631068 -8.132309326 .514462530 -7.701946744 1.461720967 -7.212617624 .355836209 -7.605293546 -.011633838 -6.560551593 -1.015163624 -7.343059893 -.947319209 ... etc. # @Etienne's comment: # This is obtained in R with # predict(lda(as.factor(Species)~.,data=iris), iris[,-5])$x 

I will not be drawing biplots because biplots can drawn with various normalizations and therefore may look different. Since I'm not R user I have difficulty to track down how you produced your plots, to repeat them. Instead, I will do PCA and LDA and show the results, in a manner similar to this (you might want to read). Both analyses done in SPSS.

About computations at extraction of discriminants in LDA please look here. We interpret discriminants usually by discriminant coefficients or standardized discriminant coefficients (the latter are more handy because differential variance in variables is taken off). This is like in PCA. But, note: the coefficients here are the regressional coefficients of modeling discriminants by variables, not vice versa, like it was in PCA. Because variables are not uncorrelated, the coefficients cannot be seen as covariances between variables and discriminants.

I will not be drawing biplots because biplots can drawn with various normalizations and therefore may look different. Since I'm not R user I have difficulty to track down how you produced your plots, to repeat them. Instead, I will do PCA and LDA and show the results, in a manner similar to this (you might want to read). Both analyses done in SPSS.

About computations at extraction of discriminants in LDA please look here. We interpret discriminants usually by discriminant coefficients or standardized discriminant coefficients (the latter are more handy because differential variance in variables is taken off). This is like in PCA. But, note: the coefficients here are the regressional coefficients of modeling discriminants by variables, not vice versa, like it was in PCA. Because variables are not uncorrelated, the coefficients cannot be seen as covariances between variables and discriminants.