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



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Íàçâàíèå: Methods of multivariate analysis

Àâòîð: Rencher A.C.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/Âåðîÿòíîñòü/Ñòàòèñòèêà è ïðèëîæåíèÿ/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: Second Edition

Ãîä èçäàíèÿ: 2002

Êîëè÷åñòâî ñòðàíèö: 732

Äîáàâëåíà â êàòàëîã: 08.06.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$R^2$ (squared multiple correlation)      332—333 337 349 355 361—362 365 375—376 422—423
$T^2$-statistic: additional information, test for      136—139
$T^2$-statistic: and F-distribution      119 124 137—138
$T^2$-statistic: and profile analysis      139—148
$T^2$-statistic: and profile analysis, one sample      139—141
$T^2$-statistic: and profile analysis, two samples      141—148
$T^2$-statistic: assumptions for      122
$T^2$-statistic: characteristic form      118 123
$T^2$-statistic: chi-square approximation for      120
$T^2$-statistic: computation of      130—132
$T^2$-statistic: computation of, by MANOVA      130
$T^2$-statistic: computation of, y regression      130—132
$T^2$-statistic: for a subvector      136—139
$T^2$-statistic: full and reduced model test      137
$T^2$-statistic: likelihood ratio test      126
$T^2$-statistic: matched pairs      134—136
$T^2$-statistic: one-sample      117—121
$T^2$-statistic: paired observations      134—136
$T^2$-statistic: properties of      119—120 123—124
$T^2$-statistic: table of critical values for $T^2$      558—561
$T^2$-statistic: two-sample      122—126
Additional information, test for      136—139 231—233
Air pollution data      502
Airline distance data      508
Algebra, matrix      see Matrix algebra
Analysis of variance: multivariate (MANOVA): additional information, test for      231—233
Analysis of variance: multivariate (MANOVA): and canonical correlation      376—377
Analysis of variance: multivariate (MANOVA): association, measures of      173—176
Analysis of variance: multivariate (MANOVA): assumptions, checking on      198—199
Analysis of variance: multivariate (MANOVA): contrasts      180—183
Analysis of variance: multivariate (MANOVA): discriminant function      165 184—185 191
Analysis of variance: multivariate (MANOVA): growth curves      221—230. See also Growth curves; Repeated measures designs
Analysis of variance: multivariate (MANOVA): H and E matrices      160—161
Analysis of variance: multivariate (MANOVA): higher order models      195—196
Analysis of variance: multivariate (MANOVA): individual variables, discriminant function      184—185 191
Analysis of variance: multivariate (MANOVA): individual variables, experimentwise error rate      183—185
Analysis of variance: multivariate (MANOVA): individual variables, protected tests      184
Analysis of variance: multivariate (MANOVA): individual variables, tests on      163—164 183—186
Analysis of variance: multivariate (MANOVA): Lawley — Hotelling test      167
Analysis of variance: multivariate (MANOVA): Lawley — Hotelling test, table of critical values      524—528
Analysis of variance: multivariate (MANOVA): likelihood ratio test      164
Analysis of variance: multivariate (MANOVA): mixed models      196—198
Analysis of variance: multivariate (MANOVA): mixed models, expected mean squares      196—197
Analysis of variance: multivariate (MANOVA): multivariate association, measures of      173—176
Analysis of variance: multivariate (MANOVA): one-way      158—161
Analysis of variance: multivariate (MANOVA): one-way contrasts      180—183
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      199—201
Analysis of variance: multivariate (MANOVA): repeated measures      204—221. See also Repeated measures designs; Growth curves
Analysis of variance: multivariate (MANOVA): Roy's test (union-intersection)      164—166
Analysis of variance: multivariate (MANOVA): Roy's test (union-intersection), table of critical values      517—520
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      231—233
Analysis of variance: multivariate (MANOVA): test on a subvector      231—233
Analysis of variance: multivariate (MANOVA): test statistics      161—173
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      169—170 176—178
Analysis of variance: multivariate (MANOVA): test statistics, power of      176—178
Analysis of variance: multivariate (MANOVA): tests on individual variables      163—174 183—186 191
Analysis of variance: multivariate (MANOVA): tests on individual variables, discriminant function      165 184—185 191
Analysis of variance: multivariate (MANOVA): tests on individual variables, experimentwise error rate      183—185
Analysis of variance: multivariate (MANOVA): tests on individual variables, protected tests      184
Analysis of variance: multivariate (MANOVA): two-way      188—195
Analysis of variance: multivariate (MANOVA): two-way contrasts      190—191
Analysis of variance: multivariate (MANOVA): two-way discriminant function      191
Analysis of variance: multivariate (MANOVA): two-way interactions      189—190
Analysis of variance: multivariate (MANOVA): two-way main effects      189—190
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      161—164
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      162—164
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, table of critical values      501—516
Analysis of variance: multivariate (MANOVA): Wilks' $\Lambda$ (likelihood ratio) test, transformations to exact F      162—163
Analysis of variance: univariate (ANOVA): one-way      156—158
Analysis of variance: univariate (ANOVA): one-way contrasts      178—180
Analysis of variance: univariate (ANOVA): one-way contrasts, orthogonal      179—180
Analysis of variance: univariate (ANOVA): one-way SSH, SSE, F-statistic      158
Analysis of variance: univariate (ANOVA): two-way      186—188
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      187—188
Analysis of variance: univariate (ANOVA): two-way model      186
anova      see Analysis of variance univariate
Association, measures of      173—176 349—351
Athletic record data      480
Bar steel data      192
Beetles data      150
Bilinear form      19—20
Biplots      531—539
Biplots, coordinates of points      533—534
Biplots, coordinates of points, correlation      534
Biplots, coordinates of points, cosine      534 537
Biplots, points for observations      531—534
Biplots, points for variables      531—534
Biplots, principal component approach      531—532 535
Biplots, singular value decomposition      532—533 535
Birth and death data      543
Bivariate normal distribution      46 84 88—89 133
Blood data      237
Blood pressure data      245
Bonferroni critical values      127
Bonferroni critical values, table      562—565
Box's M-test      257—259
Box's M-test, table of exact critical values      588—589
Bronchus data      154
Burt matrix      526—529
Byssinosis data      545—546
Calcium dat      56
Calculator speed data      210
Canonical correlation(s)      174 260 361—378
Canonical correlation(s) and discriminant analysis      376—378
Canonical correlation(s) and eigenvalues      362—363 377—378
Canonical correlation(s) and MANOVA      376—378
Canonical correlation(s) and MANOVA, dummy variables      376—377
Canonical correlation(s) and measures of association      362 373—374
Canonical correlation(s) and multiple correlation      361—362 366 376
Canonical correlation(s) and regression      368—369 374—376
Canonical correlation(s) with grouping variables      174
Canonical correlation(s) with test for independence of two subvectors      260 367—368
Canonical correlation(s), canonical variates      see Canonical variates
Canonical correlation(s), definition of      362—364
Canonical correlation(s), properties of      366—367
Canonical correlation(s), redundancy analysis      373—374
Canonical correlation(s), subset selection      376
Canonical correlation(s), tests of significance      367—371
Canonical correlation(s), tests of significance, all canonical correlations      367—369
Canonical correlation(s), tests of significance, all canonical correlations and test of independence      367—368
Canonical correlation(s), tests of significance, all canonical correlations and test of overall regression      367—368 375
Canonical correlation(s), tests of significance, all canonical correlations, comparison of tests      368—369
Canonical correlation(s), tests of significance, subset of canonical correlations      369—371
Canonical correlation(s), tests of significance, subset selection      376
Canonical correlation(s), tests of significance, test of a subset in regression      375—376
Canonical variates: and regression      374—376
Canonical variates: correlations among      364
Canonical variates: definition of      363
Canonical variates: interpretation      371—374
Canonical variates: interpretation by correlations (structure coefficients)      373
Canonical variates: interpretation by rotation      373
Canonical variates: interpretation by standardized coefficients      371—373
Canonical variates: redundancy analysis      373—374
Canonical variates: standardized coefficients      365 371—373
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 91—92 114
Cholesky decomposition      25—26
City crime data      456
Classification analysis (allocation)      299—321
Classification analysis (allocation), assigning a sampling unit to a group      299
Classification analysis (allocation), asymptotic optimality      302
Classification analysis (allocation), correct classification rates      307—309
Classification analysis (allocation), error rates      307—313. See also Error rates
Classification analysis (allocation), error rates as a stopping rule      311—313
Classification analysis (allocation), error rates, estimates of      307—313
Classification analysis (allocation), k-nearest neighbor rule      318—319
Classification analysis (allocation), nonparametric classification procedures      302 314—320
Classification analysis (allocation), nonparametric classification procedures, density estimators (kernel)      315—317
Classification analysis (allocation), nonparametric classification procedures, multinomial data (categorical variables)      314—315
Classification analysis (allocation), nonparametric classification procedures, multinomial data (categorical variables), dummy variables      315
Classification analysis (allocation), nonparametric classification procedures, nearest neighbor rule      318—320
Classification analysis (allocation), nonparametric classification procedures, nearest neighbor rule, k-nearest neighbor rule      318—319
Classification analysis (allocation), several groups      304—307
Classification analysis (allocation), several groups, linear classification functions      304—306
Classification analysis (allocation), several groups, linear classification functions, equal covariance matrices      304—305
Classification analysis (allocation), several groups, optimal classification rule (Welch)      305
Classification analysis (allocation), several groups, prior probabilities      305—307
Classification analysis (allocation), several groups, quadratic classification functions      306—307
Classification analysis (allocation), several groups, quadratic classification functions, unequal covariance matrices      306
Classification analysis (allocation), subset selection      311—313
Classification analysis (allocation), subset selection, stepwise discriminant analysis      311—313
Classification analysis (allocation), subset selection, stepwise discriminant analysis, error rate as a stopping rule      311—313
Classification analysis (allocation), two groups      300—303
Classification analysis (allocation), two groups, Fisher's classification function      300—302
Classification analysis (allocation), two groups, linear classification function      301—302
Classification analysis (allocation), two groups, optimal classification rule (Welch)      302
Classification analysis (allocation), two groups, prior probabilities      302
Cluster analysis      451—503
Cluster analysis and classification      451
Cluster analysis, average linkage method      463
Cluster analysis, centroid method      463—465
Cluster analysis, choosing the number of clusters      494—496
Cluster analysis, clustering observations      451—496
Cluster analysis, clustering variables      451 497—499
Cluster analysis, comparison of methods      478—479
Cluster analysis, complete linkage method      459—462
Cluster analysis, definition      451
Cluster analysis, dendrogram      456
Cluster analysis, dendrogram, crossover      471
Cluster analysis, dendrogram, examples of      458—459 461—462 464—465 467 469 472—473 476—477
Cluster analysis, dendrogram, inversion      471
Cluster analysis, dendrogram, reversal      471
Cluster analysis, dissimilarity      452
Cluster analysis, distance      451—454
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      453—454
Cluster analysis, distance, statistical distance      452—453
Cluster analysis, farthest neighbor method      see Complete linkage method
Cluster analysis, flexible beta method      468—471
Cluster analysis, hierarchical clustering      452 455—481
Cluster analysis, hierarchical clustering, agglomerative method      455—479
Cluster analysis, hierarchical clustering, agglomerative method, average linkage      463
Cluster analysis, hierarchical clustering, agglomerative method, centroid      463—465
Cluster analysis, hierarchical clustering, agglomerative method, centroid, mean vectors      463
Cluster analysis, hierarchical clustering, agglomerative method, complete linkage      459—462
Cluster analysis, hierarchical clustering, agglomerative method, flexible beta      468—471
Cluster analysis, hierarchical clustering, agglomerative method, median      466
Cluster analysis, hierarchical clustering, agglomerative method, single linkage      456—459
Cluster analysis, hierarchical clustering, agglomerative method, Ward's method      466—468
Cluster analysis, hierarchical clustering, comparison of methods      478—479
Cluster analysis, hierarchical clustering, dendrogram      456
Cluster analysis, hierarchical clustering, divisive method      455 479—481
Cluster analysis, hierarchical clustering, divisive method, monothetic      479
Cluster analysis, hierarchical clustering, divisive method, polythetic      479—480
Cluster analysis, hierarchical clustering, properties      471–479
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      478—479
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      481—494
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      490—492
Cluster analysis, nonhierarchical methods, partitioning      481—490
Cluster analysis, nonhierarchical methods, partitioning, k-means      482—488
Cluster analysis, nonhierarchical methods, partitioning, k-means, seeds      482—487
Cluster analysis, nonhierarchical methods, partitioning, methods based on E and H      488—490
Cluster analysis, number of clusters: choosing the number of clusters      494—496
Cluster analysis, number of clusters: choosing the number of clusters, cutting the dendrogram      494–495
Cluster analysis, number of clusters: choosing the number of clusters, methods based on E and H      495—496
Cluster analysis, number of clusters: total possible number      455
Cluster analysis, optimization methods      see Nonhierarchical methods partitioning
Cluster analysis, partitioning      452 481—490
Cluster analysis, plotting of clusters: discriminant functions      486—488 494
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      451—455
Cluster analysis, single linkage method      456—459
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      451 497—499
Cluster analysis, variables, correlations      497
Cluster analysis, Ward's method      466—468
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      526 528—529
Contingency table: two-way table      514—516 519 521
Contour plots      84—85
Contrast(s): contrast matrices in growth curves      222—225 227—230
Contrast(s): contrast matrices in repeated measures      206 208—221
Contrast(s): one-sample profile analysis      141—142
Contrast(s): one-way ANOVA      178—180
Contrast(s): one-way MANOVA      180—183
Contrast(s): orthonormal      206
Contrast(s): two-way ANOVA      188
Contrast(s): two-way MANOVA      190—191
Cork data      239
Correct classification rate      307—309
Correlation matrix: and covariance matrix      61
Correlation matrix: factor analysis on      418—419
Correlation matrix: partitioned      365
Correlation matrix: population correlation matrix      61
Correlation matrix: principal components from      383—384 393—397
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