Advances in multidimensional unfolding Busing, F.M.T.A.

Busing, F.M.T.A.

Citation

Busing, F. M. T. A. (2010, April 21). Advances in multidimensional unfolding. Retrieved from https://hdl.handle.net/1887/15279

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additive constant 46, 71, 157, 207 analysis of angular variation 204, 209 anava 204, 209

aspect ratio 211

attraction to the horizon 133, 134 barycenter method 202 biplot 202

interpolative 201 predictive 201 block design

bibd 103 incomplete

balanced 103 row-balanced 104 row-bibd 104 unconnected 109 block relaxation 168 bootstrap 130, 196, 210

balanced 196

calibration see (back-)transformation categorical principal component

analysis 90, 91, 136 categorical regression analysis 135 center

mean 83 median 83, 85 min-max 83 choice model

deterministic 83, 86, 95, 217 probabilistic 83, 86, 95 classical scaling 156, 157 cluster analysis

harmonic means 86

probabilistic distance 85, 202, 210 coefficient

canonical 209 direction 199, 209 regression 200

standardized 209 unstandardized 209 common space 177, 179, 183, 208, 211

interpretation 199 rotation 177 unrestricted 193 weighting 177

computer program see software conditional

matrix- 151 row- 12, 52, 75, 151 un- 12, 75, 151 conditionality 12, 151 confidence

ellipse 116 interval 138

nonparametric 212 configuration

start 154

congruence coefficient 102, 216 conjoint measurement 16 convex hull 84, 85, 212 cross-validation 126 d-hat see (pseudo-)distance data

appropriateness 35, 39 breakfast 3, 4, 8, 66, 101, 116 brewery 62

imputation 101, 137 mean 137 multiple 138 row-column 138 two-way 138

incomplete 101 missing 100, 101, 137

by researcher 103, 118 by respondent 105, 118 three-mode 149 tomato soup 76, 82 two-mode 13, 45, 149 unfolding 12, 98 decomposition

Cholesky 195 classical scaling 156 eigenvalue 156, 157, 194 p-stress 208 r-stress 208

singular-value 138, 155, 159, 181 space weights 208

Carroll-Chang 209 de Leeuw-Heiser 208 Tucker-Harshman 209 degeneracy index

d-index 62, 220, 221 i-index 62, 221 degeneracy problem 4, 99

approaches to 51 deletion

listwise 98, 101 pairwise 98, 101 dilation 36, 102

optimal 213 uniform 194

non- 195

dimension importance 205 dimensionality 194

changing 194 maximum 195 minimum 9, 195 optimal 211 reduced rank 195 reduction 195 direction 78

coefficient 199, 209 cosines 199 vector 76

dispersion accounted for 215 distance 3

Euclidean 48, 75

pseudo- 4, 48, 52 distinctness index 62, 221

Euclidean distance ideal point mapping 93

first choices 217

fractional programming 163 function

badness-of-fit 14, 46, 48, 54, 61, 129

n-stress 26, 100, 147, 175, 213–216

p-stress 47, 54, 55, 147, 148, 161, 175

r-stress 10, 49, 50, 100, 213 s-stress-

1

s-stress-

2

stress-

1

2

daf 215, 216 first 217 kappa 219 orders 217 phi 102, 216 rho 61, 218 ssaf 216, 219 tau 61, 102, 218, 219 vaf 61, 216 loss 147, 176, 213 majorizing 161, 163

sum of 163 normalization 48, 49 penalty 53–55, 147

adjusted 134 intercept 38 single-peaked 3 weighting 23, 24 ideal point 3, 45, 98

at infinity 93 coordinate 47 identification 190 incidence

256

graph 109

matrix 100, 101, 104 incomplete block design

balanced 101 index

Calinsky-Harabasz adjusted 203, 210

circular standard deviation 205 distinctness 62, 220, 221 intermixedness 62, 221 of angular variation 204 simplicity 205

individual space 177, 179 inequality

Cauchy-Schwarz 166, 167, 176 constraint 127, 128

triangle 100, 158 initial configuration see start

configuration intermixedness 27

intermixedness index 62, 221 interpolation 200, 201 intra-set correlation 209 iteration history 207 jackknife 196 kappa coefficient 219

landscape segmentation analysis 91 lasso 136

least squares

alternating 4, 139, 148, 175 non-negative 41, 170–172 weighted 48, 176, 186, 190 local minima 58, 121

majorization

iterative 18, 55, 139, 148, 161 linear 164, 166

quadratic 166 mds 8, 16, 20, 47, 197 mean

arithmetic 55, 61 geometric 55 harmonic 55, 61, 220

mean resultant length 204 measure see function missing at random 106

missing completely at random 103, 106 missing value 153

mar 106 mcar 103, 106 nmar 121 model

additive 22

diagonal 177, 179, 181, 194 distance 90, 93, 149

signed compensatory 22 full 177, 195

generalized Euclidean 177 ideal point 74, 98

internal 91 identity 177, 181, 194 individual differences 177

three-way 179 two-way 177

mixed vector ideal point 29 projection 90

rectangular 177, 179, 181, 195 reduced rank 177, 179 vector 21, 29, 74 , 90 weighted Euclidean 177 monotonicity 25, 172, 173

non- 10

multidimensional scaling seemds multidimensional scalogram analysis

16

multiple random starts 193, 195, 207 multiple starts 155

normalization explicit 25, 36 factor 47 proper 21 sum-of-squares 37 variance 52

normalized raw stress see (n-stress) function not missing at random 121 optimal locations 200 optimal quantifications 200

p-stress adjusted 135

row-conditional 168, 170 unconditional 162 paired comparisons

method of 8 pca 90, 136

penalized stress see (p-stress) function

penalty 99

penalty function 133, 168

penalty parameter 38, 54, 100, 126, 128, 129, 147

lack-of- 54 permutation 198, 211 plot

fit 212 regression 212 residual 212 scatter 39, 211 scree 78, 211

transformation 34, 212 prediction 135, 200, 201 preference 3

analysis

external 73, 74 internal 73, 74 curves 90 mapping 73, 74 rankings 8, 45, 98 preference scaling 90 principal axes 194

principal component analysis 90, 136 categorical 91, 136

principal coordinate analysis 157 Procrustes analysis 118, 159, 197

rotation matrix 159 scaling factor 159 translation vector 159 product familiarity 108 product optimization 83 projection 76, 90, 209 projector 202

property fitting 74, 75, 81, 199 rank-images 17

raw stress see (r-stress) function recovered preference orders 217 regression

categorical 135 isotone 172 least squares

ordinary 136 monotone 10, 18, 171, 172

bounded 18, 25 smooth 25, 127, 173 restriction 159

centroid 19, 156, 191 common space 194 configuration 175 coordinate 181 inequality 172

non-negativity 18, 36, 170 normalization 37 order 78 orthogonality 191 smoothness 25, 128, 173 variable 136, 137, 183, 209 row-balanced incomplete block design

104 scale

Guttman 8 I 9 interval 8 J 8

folded 9 ordinal 8 set

awareness 97, 105 choice 105

consideration 97, 105, 106 evaluation 97, 100, 103, 108 knowledge 97, 100, 105, 106, 120 universal 105

smallest space analysis 16 software

alscal 20, 61, 215 catpca 90, 91 catreg 135 cm 16 edipm 93

258

genfold 24, 61, 217 genfold-

2

3

newfold 11, 28, 61

prefscal 5, 26, 61, 99, 100, 148, 149, 213

profit 199 proxscal 214 smacof 19 smacof-

3

3

ssap 11 ssar-ii 16 vipscal 30, 93 solution

degenerate 3, 21, 35, 37, 49 absolutely 49, 51 partially 51 equal distance 47 object-point 12, 17, 21 objects-circle 13, 21, 22 objects-sphere 13, 16, 20 trivial 21

two-plus-two-point 15 two-point 15, 21 split-by-rows 52 stability 196

measure 130, 197, 210 start configuration

centroid 19, 156 correspondence 155 random 155, 195, 207 rational 155, 156 Ross-Cliff 155 Spearman 158 triangle 158 user-provided 154 statistic see function stress formula one 15

stress formula two 15 subset selection 135

sum-of-squares accounted for 216, 219 super-matrix 16, 29, 157

supporting point 162 ties 172, 218

primary approach to 172 secondary approach to 172 Torgerson scaling 157

Torgerson-Gower scaling 157 transformation 170

admissible 71

back- 85, 95, 127, 201, 218 initial 151, 152

initialization 152 intercept 37, 171 interval 36

penalized 41 inverse 219 linear 75, 170, 171

with intercept 48 without intercept 48 matrix-conditional 170 metric 36

row-conditional 40 monotone 3, 75, 79

monotone spline 75, 128, 153, 171 smooth 128

optimal 5, 152 ordinal 40, 75, 99 ratio 37, 171

row-conditional 56, 170 unconditional 56, 170 update 161

variable 78 unfolding 3, 7–9, 11

algorithm 12, 18, 136, 137 degenerate 7

external 74, 98 interval

penalized 38 irt model 5 least squares 139

weighted 23 metric 9

mixed ordinal-interval 19, 20 mixed ordinal-ratio 29 nonmetric 9–11 probabilistic 5 quasi-metric 27 restricted 74, 75 row-conditional 40 three-way 23, 179 two-way 23, 176, 177 unrestricted 74 weighted 40, 98 update

configuration 175, 176 regression coefficients 184 space weights 179, 181 variable 184

restricted 186, 188, 190 unrestricted 185, 188, 189 variable

active 81 additional 74, 77 attribute 75 direct 209

explanatory 75 external 75 independent 183 indirect 209 passive 81 prediction 75 variable direction 81 variable strength 81 variance 220

accounted for 61, 216

variation coefficient 53, 55, 71, 99, 100, 130, 131, 220

conditional 130 maximization of 131, 133 squared 147

Watson-Williams test 205 weight

dimension 177, 203, 204, 208, 209 preference 100, 147, 151, 207 rotation 177, 208

space 177, 179, 208 YoHoToGo scaling 157

260