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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

Principal components, proportion of variance      383
Principal components, robust      389
Principal components, sample specific components      398
Principal components, scale invariance, lack of      383
Principal components, scree graph      397—399
Principal components, selection of variables      404—406
Principal components, singular matrix and      385—386
Principal components, size and shape      402—403
Principal components, smaller principal components      382 389 401
Principal components, tests of significance for      397 399—400
Principal components, variable specific components      398
Principal components, variances of      382—383
Probe word data      70
Product notation $(\prod)$       10
Profile      139—140
Profile analysis: and contrasts      141—142
Profile analysis: and one-way ANOVA      140
Profile analysis: and repeated measures      139
Profile analysis: one-sample      139—141
Profile analysis: profile, definition of      139—140
Profile analysis: several-sample      199—204
Profile analysis: two-sample      141—148
Profile analysis: two-sample hypotheses: and two-way ANOVA      143—145
Profile analysis: two-sample hypotheses: flatness      145—146 199—201
Profile analysis: two-sample hypotheses: levels      143—145 199—200
Profile analysis: two-sample hypotheses: parallelism      141—143 199—200
Profile, profile of observation vector      454
Projection pursuit      451
Protein data      483
Psychological data      125
Quadratic classification functions      306—307
Quadratic form      19
Quantiles      92—94 97
Q–Q plot      92—94
Ramus bone data      78
Random variable(s): bivariate      45
Random variable(s): bivariate, bivariate normal distribution      46 84 88—89
Random variable(s): bivariate, correlation of      49—50
Random variable(s): bivariate, correlation of as cosine      49—50
Random variable(s): bivariate, covariance of      46—48
Random variable(s): bivariate, covariance of, linear relationships      47
Random variable(s): bivariate, independent      46
Random variable(s): bivariate, independent test for independence      265—266
Random variable(s): bivariate, independent test for independence, table of exact critical values      590
Random variable(s): bivariate, orthogonal      47—48
Random variable(s): bivariate, scatter plot      50—51
Random variable(s): linear combinations      see Linear combination(s) of variables
Random variable(s): univariate      43
Random variable(s): univariate, expected value of      43
Random variable(s): univariate, mean of      43
Random variable(s): univariate, variance of      44
Random variable(s): vector      53—56
Random vector(s)      52—56
Random vector(s), distance between      76—77 83 115 118 123 271—272
Random vector(s), linear functions of      66—73. See also Linear combination(s) of variables
Random vector(s), mean of      54—56
Random vector(s), partitioned random vector      62—66
Random vector(s), standardized      86
Random vector(s), subvectors      62—66
Rank of a matrix      22—23
Rao's paradox      116
Redundancy analysis      373—374
Regression, (squared multiple correlation)      332—333 337 349 355.
Regression, centered x's      327—329
Regression, estimation of $\beta$ : centered x's      327—328
Regression, estimation of $\beta$ : covariances      328—329
Regression, estimation of $\beta$ : least squares      325—326
Regression, estimation of $\sigma^2$       326—327
Regression, fixed x's      323—333
Regression, model      323—324
Regression, model assumptions      323—324
Regression, model corrected for means (centered)      327
Regression, monotonic      509—510
Regression, multiple (one y and several x's)      130—132 323—337. multivariate
Regression, multiple correlation      332
Regression, multivariate (several y's and several x's)      322—323 337—358
Regression, multivariate (several y's and several x's), association, measures of      349—351
Regression, multivariate (several y's and several x's), centered x's      342—343
Regression, multivariate (several y's and several x's), estimation of $\Sigma$       342
Regression, multivariate (several y's and several x's), estimation of B (matrix of regression coefficients): centered x's      342—343
Regression, multivariate (several y's and several x's), estimation of B (matrix of regression coefficients): covariances      343
Regression, multivariate (several y's and several x's), estimation of B (matrix of regression coefficients): least squares      339—341
Regression, multivariate (several y's and several x's), estimation of B (matrix of regression coefficients): properties of estimators      341—342
Regression, multivariate (several y's and several x's), fixed x's      337—349
Regression, multivariate (several y's and several x's), full and reduced model: on the x's      347—349
Regression, multivariate (several y's and several x's), full and reduced model: on the y's      353—355
Regression, multivariate (several y's and several x's), full and reduced model: with canonical correlations      375—376
Regression, multivariate (several y's and several x's), Gauss — Markov theorem      341
Regression, multivariate (several y's and several x's), H matrix      343—344
Regression, multivariate (several y's and several x's), model      337—339
Regression, multivariate (several y's and several x's), model, assumptions      339
Regression, multivariate (several y's and several x's), model, corrected for means (centered)      342—343
Regression, multivariate (several y's and several x's), overall regression test      343—347
Regression, multivariate (several y's and several x's), overall regression test with canonical correlations      375
Regression, multivariate (several y's and several x's), overall regression test, comparison of test statistics      345
Regression, multivariate (several y's and several x's), overall regression test, Lawley — Hotelling test      345
Regression, multivariate (several y's and several x's), overall regression test, Pillai's test      345
Regression, multivariate (several y's and several x's), overall regression test, rank of B      345
Regression, multivariate (several y's and several x's), overall regression test, Roy's test (union-intersection)      344—345
Regression, multivariate (several y's and several x's), overall regression test, Wilks' $\Lambda$ test (likelihood ratio)      344
Regression, multivariate (several y's and several x's), random x's      358
Regression, multivariate (several y's and several x's), regression coefffcients, matrix of (B)      88 338
Regression, multivariate (several y's and several x's), subset of the x's      351—353
Regression, multivariate (several y's and several x's), subset of the x's with canonical correlations      375—376
Regression, multivariate (several y's and several x's), subset of the y's      353—355
Regression, multivariate (several y's and several x's), subset selection      351—358
Regression, multivariate (several y's and several x's), subset selection, all possible subsets      355—358
Regression, multivariate (several y's and several x's), subset selection, all possible subsets, criteria for selection       355—358
Regression, multivariate (several y's and several x's), subset selection, stepwise procedures      351—355
Regression, multivariate (several y's and several x's), subset selection, stepwise procedures, partial Wilks' $\Lambda$       352—354
Regression, multivariate (several y's and several x's), subset selection, stepwise procedures, subset of the x's      351—353
Regression, multivariate (several y's and several x's), subset selection, stepwise procedures, subset of the y's      353—355
Regression, multivariate (several y's and several x's), tests of hypotheses      343—349
Regression, multivariate (several y's and several x's), tests of hypotheses E matrix      339 342—344
Regression, random x's      322—323 337
Regression, regression coefficients      323
Regression, SSE      325—326 330—331 333—336 456
Regression, SSR      330—331
Regression, subset selection      333—337
Regression, subset selection, all possible subset, criteria for selection $(R^2_p, s^2_p, C_p )&      333—335
Regression, subset selection, all possible subset, criteria for selection $(R^2_p, s^2_p, C_p )& comparison of criteria      335
Regression, subset selection, all possible subsets      333—335
Regression, subset selection, stepwise selection      335—337
Regression, tests of hypotheses      329—332
Regression, tests of hypotheses, full and reduced model      330—332
Regression, tests of hypotheses, overall regression test      329—330
Regression, tests of hypotheses, partial F-test      331—332
Regression, tests of hypotheses, subset of the $\beta$ 's      330—332
Regression, variables: dependent (y)      322
Regression, variables: independent (x)      322
Regression, variables: predictor (x)      322
Regression, variables: response (y)      322
Repeated data set      218
Repeated measures designs      204—221. See also Growth curves
Repeated measures designs and profile analysis      139
Repeated measures designs, assumptions      204—207
Repeated measures designs, computation of test statistics      212—213
Repeated measures designs, contrast matrices      206 208—221
Repeated measures designs, doubly multivariate data      221
Repeated measures designs, higher order designs      213—221
Repeated measures designs, multivariate approach, advantages of      205—207
Repeated measures designs, one sample      208—211
Repeated measures designs, one sample and randomized block designs      208
Repeated measures designs, one sample, likelihood ratio test      209—210
Repeated measures designs, several samples      211—212
Repeated measures designs, univariate approach      204—207
Republican vote data      53
Research units      1
Road distance data      541
Rootstock data      171

Rotation      see Factor analysis
Roy's test statistic: definition of      164—165
Roy's test statistic: table of critical values      574—577
Sampling units      1
scalar      6
Scale of measurement      1
Scatter plot      50—51 98 105
Seishu data      263
Selection of variables      233 333—337 351—358
Singular value decomposition      36 522 524 532—533
Singular value decomposition, generalized singular value decomposition      522
Size and shape      402—403
skewness      94—95 98—99 104
Snapbean data      236
Sons data      79
Specific variance      see Factor analysis
Spectral decomposition      35 382 416—418 505—506
Squared multiple correlation      see $R^2$

Standard deviation      44
Standardized vector      86
Steel data      273
Stepwise selection of variables      233 335—337 351—355
Stress      510—512
Subvectors      62—66
Subvectors, conditional distribution of      88
Subvectors, covariance matrix of      62—66
Subvectors, distribution of sum of      88
Subvectors, independence of      63 87
Subvectors, mean vector      62—64 66
Subvectors, tests of      136—139 231—233 347—349 353—359
Summation notation $(\Sigma)$       9
Survival data      239—241
t-tests: characteristic form      117 122
t-tests: contrasts      179
t-tests: equal levels in profile analysis      145
t-tests: growth curves      224 228
t-tests: matched pairs      132—133
t-tests: one sample      117
t-tests: paired observations      132—133
t-tests: repeated measures      210—211
t-tests: two samples      121—122 127
Taxonomy, numerical      see Cluster analysis
Temperature data      269
Tests of hypotheses: accepting       118
Tests of hypotheses: covariance matrices      248—268
Tests of hypotheses: covariance matrices, a specified matrix $\Sigma_0$       248—249
Tests of hypotheses: covariance matrices, one covariance matrix      248—254
Tests of hypotheses: covariance matrices, one covariance matrix independence: individual variables      265—266
Tests of hypotheses: covariance matrices, one covariance matrix independence: individual variables, table of exact critical values      590
Tests of hypotheses: covariance matrices, one covariance matrix independence: several subvectors      261—264
Tests of hypotheses: covariance matrices, one covariance matrix independence: two subvectors      259—261
Tests of hypotheses: covariance matrices, one covariance matrix independence: two subvectors and canonical correlations      260
Tests of hypotheses: covariance matrices, sphericity      250—252
Tests of hypotheses: covariance matrices, uniformity, compound symmetry      206 252—254
Tests of hypotheses: for additional information      136—139 231—233 347—349 353—359
Tests of hypotheses: for additional information, partial F-tests      127 138 232
Tests of hypotheses: for linear combinations: one sample $(H_0:C =_{\mu}=0)$       117 140—141 208—211
Tests of hypotheses: for linear combinations: two samples $(H_0:C_{\mu_1}=C_{\mu_2})$       142—143
Tests of hypotheses: likelihood ratio test      126. See also Likelihood ratio tests
Tests of hypotheses: mean vectors: likelihood ratio tests      126
Tests of hypotheses: mean vectors: one sample, $\Sigma$ known      114—117
Tests of hypotheses: mean vectors: one sample, $\Sigma$ unknown      117—121
Tests of hypotheses: mean vectors: several samples      158—173
Tests of hypotheses: mean vectors: two-sample -test      122—126
Tests of hypotheses: multivariate vs. univariate testing      1—2 112—113 115—117 127—130
Tests of hypotheses: on a subvector      136—139 231—233 347—349 353—359
Tests of hypotheses: on individual variables      126—130
Tests of hypotheses: on individual variables, Bonferroni critical values for      127
Tests of hypotheses: on individual variables, Bonferroni critical values for, tables      562—565
Tests of hypotheses: on individual variables, discriminant functions      126—132
Tests of hypotheses: on individual variables, experimentwise error rate      128—129
Tests of hypotheses: on individual variables, partial F-tests      127 232
Tests of hypotheses: on individual variables, protected tests      128—129
Tests of hypotheses: on regression coefficients      329—332 343—349
Tests of hypotheses: paired observations (matched pairs)      132—136
Tests of hypotheses: paired observations (matched pairs), multivariate      134—136
Tests of hypotheses: paired observations (matched pairs), univariate      132—133
Tests of hypotheses: partial F-tests      127 138 232
Tests of hypotheses: power of a test      113
Tests of hypotheses: protected tests      128—129
Tests of hypotheses: several covariance matrices      254—259
Tests of hypotheses: several covariance matrices, Box's M-test      257—259
Tests of hypotheses: several covariance matrices, Box's M-test, table of exact critical values      588—589
Tests of hypotheses: univariate tests: ANOVA F-test      156—158 186—188
Tests of hypotheses: univariate tests: one-sample test on a mean, $\sigma$ known      113
Tests of hypotheses: univariate tests: one-sample test on a mean, $\sigma$ unknown      117
Tests of hypotheses: univariate tests: paired observation test      132—133
Tests of hypotheses: univariate tests: tests on variances      254—255
Tests of hypotheses: univariate tests: two-sample t-test      121—122 127
Tests of hypotheses: univariate tests: variances, equality of      254—255
Total sample variance      74 383 409 418—419 427
Trace of a matrix      30 34 69
Trout data      242
Two-sample test for equal mean vectors      122—126
Union-intersection test      164—165
Unit: experimental      1
Unit: research      1
Unit: sampling      1
Univariate normal distribution      82—83 86
Univariate normality, goodness-of-fit test      96—97
Univariate normality, normal probability paper      94
Univariate normality, quantiles      92—94 97
Univariate normality, Q–Q plot      92—94
Univariate normality, skewness and kurtosis      94—95
Univariate normality, skewness and kurtosis, tables of critical values      549—551
Univariate normality, tests for      92—96
Univariate normality, tests for D’Agostino's D-statistic      96
Univariate normality, tests for D’Agostino's D-statistic, table of critical values      552
Univariate normality, transformation of correlation      96
Variables      1. See also Random variables
Variables, commensurate      1
Variables, dummy variables      173—174 282 315 376—377
Variables, linear combinations of      66—73
Variance matrix      see Covariance matrix
Variance-covariance matrix      see Covariance matrix
Variance: generalized sample variance      73
Variance: pooled variance      121
Variance: population variance $(\sigma^2)$       44
Variance: sample variance       44
Variance: total sample variance      74
Varimax rotation      434—435
Vector(s): 0 vector      9
Vector(s): definition of      6
Vector(s): distance: between two vectors      76—77
Vector(s): distance: from origin to a point      14
Vector(s): distance: Mahalanobis      76—77
Vector(s): geometry of      6
Vector(s): j vector      9
Vector(s): length of      14
Vector(s): linear combination of      19
Vector(s): linear independence and dependence of      22
Vector(s): normalized      31
Vector(s): notation for vector      6
Vector(s): observation vector      53—54
Vector(s): orthogonal      31 50
Vector(s): perpendicular      50
Vector(s): product of      14—16
Vector(s): product of, dot product      14
Vector(s): rows and columns of a matrix      15—16
Vector(s): standardized      86
Vector(s): subvectors      62—66
Vector(s): sum of products      14
Vector(s): sum of squares      14
Vector(s): transpose of      6—7
Vector(s): zero vector      9
Voting data      512
Weight gain data      243
Wheat data      503
Wilks' test statistic: definition of      161—164
Wilks' test statistic: partial-statistic      232

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