Advanced Statistical Methods in Insurance 7. Multivariate Data All Pairwise Scattergrams Iris Data Set: 3 Species 50 Cases of each with p=4 measurements per case 2 Hudec & Schlögl 1
3-d Scatterplots iris[, 1] iris[, 1] iris[, 3] iris[, 2] iris[, 3] iris[, 2] 3 Hudec & Schlögl Visualization of 4 variables in a Scatterplot 5 3.0 3.5 4.0 4.5 2.0 2. 4 5 6 7 8 2 Vars define position 2 Vars define shape 4 Hudec & Schlögl 2
Conditioning Plots Cleveland, W. S. (1993) 1 2 3 4 5 6 2.0 2.5 3.0 3.5 4.0 2.0 2.5 3.0 3.5 4.0 [ ] 4.5 5.5 6.5 7.5 4.5 5.5 6.5 7.5 [ 5 2.0 2.5 3.0 3.5 4.0 Hudec & Schlögl Conditioning Variable Plots i4 i4 i4 i4 i4 i4 Use 4 th Variable for Conditioning 6 Hudec & Schlögl 3
Parallel Plots (Profile Plots) Species Petal.Width Petal.Length Sepal.Width Sepal.Length Min 7 Hudec & Schlögl Max Conditioned Parallel Plots (Profile Plots) Petal.Width virginica Petal.Length Sepal.Width Sepal.Length Petal.Width Petal.Length th Sepal.Width Sepal.Length setosa versicolor Min Max 8 Hudec & Schlögl 4
Andrews Curves 0 5 15-3 -2-1 0 1 2 3 a1 = 1/ 2 p j f i(t) = a j(t) x sin( t) for j = 2, 4, K ij 2 a j = j= 1 j 1 cos( t) for j = 3,5, K 2 9 Hudec & Schlögl Chernoff-Faces Hudec & Schlögl 5
Glyphs Multiple-symbol Approach 11 Hudec & Schlögl Cars Database Manufacturer Model Type Min.Price Price Max.Price MPG.city MPG.highway AirBags DriveTrain 1 Acura Integra Small 12.9 15.9 18.8 25 31 None Front 2 Acura Legend Midsize 29.2 33.9 38.7 18 25 Driver & Passenger Front 3 Audi 90 Compact 25.9 29.1 32.3 20 26 Driver only Front 4 Audi 0 Midsize 30.8 37.7 44.6 19 26 Driver & Passenger Front 5 BMW 535i Midsize 23.7 30.0 36.2 22 30 Driver only Rear 6 Buick Century Midsize 14.2 15.7 17.3 22 31 Driver only Front Cylinders EngineSize Horsepower RPM Rev.per.mile Man.trans.avail Fuel.tank.capacity Passengers Length 1 4 1.8 140 6300 2890 Yes 13.2 5 177 2 6 3.2 200 5500 2335 Yes 18.0 5 195 3 6 2.8 172 5500 2280 Yes 16.9 5 180 4 6 2.8 172 5500 2535 Yes 21.1 6 193 5 4 3.5 208 5700 2545 Yes 21.1 4 186 6 4 2.2 1 5200 2565 No 16.4 6 189 Wheelbase Width Turn.circle Rear.seat.room Luggage.room Weight Origin Make 1 2 68 37 26.5 11 2705 non-usa Acura Integra 2 115 71 38 30.0 15 3560 non-usa Acura Legend 3 2 67 37 28.0 14 3375 non-usa Audi 90 4 6 70 37 31.0 17 3405 non-usa Audi 0 5 9 69 39 27.0 13 3640 non-usa BMW 535i 6 5 69 41 28.0 16 2880 USA Buick Century 12 Hudec & Schlögl 6
15 1 5 4000 140 60 20 2000 in.pric Price ax.pric 20 15 PG.ci G.high 20 1 ginesi rsepow 50 4000 RPM v.per.m 1500 ank.ca 2000 20 60 140 ssenge Length heelba Width rn.circ.seat.r gage.r Weigh 20 20 50 1500 2 8 90 32 32 90 2 8 13 Hudec & Schlögl -1.0-0.5 0.0 0.5 1.0 Wheelbase Length Weight Fuel.tank.capacity Width EngineSize Turn.circle Price Min.Price Max.Price Horsepower Luggage.room Rear.seat.room Passengers MPG.highway MPG.city Rev.per.mile RPM -47-64 -67-62 69 67 73 49 47 52 50 72 73 81 76 87 820-44 -69-67 -54 49 55 71 55 44 55 50 74 78 82 69 81 082-43 -74-84 -81 55 53 64 74 61 67 65 78 85 87 890 81 87-33 -61-81 -79 47 51 61 71 58 64 62 67 76 80 089 69 76-54 -78-72 -64 49 47 67 64 41 49 46 82 87 0 80 87 82 81-55 -82-71 -63 37 50 68 73 54 65 60 780 87 76 85 78 73-51 -73-67 -59 45 47 59 56 35 43 39 078 82 67 78 74 72 0-43 -59-56 6 31 37 79 98 970 39 60 46 62 65 50 50-4 -47-62 -58 6 38 41 80 91 097 43 65 49 64 67 55 52 3-37 -55-52 5 25 32 740 91 98 35 54 41 58 61 44 47 4-60 -67-62 1 26 36 074 80 79 56 73 64 71 74 55 49-52 -59-49 -37 65 650 36 32 41 37 59 68 67 61 64 71 73-34 -38-38 -37 69 065 26 25 38 31 47 50 47 51 53 55 67-47 -33-42 -470 69 65 1 5 6 6 45 37 49 47 55 49 69 31 59 940-47 -37-37 -62-52 -58-56 -59-63 -64-79 -81-54 -62 36 70 094-42 -38-49 -67-55 -62-59 -67-71 -72-81 -84-67 -67 490 70 59-33 -38-59 -60-37 -47-43 -73-82 -78-61 -74-69 -64 049 36 31-47 -34-52 4 3-4 0-51 -55-54 -33-43 -44-47 RPM Rev.per.mile MPG.city MPG.highway Passengers Rear.seat.room Luggage.room Horsepower Max.Price Min.Price Price Turn.circle EngineSize Width Fuel.tank.capacity Weight Length Wheelbase 14 Hudec & Schlögl 7
3d-Visualisation of Functions f(x, y) 0.08 0.06 wireframe(funval~grid[,1]*grid[,2], col=2, drape=t, xlab="", ylab="",zlab="", at=quantile(funval, 0:24/25), col.regions=heat.colors(25), par.settings=list(box.3d=f)) 15 Hudec & Schlögl 0.04 002 0.02 0.16 0.14 8 6 0.09 0.01 002 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 0.11 0. 0.11 0.12 0.13 0.14 0.15 0.12 0.13 0.14 0.15 0.08 8 6 0.12 0. 0.08 0.06 4 4 2 2 4 6 8 2 4 6 8 2 Left: contourplot(funval~grid[,1]*grid[,2], cuts=20, col="blue ) Right: levelplot(funval~grid[,1]*grid[,2],cuts=20,col.regions=heat.colors(25)) 0.04 0.02 0.00 16 Hudec & Schlögl 8