Rencher A.C. — Methods of multivariate analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Rencher A.C. — Methods of multivariate analysis

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Название: Methods of multivariate analysis

Автор: Rencher A.C.

Аннотация:

This textbook extends univariate procedures with one dependent variable to analogous multivariate techniques involving several dependent variables, and finds functions of variables that discriminate among groups in the data and that reveal the basic dimensionality and characteristic patterns of the data. The second edition adds two chapters on cluster analysis and graphical techniques.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2002

Количество страниц: 732

Добавлена в каталог: 08.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Correlation matrix: sample correlation matrix      60—61
Correlation matrix: sample correlation matrix from covariance matrix      61
Correlation matrix: sample correlation matrix from data      60
Correlation: and cosine of angle between two vectors      49—50
Correlation: and law of cosines      49—50
Correlation: and orthogonality of two vectors      50
Correlation: canonical      see Canonical correlation(s)
Correlation: intra-class correlation      198—199
Correlation: multiple      see Multiple correlation
Correlation: of two linear combinations      67 72—73
Correlation: population correlation $(\rho)$       49
Correlation: sample correlation (r)      49
Correspondence analysis      514—530
Correspondence analysis, contingency table: higher-way table      526 528—529
Correspondence analysis, contingency table: two-way table      514—516 519 521
Correspondence analysis, coordinates for row and column points      521—525
Correspondence analysis, coordinates for row and column points, distances between column points      523—524
Correspondence analysis, coordinates for row and column points, distances between row points      523—524
Correspondence analysis, coordinates for row and column points, singular value decomposition      522
Correspondence analysis, coordinates for row and column points, singular value decomposition, generalized singular value decomposition      522
Correspondence analysis, correspondence matrix      515—516
Correspondence analysis, definition (graph of contingency table)      514—515
Correspondence analysis, independence of rows and columns, chi-square      515 520—521
Correspondence analysis, independence of rows and columns, chi-square in terms of frequencies      520
Correspondence analysis, independence of rows and columns, chi-square in terms of inertia      521
Correspondence analysis, independence of rows and columns, chi-square in terms of relative frequencies      520
Correspondence analysis, independence of rows and columns, chi-square in terms of row and column profiles      520—521
Correspondence analysis, independence of rows and columns, testing      519—521
Correspondence analysis, inertia      515 524
Correspondence analysis, multiple correspondence analysis      526—530
Correspondence analysis, multiple correspondence analysis, Burt matrix      526—529
Correspondence analysis, multiple correspondence analysis, indicator matrix      526—527
Correspondence analysis, profiles of rows and columns      515—519
Correspondence analysis, rows and columns      514—525
Correspondence analysis, rows and columns, association      514
Correspondence analysis, rows and columns, inertia      515 524
Correspondence analysis, rows and columns, interaction      514—515
Correspondence analysis, rows and columns, points for plotting      521—525
Correspondence analysis, rows and columns, profiles      515—519
Correspondence analysis, singular value decomposition      522 524
Correspondence analysis, singular value decomposition, generalized singular value decomposition      522
Covariance matrix: and correlation matrix      61
Covariance matrix: compound symmetry      206
Covariance matrix: of linear combinations of variables      69—73
Covariance matrix: partitioned      62—66 362
Covariance matrix: partitioned, dependence of y and x and cov(y, x)      63
Covariance matrix: partitioned, difference between cov $$\begin{pmatrix}y\\x\end{pmatrix}$ and cov(y, x)      63
Covariance matrix: partitioned, three or more subsets      64—66
Covariance matrix: pooled covariance matrix      122—123
Covariance matrix: population covariance matrix $(\Sigma)$       58—59
Covariance matrix: sample covariance matrix (S)      57—60
Covariance matrix: sample covariance matrix (S) and sample mean vector, independence of      92
Covariance matrix: sample covariance matrix (S) from observations      57—58
Covariance matrix: sample covariance matrix (S), distribution of      91—92
Covariance matrix: sample covariance matrix (S), distribution of, Wishart distribution      91—92
Covariance matrix: sample covariance matrix (S), from data matrix      58
Covariance matrix: sample covariance matrix (S), positive definiteness of      67
Covariance matrix: sphericity      206 250—252
Covariance matrix: tests on      248—268. See also Tests of hypotheses covariance
Covariance matrix: unbiasedness of      59
Covariance matrix: uniformity      206 252—254
Covariance: and independence      46—47
Covariance: and orthogonality      47—48
Covariance: of two linear combinations      67—68 72
Covariance: population covariance $(\sigma_{xy})$       46—47
Covariance: sample covariance $(s_{xy})$       46—48
Covariance: sample covariance $(s_{xy})$ and linear relationships      47
Covariance: sample covariance $(s_{xy})$ , expected value of      47
Cross validation      310—311
Cyclical data      153
Data matrix (Y)      55
Data sets: air pollution data      502
Data sets: airline distance data      508
Data sets: athletic record data      480
Data sets: bar steel data      192
Data sets: beetles data      150
Data sets: birth and death data      543
Data sets: blood data      237
Data sets: blood pressure data      245
Data sets: bronchus data      154
Data sets: byssinosis data      545—546
Data sets: calcium data      56
Data sets: calculator speed data      210
Data sets: chemical data      340
Data sets: city crime data      456
Data sets: coated pipe data      135
Data sets: cork data      239
Data sets: cyclical data      153
Data sets: dental data      227
Data sets: diabetes data      65
Data sets: do-it-yourself data      529
Data sets: dogs data      243—244
Data sets: dystrophy data      152
Data sets: engineer data      151
Data sets: fabric wear data      238
Data sets: fish data      235
Data sets: football data      280—281
Data sets: glucose data      80—81
Data sets: guinea pig data      201
Data sets: height-weight data      45
Data sets: hematology data      109—110
Data sets: mandible data      247
Data sets: mice data      241
Data sets: Norway crime data      544
Data sets: people data      526
Data sets: perception data      419
Data sets: piston ring data      518
Data sets: plasma data      246
Data sets: politics data      542
Data sets: probe word data      70
Data sets: protein data      483
Data sets: psychological data      125
Data sets: ramus bone data      78
Data sets: repeated data      218
Data sets: Republican vote data      53
Data sets: road distance data      541
Data sets: rootstock data      171
Data sets: Seishu data      263
Data sets: snapbean data      236
Data sets: sons data      79
Data sets: steel data      273
Data sets: survival data      239—241
Data sets: temperature data      269
Data sets: trout data      242
Data sets: voting data      512
Data sets: weight gain data      243
Data sets: wheat data      503
Data sets: words data      154
Data, types of      3–4. See also Multivariate data
Density function      43
Dental data      227
Descriptive statistics      2
Determinant      26—29
Determinant as product of eigenvalues      34
Determinant of diagonal matrix      27
Determinant of inverse      29
Determinant of nonsingular matrix      28
Determinant of partitioned matrix      29
Determinant of positive definite matrix      28
Determinant of product      28
Determinant of scalar multiple of a matrix      28
Determinant of singular matrix      28
Determinant, definition of      26—27
Diabetes data      65
Diagonal matrix      8
Discriminant analysis (descriptive)      270—296
Discriminant analysis (descriptive) and canonical correlation      282 376—378
Discriminant analysis (descriptive) and classification analysis      270
Discriminant analysis (descriptive) and eigenvalues      278—279
Discriminant analysis (descriptive), discriminant functions: for several groups      165 184—185 191 277—279

Discriminant analysis (descriptive), discriminant functions: for several groups, measures of association for      282
Discriminant analysis (descriptive), discriminant functions: for two groups      126—132 271—275
Discriminant analysis (descriptive), discriminant functions: for two groups and distance      272
Discriminant analysis (descriptive), interpretation of discriminant functions      288—291
Discriminant analysis (descriptive), interpretation of discriminant functions, correlations (structure coefficients)      291
Discriminant analysis (descriptive), interpretation of discriminant functions, partial F-values      290
Discriminant analysis (descriptive), interpretation of discriminant functions, rotation      291
Discriminant analysis (descriptive), interpretation of discriminant functions, standardized coefficients      289
Discriminant analysis (descriptive), purposes of      277
Discriminant analysis (descriptive), scatter plots      291—293
Discriminant analysis (descriptive), selection of variables      233 293—296
Discriminant analysis (descriptive), several groups      277—279
Discriminant analysis (descriptive), standardized discriminant functions      282—284
Discriminant analysis (descriptive), stepwise discriminant analysis      233 293—296
Discriminant analysis (descriptive), tests of significance      284—288
Discriminant analysis (descriptive), two groups      271—275
Discriminant analysis (descriptive), two groups and multiple regression      130—132 275—276
Discriminant analysis (predictive)      see Classification analysis
Dispersion matrix      see Covariance matrix
Distance between vectors      76—77 83 115 118 123 271—272
Distribution: beta      97
Distribution: bivariate normal      46 84 88—89
Distribution: chi-square      86
Distribution: elliptically symmetric      103
Distribution: F      119 138 158 162—163 179 254—255
Distribution: multivariate normal      see Multivariate normal distribution; Multivariate normality tests
Distribution: univariate normal      82—83 86
Distribution: univariate normal, tests for      see Univariate normality tests
Distribution: Wishart      91—92
Do-it-yourself data      529
Dogs data      243—244
Dummy variables      173—174 282 315 376—377
Dystrophy data      152
E matrix      160—161 339 342—344
Eigenvalues      32—37 168 362—365 382—384 397—398 416—419 422—423
Eigenvectors      32—35 363—365 382—384 397—398 416—418 420—422
Elliptically symmetric distribution      103
EM algorithm      75 491
Engineer data      151
Error rate(s)      307—313
Error rate(s), actual error rate      308
Error rate(s), apparent error rate      307
Error rate(s), apparent error rate, bias in      308 309—311
Error rate(s), classification table      307—308
Error rate(s), cross validation      310—311
Error rate(s), experimentwise error rate      1—2 128—129 183—185
Error rate(s), holdout method      310—311 318
Error rate(s), leaving-one-out method      310—311 318
Error rate(s), partitioning the sample      310
Error rate(s), resubstitution      307—308
Expected value: of random matrix      59
Expected value: of random vector [E(y)]      55—56
Expected value: of sample covariance matrix [E(S)]      59
Expected value: of sample mean $[E(\bar{y})]$       44
Expected value: of sample mean vector $[E(\bar{y})]$       56
Expected value: of sample variance       44
Expected value: of sum or product of random variables      46
Expected value: of univariate random variable [E(y)]      43
Experimental units      1
F-test(s): ANOVA      158 188
F-test(s): between-subjects tests in repeated measures      212 216 221
F-test(s): comparing two variances      254—255
F-test(s): contrasts      179
F-test(s): equivalent to       119 124 137—138
F-test(s): in multiple regression      138 330—332
F-test(s): partial F-test      127 138 232 293—296
F-test(s): stepwise selection      233 293—296 336
F-test(s): test for additional information      137
F-test(s): test for individual variables in MANOVA      183—186
F-test(s): Wilks' $\Lambda$ : exact F transformation for      162—163
F-test(s): Wilks' $\Lambda$ : F approximation for      162—163
Fabric wear data      238
Factor analysis      408—450
Factor analysis and principal components      408—409 447—448
Factor analysis and regression      410 439—440
Factor analysis, assumptions      410—412
Factor analysis, assumptions, failure of assumptions, consequences of      414 444—445
Factor analysis, common factors      409
Factor analysis, communalities      413 418 422—423 427—428
Factor analysis, communalities, estimation of      418 422 424 428
Factor analysis, eigenvalues      416—419 422—423 427 442 446
Factor analysis, eigenvectors      416—418 420 422
Factor analysis, factor scores      438—443
Factor analysis, factor scores, averaging method      440
Factor analysis, factor scores, regression method      439—440
Factor analysis, factors      408—414
Factor analysis, factors, common      409
Factor analysis, factors, definition of      408—409
Factor analysis, factors, interpretation of      409 438
Factor analysis, factors, number of      426—430
Factor analysis, Heywood case      424—425
Factor analysis, loadings: definition of      409
Factor analysis, loadings: estimation of      415—426
Factor analysis, loadings: estimation of, comparison of methods      424
Factor analysis, loadings: estimation of, fit of the model      419
Factor analysis, loadings: estimation of, from S or R      418—419 421—422
Factor analysis, loadings: estimation of, iterated principal factor method      424—425
Factor analysis, loadings: estimation of, iterated principal factor method, Heywood case      424—425
Factor analysis, loadings: estimation of, maximum likelihood method      425—426
Factor analysis, loadings: estimation of, principal component method      415—421
Factor analysis, loadings: estimation of, principal factor method      421—424
Factor analysis, model      409—414
Factor analysis, modeling covariances or correlations      408 410 412 414 417
Factor analysis, number of factors to retain      426—430
Factor analysis, number of factors to retain, average eigenvalue      427—428
Factor analysis, number of factors to retain, comparison of methods      428—430
Factor analysis, number of factors to retain, hypothesis test      427—428
Factor analysis, number of factors to retain, indeterminacy of for certain data sets      428—429
Factor analysis, number of factors to retain, scree plot      427—428
Factor analysis, number of factors to retain, variance accounted for      427—428
Factor analysis, orthogonal factors      409—415 431—435
Factor analysis, rotation      414—415 417 430—437
Factor analysis, rotation, complexity of the variables      431
Factor analysis, rotation, interpretation of factors      409 438
Factor analysis, rotation, oblique rotation      431 435—437
Factor analysis, rotation, oblique rotation and orthogonality      437
Factor analysis, rotation, oblique rotation, pattern matrix      436
Factor analysis, rotation, orthogonal rotation      431—435
Factor analysis, rotation, orthogonal rotation, analytical      434
Factor analysis, rotation, orthogonal rotation, communalities      415 431
Factor analysis, rotation, orthogonal rotation, graphical      431—433
Factor analysis, rotation, orthogonal rotation, varimax      434—435
Factor analysis, rotation, simple structure      431
Factor analysis, scree plot      427—428
Factor analysis, simple structure      431
Factor analysis, singular matrix and      422
Factor analysis, specific variance      410 417
Factor analysis, specificity      see Specific variance
Factor analysis, total variance      418—419 427
Factor analysis, validity of factor analysis model      443—447
Factor analysis, validity of factor analysis model, how well model fits the data      419 444
Factor analysis, validity of factor analysis model, measure of sampling adequacy      445
Factor analysis, variance due to a factor      418—419
Fish data      235
Fisher's classification function      300—302
Football data      280—281
Gauss — Markov theorem      341
Generalized population variance      83—85 105
Generalized sample variance      73
Generalized sample variance, total sample variance      73 383 409 418 427
Generalized singular value decomposition      522
Geometric mean      174
Glucose data      80
Graphical display of multivariate data      52—53
Graphical procedures      504—547
Graphical procedures, biplots      see Biplots
Graphical procedures, correspondence analysis      see Correspondence analysis
Graphical procedures, multidimensional scaling      see Multidimensional scaling
Growth curves      221—230
Growth curves, contrast matrices      222—225 227—230

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