package package ca function function ca mjca (simple) - PowerPoint PPT Presentation

Assos Venue for CARME in ASSOS View of Aegean Sea and island of Lesbos. Turkey, August 2010. Simple correspondence analysis (CA), Simple correspondence analysis (CA), Multiple correspondence analysis (MCA), Multiple correspondence analysis (MCA), Joint correspondence analysis (JCA), Joint correspondence analysis (JCA), Michael Greenacre Michael Greenacre as well as all subset versions of these, as well as all subset versions of these, Universitat Pompeu Fabra Universitat Pompeu Fabra using R using package package ca . Barcelona Barcelona Oleg Nenadi ć & Michael Greenacre University of Göttingen & Universitat Pompeu Fabra

package package ca function function ca mjca (simple) correspondence multiple correspondence analysis analysis (CA) (MCA) adjusted MCA joint correspondence analysis (JCA) subset versions subset versions subset CA, subset MCA, adjusted subset MCA, subset JCA

Contribution coordinates Contribution coordinates asymmetric asymmetric map: map: contribution ntribution coordina oordinates: tes: map="rowprincipal" map="rowgreen" -6 -4 -2 0 2 4 6 • • 0.8 0.8 8 • 18:0 • 0.6 0.6 6 • • • • 0.4 • • 0.4 4 18:0 i-16:0 • • • • 0.2 • • 22:1(n-11) 0.2 2 20:1(n-9) 17:0 a-15:0 • i-15:0 a-17:0 •• 24:1(n-9) • • • 20:2(n-6) • • 15:0 0.0 20:3(n-3) • • 18:1(n-9) 22:1(n-11) 18:2(n-6) • • 20:1(n-9) 18:3(n-3) 22:1(n-9) 16:1(n-5) 16:0 • • • 14:0 • • 20:0 • • • 22:1(n-7) • • • 0.0 • • • • 20:1(n-7) 20:3(n-6) • 20:4(n-3) 0 14:1(n-5) • • • 22:6(n-3) • • 18:1(n-7) • 22:5(n-3) • 16:2(n-4) • • • • • • • 16:3(n-4) i-17:0 • 20:4(n-6) • 20:5(n-3) 18:3(n-6) • 15:1(n-6) 18:4(n-3) • -0.2 • • • 16:1(n-7) • • • 20:1(n-11) • • -0.2 • 16:4(n-1) 18:4(n-3) -2 • • • • • • 20:5(n-3) • • • • • • -0.4 • -0.4 -4 16:1(n-7) 16:1(n-9) -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 See Biplots See Biplots in Practice n Practice (Greenacre (Greenacre 2010) 010) www.multivariatestatistics.org

Problem of variance explained Problem of variance explained > summary(mjca(wg93[,1:4], lambda="indicator")) Principal inertias (eigenvalues): dim value % cum% scree plot 1 0.457379 11.4 11.4 ************************* 2 0.430966 10.8 22.2 *********************** 3 0.321926 8.0 30.3 *************** : : : : increasing inertia explained > summary(mjca(wg93[,1:4], lambda="Burt")) Principal inertias (eigenvalues): dim value % cum% scree plot 1 0.209196 18.6 18.6 ************************* 2 0.185732 16.5 35.0 ********************** 3 0.103636 9.2 44.2 *********** : : : : > summary(mjca(wg93[,1:4], lambda="adjusted")))) #DEFAULT Principal inertias (eigenvalues): dim value % cum% scree plot 1 0.076455 44.9 44.9 ************************* 2 0.058220 34.2 79.1 ******************* 3 0.009197 5.4 84.5 *** : : : : > summary(mjca(wg93[,1:4]), lambda="JCA")) Percentage explained by JCA in 2 dimensions: 85.7% (Eigenvalues are not nested) [Iterations in JCA: 44 , epsilon = 9.91e-05]

Same problem for individual points Same problem for individual points > summary(mjca(wg93[,1:4], lambda="Burt")) Principal inertias (eigenvalues): dim value % cum% scree plot 1 0.209196 18.6 18.6 ************************* 2 0.185732 16.5 35.0 ********************** 3 0.103636 9.2 44.2 *********** : : : : : name mass qlt inr k=1 cor ctr k=2 cor ctr 1 | A1 | 34 445 55 | -840 391 53 | -314 54 8 | 2 | A2 | 92 169 38 | -250 136 13 | 123 33 3 | 3 | A3 | 59 344 47 | 204 47 5 | 517 298 36 | 4 | A4 | 51 350 50 | 533 258 32 | -318 92 12 | 5 | A5 | 14 401 60 | 913 170 25 | -1064 231 36 | 6 | B1 | 20 621 62 | -1338 519 80 | -590 101 16 | 7 | B2 | 50 158 47 | -293 80 9 | 287 77 10 | 8 | B3 | 59 227 45 | -158 29 3 | 415 198 24 | 9 | B4 | 81 210 41 | 327 185 19 | 121 25 3 | 10 | B5 | 40 722 60 | 619 229 34 | -908 493 77 | 11 | C1 | 44 732 60 | -987 632 93 | -392 100 16 | 12 | C2 | 91 164 38 | -113 27 3 | 255 137 14 | 13 | C3 | 57 296 48 | 283 84 10 | 450 212 27 | 14 | C4 | 44 345 52 | 617 289 37 | -274 57 8 | 15 | C5 | 15 471 60 | 671 99 15 | -1300 372 59 | 16 | D1 | 17 251 56 | -551 83 11 | -785 168 25 | 17 | D2 | 67 14 42 | 101 14 1 | 3 0 0 | 18 | D3 | 58 303 48 | 176 33 4 | 499 269 34 | 19 | D4 | 65 25 43 | 101 14 1 | 91 11 1 | 20 | D5 | 43 272 50 | -324 81 10 | -496 191 25 |

Same problem for individual points Same problem for individual points > summary(mjca(wg93[,1:4], lambda="Burt")) Principal inertias (eigenvalues): dim value % cum% scree plot 1 0.209196 18.6 18.6 ************************* 2 0.185732 16.5 35.0 ********************** 3 0.103636 9.2 44.2 *********** > mjca(wg93[,1:4])$Burt A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 A1 119 0 0 0 0 27 28 30 22 12 49 40 18 7 5 15 25 17 34 28 A2 0 322 0 0 0 38 74 84 96 30 67 142 60 41 12 22 102 76 68 54 A3 0 0 204 0 0 3 48 63 73 17 18 75 70 34 7 10 44 68 58 24 A4 0 0 0 178 0 3 21 23 79 52 16 50 40 56 16 9 52 28 54 35 A5 0 0 0 0 48 0 3 5 11 29 2 9 9 16 12 4 9 13 12 10 B1 27 38 3 3 0 71 0 0 0 0 43 19 4 3 2 9 17 10 10 25 B2 28 74 48 21 3 0 174 0 0 0 36 88 34 15 1 16 51 42 45 20 B3 30 84 63 23 5 0 0 205 0 0 37 90 57 19 2 10 53 63 51 28 B4 22 96 73 79 11 0 0 0 281 0 27 88 75 74 17 6 66 70 92 47 B5 12 30 17 52 29 0 0 0 0 140 9 31 27 43 30 19 45 17 28 31 C1 49 67 18 16 2 43 36 37 27 9 152 0 0 0 0 25 24 15 38 50 C2 40 142 75 50 9 19 88 90 88 31 0 316 0 0 0 15 97 67 89 48 C3 18 60 70 40 9 4 34 57 75 27 0 0 197 0 0 5 51 83 41 17 C4 7 41 34 56 16 3 15 19 74 43 0 0 0 154 0 6 44 30 51 23 C5 5 12 7 16 12 2 1 2 17 30 0 0 0 0 52 9 16 7 7 13 D1 15 22 10 9 4 9 16 10 6 19 25 15 5 6 9 60 0 0 0 0 D2 25 102 44 52 9 17 51 53 66 45 24 97 51 44 16 0 232 0 0 0 D3 17 76 68 28 13 10 42 63 70 17 15 67 83 30 7 0 0 202 0 0 D4 34 68 58 54 12 10 45 51 92 28 38 89 41 51 7 0 0 0 226 0 D5 28 54 24 35 10 25 20 28 47 31 50 48 17 23 13 0 0 0 0 151

Joint correspondence analysis Joint correspondence analysis > mjca(wg93[,1:4], lambda="JCA")$Burt.upd A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 A1 31 53 19 14 3 27 28 30 22 12 49 40 18 7 5 15 25 17 34 28 A2 53 131 77 52 10 38 74 84 96 30 67 142 60 41 12 22 102 76 68 54 A3 19 77 63 39 7 3 48 63 73 17 18 75 70 34 7 10 44 68 58 24 A4 14 52 39 54 20 3 21 23 79 52 16 50 40 56 16 9 52 28 54 35 A5 3 10 7 20 9 0 3 5 11 29 2 9 9 16 12 4 9 13 12 10 B1 27 38 3 3 0 21 20 18 8 3 43 19 4 3 2 9 17 10 10 25 B2 28 74 48 21 3 20 46 54 50 4 36 88 34 15 1 16 51 42 45 20 B3 30 84 63 23 5 18 54 65 64 4 37 90 57 19 2 10 53 63 51 28 B4 22 96 73 79 11 8 50 64 104 55 27 88 75 74 17 6 66 70 92 47 B5 12 30 17 52 29 3 4 4 55 74 9 31 27 43 30 19 45 17 28 31 C1 49 67 18 16 2 43 36 37 27 9 82 55 4 3 7 25 24 15 38 50 C2 40 142 75 50 9 19 88 90 88 31 55 126 79 46 9 15 97 67 89 48 C3 18 60 70 40 9 4 34 57 75 27 4 79 66 41 6 5 51 83 41 17 C4 7 41 34 56 16 3 15 19 74 43 3 46 41 45 18 6 44 30 51 23 C5 5 12 7 16 12 2 1 2 17 30 7 9 6 18 11 9 16 7 7 13 D1 15 22 10 9 4 9 16 10 6 19 25 15 5 6 9 9 15 5 13 18 D2 25 102 44 52 9 17 51 53 66 45 24 97 51 44 16 15 62 56 61 38 D3 17 76 68 28 13 10 42 63 70 17 15 67 83 30 7 5 56 64 56 21 D4 34 68 58 54 12 10 45 51 92 28 38 89 41 51 7 13 61 56 60 36 D5 28 54 24 35 10 25 20 28 47 31 50 48 17 23 13 18 38 21 36 38 • default: two-dimensional solution • at convergence the diagonal blocks are perfectly fitted

Joint correspondence analysis oint correspondence analysis > summary(mjca(wg93[,1:4], lambda="JCA")) Principal inertias (eigenvalues): dim value 1 0.099091 2 0.065033 : : -------- Total: 0.182425 Diagonal inertia discounted from eigenvalues: 0.0547405 Percentage explained by JCA in 2 dimensions: 85.7% (Eigenvalues are not nested) [Iterations in JCA: 44 , epsilon = 9.91e-05]   ( 0 . 099091 0 . 065033 ) 0 . 0547405  0 . 857  0 . 182425 0 . 0547405 Subset version of JCA available in new version: i.e., a subset of the categories is specified, and the analysis fits these optimally, using the original margins of the Burt matrix, omitting the (subsets of) categories in the diagonal blocks.