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Rencher A.C. Ч Methods of multivariate analysis
Rencher A.C. Ч Methods of multivariate analysis

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Ќазвание: Methods of multivariate analysis

јвтор: Rencher A.C.

јннотаци€:

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: en

–убрика: ћатематика/¬еро€тность/—татистика и приложени€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: Second Edition

√од издани€: 2002

 оличество страниц: 732

ƒобавлена в каталог: 08.06.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$R^2$ (squared multiple correlation)      332Ч333 337 349 355 361Ч362 365 375Ч376 422Ч423
$T^2$-statistic: additional information, test for      136Ч139
$T^2$-statistic: and F-distribution      119 124 137Ч138
$T^2$-statistic: and profile analysis      139Ч148
$T^2$-statistic: and profile analysis, one sample      139Ч141
$T^2$-statistic: and profile analysis, two samples      141Ч148
$T^2$-statistic: assumptions for      122
$T^2$-statistic: characteristic form      118 123
$T^2$-statistic: chi-square approximation for      120
$T^2$-statistic: computation of      130Ч132
$T^2$-statistic: computation of, by MANOVA      130
$T^2$-statistic: computation of, y regression      130Ч132
$T^2$-statistic: for a subvector      136Ч139
$T^2$-statistic: full and reduced model test      137
$T^2$-statistic: likelihood ratio test      126
$T^2$-statistic: matched pairs      134Ч136
$T^2$-statistic: one-sample      117Ч121
$T^2$-statistic: paired observations      134Ч136
$T^2$-statistic: properties of      119Ч120 123Ч124
$T^2$-statistic: table of critical values for $T^2$      558Ч561
$T^2$-statistic: two-sample      122Ч126
Additional information, test for      136Ч139 231Ч233
Air pollution data      502
Airline distance data      508
Algebra, matrix      see Matrix algebra
Analysis of variance: multivariate (MANOVA): additional information, test for      231Ч233
Analysis of variance: multivariate (MANOVA): and canonical correlation      376Ч377
Analysis of variance: multivariate (MANOVA): association, measures of      173Ч176
Analysis of variance: multivariate (MANOVA): assumptions, checking on      198Ч199
Analysis of variance: multivariate (MANOVA): contrasts      180Ч183
Analysis of variance: multivariate (MANOVA): discriminant function      165 184Ч185 191
Analysis of variance: multivariate (MANOVA): growth curves      221Ч230. See also Growth curves; Repeated measures designs
Analysis of variance: multivariate (MANOVA): H and E matrices      160Ч161
Analysis of variance: multivariate (MANOVA): higher order models      195Ч196
Analysis of variance: multivariate (MANOVA): individual variables, discriminant function      184Ч185 191
Analysis of variance: multivariate (MANOVA): individual variables, experimentwise error rate      183Ч185
Analysis of variance: multivariate (MANOVA): individual variables, protected tests      184
Analysis of variance: multivariate (MANOVA): individual variables, tests on      163Ч164 183Ч186
Analysis of variance: multivariate (MANOVA): Lawley Ч Hotelling test      167
Analysis of variance: multivariate (MANOVA): Lawley Ч Hotelling test, table of critical values      524Ч528
Analysis of variance: multivariate (MANOVA): likelihood ratio test      164
Analysis of variance: multivariate (MANOVA): mixed models      196Ч198
Analysis of variance: multivariate (MANOVA): mixed models, expected mean squares      196Ч197
Analysis of variance: multivariate (MANOVA): multivariate association, measures of      173Ч176
Analysis of variance: multivariate (MANOVA): one-way      158Ч161
Analysis of variance: multivariate (MANOVA): one-way contrasts      180Ч183
Analysis of variance: multivariate (MANOVA): one-way contrasts, orthogonal      181
Analysis of variance: multivariate (MANOVA): one-way model      159
Analysis of variance: multivariate (MANOVA): one-way, unbalanced      168
Analysis of variance: multivariate (MANOVA): Pillai's test      166
Analysis of variance: multivariate (MANOVA): profile analysis      199Ч201
Analysis of variance: multivariate (MANOVA): repeated measures      204Ч221. See also Repeated measures designs; Growth curves
Analysis of variance: multivariate (MANOVA): Roy's test (union-intersection)      164Ч166
Analysis of variance: multivariate (MANOVA): Roy's test (union-intersection), table of critical values      517Ч520
Analysis of variance: multivariate (MANOVA): stepwise discriminant analysis      233
Analysis of variance: multivariate (MANOVA): stepwise selection of variables      233
Analysis of variance: multivariate (MANOVA): test for additional information      231Ч233
Analysis of variance: multivariate (MANOVA): test on a subvector      231Ч233
Analysis of variance: multivariate (MANOVA): test statistics      161Ч173
Analysis of variance: multivariate (MANOVA): test statistics and $T^2$      169
Analysis of variance: multivariate (MANOVA): test statistics eigenvalues      168
Analysis of variance: multivariate (MANOVA): test statistics, comparison of      169Ч170 176Ч178
Analysis of variance: multivariate (MANOVA): test statistics, power of      176Ч178
Analysis of variance: multivariate (MANOVA): tests on individual variables      163Ч174 183Ч186 191
Analysis of variance: multivariate (MANOVA): tests on individual variables, discriminant function      165 184Ч185 191
Analysis of variance: multivariate (MANOVA): tests on individual variables, experimentwise error rate      183Ч185
Analysis of variance: multivariate (MANOVA): tests on individual variables, protected tests      184
Analysis of variance: multivariate (MANOVA): two-way      188Ч195
Analysis of variance: multivariate (MANOVA): two-way contrasts      190Ч191
Analysis of variance: multivariate (MANOVA): two-way discriminant function      191
Analysis of variance: multivariate (MANOVA): two-way interactions      189Ч190
Analysis of variance: multivariate (MANOVA): two-way main effects      189Ч190
Analysis of variance: multivariate (MANOVA): two-way model      189
Analysis of variance: multivariate (MANOVA): two-way test statistics      190
Analysis of variance: multivariate (MANOVA): two-way tests on individual variables      191
Analysis of variance: multivariate (MANOVA): unbalanced one-way      168
Analysis of variance: multivariate (MANOVA): union-intersection test      164
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test      161Ч164
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, chi-square approximation      162
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, F approximation      162
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, partial $\Lambda$-statistic      232
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, properties of      162Ч164
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, table of critical values      501Ч516
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, transformations to exact F      162Ч163
Analysis of variance: univariate (ANOVA): one-way      156Ч158
Analysis of variance: univariate (ANOVA): one-way contrasts      178Ч180
Analysis of variance: univariate (ANOVA): one-way contrasts, orthogonal      179Ч180
Analysis of variance: univariate (ANOVA): one-way SSH, SSE, F-statistic      158
Analysis of variance: univariate (ANOVA): two-way      186Ч188
Analysis of variance: univariate (ANOVA): two-way contrasts      188
Analysis of variance: univariate (ANOVA): two-way F-test      188
Analysis of variance: univariate (ANOVA): two-way interaction      187
Analysis of variance: univariate (ANOVA): two-way main effects      187Ч188
Analysis of variance: univariate (ANOVA): two-way model      186
anova      see Analysis of variance univariate
Association, measures of      173Ч176 349Ч351
Athletic record data      480
Bar steel data      192
Beetles data      150
Bilinear form      19Ч20
Biplots      531Ч539
Biplots, coordinates of points      533Ч534
Biplots, coordinates of points, correlation      534
Biplots, coordinates of points, cosine      534 537
Biplots, points for observations      531Ч534
Biplots, points for variables      531Ч534
Biplots, principal component approach      531Ч532 535
Biplots, singular value decomposition      532Ч533 535
Birth and death data      543
Bivariate normal distribution      46 84 88Ч89 133
Blood data      237
Blood pressure data      245
Bonferroni critical values      127
Bonferroni critical values, table      562Ч565
Box's M-test      257Ч259
Box's M-test, table of exact critical values      588Ч589
Bronchus data      154
Burt matrix      526Ч529
Byssinosis data      545Ч546
Calcium dat      56
Calculator speed data      210
Canonical correlation(s)      174 260 361Ч378
Canonical correlation(s) and discriminant analysis      376Ч378
Canonical correlation(s) and eigenvalues      362Ч363 377Ч378
Canonical correlation(s) and MANOVA      376Ч378
Canonical correlation(s) and MANOVA, dummy variables      376Ч377
Canonical correlation(s) and measures of association      362 373Ч374
Canonical correlation(s) and multiple correlation      361Ч362 366 376
Canonical correlation(s) and regression      368Ч369 374Ч376
Canonical correlation(s) with grouping variables      174
Canonical correlation(s) with test for independence of two subvectors      260 367Ч368
Canonical correlation(s), canonical variates      see Canonical variates
Canonical correlation(s), definition of      362Ч364
Canonical correlation(s), properties of      366Ч367
Canonical correlation(s), redundancy analysis      373Ч374
Canonical correlation(s), subset selection      376
Canonical correlation(s), tests of significance      367Ч371
Canonical correlation(s), tests of significance, all canonical correlations      367Ч369
Canonical correlation(s), tests of significance, all canonical correlations and test of independence      367Ч368
Canonical correlation(s), tests of significance, all canonical correlations and test of overall regression      367Ч368 375
Canonical correlation(s), tests of significance, all canonical correlations, comparison of tests      368Ч369
Canonical correlation(s), tests of significance, subset of canonical correlations      369Ч371
Canonical correlation(s), tests of significance, subset selection      376
Canonical correlation(s), tests of significance, test of a subset in regression      375Ч376
Canonical variates: and regression      374Ч376
Canonical variates: correlations among      364
Canonical variates: definition of      363
Canonical variates: interpretation      371Ч374
Canonical variates: interpretation by correlations (structure coefficients)      373
Canonical variates: interpretation by rotation      373
Canonical variates: interpretation by standardized coefficients      371Ч373
Canonical variates: redundancy analysis      373Ч374
Canonical variates: standardized coefficients      365 371Ч373
categorical variables      see Dummy variables
Central Limit Theorem (Multivariate)      91
Characteristic form: of $T^2$-statistic      118 123
Characteristic form: of t-statistic      117 122
Characteristic roots      see Eigenvalues
Chemical data      340
Chi-square distribution      86 91Ч92 114
Cholesky decomposition      25Ч26
City crime data      456
Classification analysis (allocation)      299Ч321
Classification analysis (allocation), assigning a sampling unit to a group      299
Classification analysis (allocation), asymptotic optimality      302
Classification analysis (allocation), correct classification rates      307Ч309
Classification analysis (allocation), error rates      307Ч313. See also Error rates
Classification analysis (allocation), error rates as a stopping rule      311Ч313
Classification analysis (allocation), error rates, estimates of      307Ч313
Classification analysis (allocation), k-nearest neighbor rule      318Ч319
Classification analysis (allocation), nonparametric classification procedures      302 314Ч320
Classification analysis (allocation), nonparametric classification procedures, density estimators (kernel)      315Ч317
Classification analysis (allocation), nonparametric classification procedures, multinomial data (categorical variables)      314Ч315
Classification analysis (allocation), nonparametric classification procedures, multinomial data (categorical variables), dummy variables      315
Classification analysis (allocation), nonparametric classification procedures, nearest neighbor rule      318Ч320
Classification analysis (allocation), nonparametric classification procedures, nearest neighbor rule, k-nearest neighbor rule      318Ч319
Classification analysis (allocation), several groups      304Ч307
Classification analysis (allocation), several groups, linear classification functions      304Ч306
Classification analysis (allocation), several groups, linear classification functions, equal covariance matrices      304Ч305
Classification analysis (allocation), several groups, optimal classification rule (Welch)      305
Classification analysis (allocation), several groups, prior probabilities      305Ч307
Classification analysis (allocation), several groups, quadratic classification functions      306Ч307
Classification analysis (allocation), several groups, quadratic classification functions, unequal covariance matrices      306
Classification analysis (allocation), subset selection      311Ч313
Classification analysis (allocation), subset selection, stepwise discriminant analysis      311Ч313
Classification analysis (allocation), subset selection, stepwise discriminant analysis, error rate as a stopping rule      311Ч313
Classification analysis (allocation), two groups      300Ч303
Classification analysis (allocation), two groups, Fisher's classification function      300Ч302
Classification analysis (allocation), two groups, linear classification function      301Ч302
Classification analysis (allocation), two groups, optimal classification rule (Welch)      302
Classification analysis (allocation), two groups, prior probabilities      302
Cluster analysis      451Ч503
Cluster analysis and classification      451
Cluster analysis, average linkage method      463
Cluster analysis, centroid method      463Ч465
Cluster analysis, choosing the number of clusters      494Ч496
Cluster analysis, clustering observations      451Ч496
Cluster analysis, clustering variables      451 497Ч499
Cluster analysis, comparison of methods      478Ч479
Cluster analysis, complete linkage method      459Ч462
Cluster analysis, definition      451
Cluster analysis, dendrogram      456
Cluster analysis, dendrogram, crossover      471
Cluster analysis, dendrogram, examples of      458Ч459 461Ч462 464Ч465 467 469 472Ч473 476Ч477
Cluster analysis, dendrogram, inversion      471
Cluster analysis, dendrogram, reversal      471
Cluster analysis, dissimilarity      452
Cluster analysis, distance      451Ч454
Cluster analysis, distance, distance matrix      453
Cluster analysis, distance, Euclidean distance      452
Cluster analysis, distance, Minkowski metric      453
Cluster analysis, distance, profile of observation vector: level      454
Cluster analysis, distance, profile of observation vector: shape      454
Cluster analysis, distance, profile of observation vector: variation      454
Cluster analysis, distance, scale of measurement      453Ч454
Cluster analysis, distance, statistical distance      452Ч453
Cluster analysis, farthest neighbor method      see Complete linkage method
Cluster analysis, flexible beta method      468Ч471
Cluster analysis, hierarchical clustering      452 455Ч481
Cluster analysis, hierarchical clustering, agglomerative method      455Ч479
Cluster analysis, hierarchical clustering, agglomerative method, average linkage      463
Cluster analysis, hierarchical clustering, agglomerative method, centroid      463Ч465
Cluster analysis, hierarchical clustering, agglomerative method, centroid, mean vectors      463
Cluster analysis, hierarchical clustering, agglomerative method, complete linkage      459Ч462
Cluster analysis, hierarchical clustering, agglomerative method, flexible beta      468Ч471
Cluster analysis, hierarchical clustering, agglomerative method, median      466
Cluster analysis, hierarchical clustering, agglomerative method, single linkage      456Ч459
Cluster analysis, hierarchical clustering, agglomerative method, Ward's method      466Ч468
Cluster analysis, hierarchical clustering, comparison of methods      478Ч479
Cluster analysis, hierarchical clustering, dendrogram      456
Cluster analysis, hierarchical clustering, divisive method      455 479Ч481
Cluster analysis, hierarchical clustering, divisive method, monothetic      479
Cluster analysis, hierarchical clustering, divisive method, polythetic      479Ч480
Cluster analysis, hierarchical clustering, properties      471Ц479
Cluster analysis, hierarchical clustering, properties, chaining      474
Cluster analysis, hierarchical clustering, properties, contraction      474
Cluster analysis, hierarchical clustering, properties, dilation      474
Cluster analysis, hierarchical clustering, properties, monotonicity      471
Cluster analysis, hierarchical clustering, properties, outliers      478Ч479
Cluster analysis, hierarchical clustering, properties, space contracting      474
Cluster analysis, hierarchical clustering, properties, space dilating      474
Cluster analysis, hierarchical clustering, properties, ultrametric      471
Cluster analysis, incremental sum of squares method      see Ward's method
Cluster analysis, median method      466
Cluster analysis, nearest neighbor method      see Single linkage method
Cluster analysis, nonhierarchical methods      481Ч494
Cluster analysis, nonhierarchical methods, density estimation      493
Cluster analysis, nonhierarchical methods, density estimation, dense point      493
Cluster analysis, nonhierarchical methods, density estimation, modes      493
Cluster analysis, nonhierarchical methods, mixtures of distributions      490Ч492
Cluster analysis, nonhierarchical methods, partitioning      481Ч490
Cluster analysis, nonhierarchical methods, partitioning, k-means      482Ч488
Cluster analysis, nonhierarchical methods, partitioning, k-means, seeds      482Ч487
Cluster analysis, nonhierarchical methods, partitioning, methods based on E and H      488Ч490
Cluster analysis, number of clusters: choosing the number of clusters      494Ч496
Cluster analysis, number of clusters: choosing the number of clusters, cutting the dendrogram      494Ц495
Cluster analysis, number of clusters: choosing the number of clusters, methods based on E and H      495Ч496
Cluster analysis, number of clusters: total possible number      455
Cluster analysis, optimization methods      see Nonhierarchical methods partitioning
Cluster analysis, partitioning      452 481Ч490
Cluster analysis, plotting of clusters: discriminant functions      486Ч488 494
Cluster analysis, plotting of clusters: principal components      451 484
Cluster analysis, plotting of clusters: projection pursuit      451
Cluster analysis, profile of observation vector: level      454
Cluster analysis, profile of observation vector: shape      454
Cluster analysis, profile of observation vector: variation      454
Cluster analysis, similarity      451Ч455
Cluster analysis, single linkage method      456Ч459
Cluster analysis, tree diagram      see dendrogram
Cluster analysis, validity of a cluster solution      496
Cluster analysis, validity of a cluster solution, cross validation      496
Cluster analysis, validity of a cluster solution, hypothesis test      496
Cluster analysis, variables and factor analysis      498
Cluster analysis, variables, clustering of      451 497Ч499
Cluster analysis, variables, correlations      497
Cluster analysis, Ward's method      466Ч468
Coated pipe data      135
Coefficient of determination      see $R^2$
Commensurate variables      see Variables commensurate
Communality      see Factor analysis
Confidence interval (reference)      119 127
Contingency table: graphical analysis of      see Correspondence analysis
Contingency table: higher-way table      526 528Ч529
Contingency table: two-way table      514Ч516 519 521
Contour plots      84Ч85
Contrast(s): contrast matrices in growth curves      222Ч225 227Ч230
Contrast(s): contrast matrices in repeated measures      206 208Ч221
Contrast(s): one-sample profile analysis      141Ч142
Contrast(s): one-way ANOVA      178Ч180
Contrast(s): one-way MANOVA      180Ч183
Contrast(s): orthonormal      206
Contrast(s): two-way ANOVA      188
Contrast(s): two-way MANOVA      190Ч191
Cork data      239
Correct classification rate      307Ч309
Correlation matrix: and covariance matrix      61
Correlation matrix: factor analysis on      418Ч419
Correlation matrix: partitioned      365
Correlation matrix: population correlation matrix      61
Correlation matrix: principal components from      383Ч384 393Ч397
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