Subject Index - WPI · 2000. 4. 11. · one-way layout, example, 340 one-way tests ... procedure,...

Subject Index

Aabsorption of effects

ANOVA procedure, 350GLM procedure, 1481, 1532

accelerated failure time modelsLIFEREG procedure, 1761

ACECLUS procedureanalyzing data in groups, 310, 328between-cluster SSCP matrix, 303clustering methods, 321compared with other procedures, 307computational resources, 326controlling iterations, 305decomposition of the SSCP matrix, 303eigenvalues and eigenvectors, 314–315, 322, 326–

327initial estimates, 305, 320memory requirements, 326missing values, 325output data sets, 325output table names, 327time requirements, 326within-cluster SSCP matrix, 303

active set methodsNLMIXED procedure, 2468

adaptive Gaussian quadratureNLMIXED procedure, 2458

additive modelsTRANSREG procedure, 3395

adjacent-category logitsSee also response functionsspecifying in CATMOD procedure, 734using (CATMOD), 749

adjacent-level contrasts, 364adjusted means

See least-squares means, 1488adjusted odds ratio, 1315adjustedp-value

MULTTEST procedure, 2313, 2332adjusted R2 selection (REG), 2949adjusted residuals

GENMOD procedure, 1419adjusted treatment means

LATTICE procedure, 1753after expansion knots

TRANSREG procedure, 3392agglomerative hierarchical clustering analysis, 835AGK estimate

STDIZE procedure, 3136

agreement, measures of, 1306Akaike’s information criterion

example (MIXED), 2178, 2191, 2219LOGISTIC procedure, 1947MIXED procedure, 2100, 2154, 2164

aliasingGENMOD procedure, 1374

aliasing structure (GLM), 1628GLM procedure, 1505

alpha factor analysis, 1123, 1137alpha level

ANOVA procedure, 357FREQ procedure, 1260, 1269GLM procedure, 1490, 1499, 1505, 1509NPAR1WAY procedure, 2521REG procedure, 2892TRANSREG procedure, 3395TTEST procedure, 3574

ALR algorithmGENMOD procedure, 1455

alternating least squaresMDS procedure, 2050

Alternating Logistic Regressions (ALR)GENMOD procedure, 1455

analysis of contrastsSURVEYREG procedure, 3244

analysis of covarianceexamples (GLM), 1593MODEL statements (GLM), 1519

analysis of covariation (NESTED), 2364analysis of variance

See also ANOVA procedureSee also TTEST procedurecategorical data, 697CATMOD procedure, 699mixed models (GLM), 1614MODEL statements (GLM), 1519multivariate (ANOVA), 352multivariate (CANDISC), 670multivariate (GLM), 1493, 1558, 1600nested design, 2359one-way layout, example, 340one-way tests (NPAR1WAY), 2526one-way, variance-weighted, 360, 1503quadratic response surfaces, 3044repeated measures (CATMOD), 754repeated measures (GLM), 1560, 1609, 1618SURVEYREG procedure, 3236three-way design (GLM), 1596

3700 � Subject Index

unbalanced (GLM), 1469, 1538, 1589within-subject factors, repeated measurements,

364analyzing data in groups, 2450

ACECLUS procedure, 310CANCORR procedure, 647FACTOR procedure, 1144FASTCLUS procedure, 1212MDS procedure, 2059MODECLUS procedure, 2231, 2248PRINCOMP procedure, 2746SCORE procedure, 3070STDIZE procedure, 3131TREE procedure, 3546VARCLUS procedure, 3605

Andersen-Gill modelSee also multiplicative hazards modelPHREG procedure, 2596, 2642

angle classesVARIOGRAM procedure, 3658, 3660, 3662,

3664–3665angle tolerance

VARIOGRAM procedure, 3658, 3660, 3662,3664–3665

anisotropicmodels (KRIGE2D), 1729–1732models (VARIOGRAM), 3663nugget effect (KRIGE2D), 1732

annotateglobal data set (LIFETEST), 1810global data set (REG), 2892local data set (LIFETEST), 1812local data set (REG), 2920

ANOVA (row mean scores) statistic, 1314codings (TRANSREG), 3477SURVEYREG procedure, 3243table (TRANSREG), 3400, 3433, 3467

ANOVA procedureabsorption of effects, 350alpha level, 357at sign (@) operator, 367balanced data, 339bar (|) operator, 367Bartlett’s test, 358block diagonal matrices, 339Brown and Forsythe’s test, 359canonical analysis, 354characteristic roots and vectors, 353compared to other procedures, 1468complete block design, 344computational methods, 371confidence intervals, 357contrasts, 363dependent variable, 339disk space, 349effect specification, 366factor name, 362homogeneity of variance tests, 358hypothesis tests, 365

independent variable, 339interactive use, 369interactivity and missing values, 370introductory example, 340level values, 362–363Levene’s test for homogeneity of variance, 359means, 356memory requirements, 350, 371missing values, 349, 370model specification, 366multiple comparison procedures, 356multiple comparisons, 357–360multivariate analysis of variance, 349, 352O’Brien’s test, 359ODS table names, 373orthonormalizing transformation matrix, 354output data sets, 350, 370pooling, automatic, 369repeated measures, 361–362sphericity tests, 364SSCP matrix for multivariate tests, 353transformations, 362–363transformations for MANOVA, 353unbalanced data, caution, 339Welch’s ANOVA, 360WHERE statement, 369

Ansari-Bradley scoresNPAR1WAY procedure, 2529

ante-dependence structureMIXED procedure, 2137

apparent error rate, 1037approximate

covariance, options (CALIS), 507standard errors (CALIS), 464, 475, 535, 572

approximate covariance estimationclustering, 303

arraysNLMIXED procedure, 2448

association, measures ofFREQ procedure, 1287

asterisk (*) operatorTRANSREG procedure, 3381

asymmetricdata (MDS), 2058lambda (FREQ), 1287, 1295

asymptotic covarianceCALIS procedure, 463, 532MIXED procedure, 2098

asymptotic variancesCALIS procedure, 533

asymptotically distribution free estimationCALIS procedure, 462, 533

at sign (@) operatorANOVA procedure, 367CATMOD procedure, 747GLM procedure, 1520MIXED procedure, 2158, 2214TRANSREG procedure, 3381

autocorrelation

SAS OnlineDoc: Version 8

Subject Index � 3701

REG procedure, 2986autoregressive structure

example (MIXED), 2186MIXED procedure, 2137

average linkageCLUSTER procedure, 844, 854

average variance of meansLATTICE procedure, 1752

BB-spline basis

TRANSREG procedure, 3383, 3433backward elimination

LOGISTIC procedure, 1930, 1946PHREG procedure, 2583, 2605REG procedure, 2876, 2947

badness of fitMDS procedure, 2053, 2056–2057, 2063–2064

balanced dataANOVA procedure, 339example, complete block, 1580

balanced design, 2359balanced square lattice

LATTICE procedure, 1747banded Toeplitz structure

MIXED procedure, 2137bandwidth

optimal (DISCRIM), 1036selection (KDE), 1704VARIOGRAM procedure, 3658, 3662, 3667

bar (|) operatorANOVA procedure, 367CATMOD procedure, 746GENMOD procedure, 1412GLM procedure, 1519MIXED procedure, 2157–2158, 2214TRANSREG procedure, 3381

Bartlett’s testANOVA procedure, 358GLM procedure, 1501, 1553

Base SAS software, 21baseline survivor function (PHREG)

confidence level, 2580confidence limits, 2579–2580, 2603estimation method, 2580standard error, 2579, 2603

Bayes estimationNLMIXED procedure, 2458

Bayes’ theoremDISCRIM procedure, 1031LOGISTIC procedure, 1928, 1958

Bayesian analysisMIXED procedure, 2125

Bayesian confidence intervalssplines, 3339

Behrens-Fisher problem, 3569Bernouilli distribution

NLMIXED procedure, 2452best subset selection

LOGISTIC procedure, 1923, 1930, 1946PHREG procedure, 2584, 2605, 2616

between-cluster SSCP matrixACECLUS procedure, 303

between-subject factorsrepeated measures, 1511, 1562

Bhapkar’s test, 810bimodality coefficient

CLUSTER procedure, 850, 862bin-sort algorithm, 1206binary distribution

NLMIXED procedure, 2452binning

KDE procedure, 1700binomial distribution

GENMOD procedure, 1404NLMIXED procedure, 2452

binomial proportion test, 1298examples, 1339

biological assay data, 2833, 2852biplot

PRINQUAL procedure, 2807bivariate density estimation

DISCRIM procedure, 1074biweight kernel (DISCRIM), 1034block diagonal matrices

ANOVA procedure, 339BLUE

MIXED procedure, 2154BLUP

MIXED procedure, 2154Bonferronit test, 357, 1499, 1544Bonferroni adjustment

GLM procedure, 1489MIXED procedure, 2111MULTTEST procedure, 2317, 2333

bootstrap adjustmentMULTTEST procedure, 2316–2317, 2333, 2343

boundary constraints, 2449MIXED procedure, 2123, 2125, 2172

boundsNLMIXED procedure, 2449

Bowker’s test of symmetry, 1306–1307box plot, defined, 395Box’s epsilon, 1564box-and-whisker plots

schematic, 428side-by-side, 395skeletal, 427statistics represented, 397, 418styles of, 418

BOXPLOT procedurecontinuous group variables, 420missing values, 420percentile computation, 419

branch and bound algorithmLOGISTIC procedure, 1946PHREG procedure, 2605, 2616

Breslow method



likelihood (PHREG), 2582, 2594Breslow-Day test, 1318Brewer’s method

SURVEYSELECT procedure, 3288, 3304Brown and Forsythe’s test


Brown-Mood test, 2528Broyden-Fletcher-Goldfarb-Shanno update, 2447Burt table

CORRESP procedure, 954

Ccalibration data set

DISCRIM procedure, 1013, 1041CALIS procedure

approximate covariance, 507approximate standard errors, 464, 475, 535, 572asymptotic covariance, 463, 532asymptotic variances, 533asymptotically distribution free estimation, 462,

533chi-square indices, 540chi-square, adjusted, 541chi-square, displaying, 570–572chi-square, reweighted, 542coefficient of determination, 473compared to MIXED procedure, 2089computation method, Hessian matrix, 477computation method, Lagrange multipliers, 477computation method, standard errors, 477computational problems, 564–567computational problems, identification, 556, 566,

610–611, 617, 625constrained estimation, 453constraints, 453, 495–497, 562constraints, program statements, 453, 514, 517,

561COSAN model, 440–441, 479degrees of freedom, 461, 464, 478, 563determination index, 543displayed output options, 471, 508disturbances, prefix, 488EQS program, 443estimation criteria, 533estimation methods, 437, 462, 531–534exogenous variables, 549factor analysis model, 442–443, 493–494factor analysis model, COSAN statement, 480factor analysis model, LINEQS statement, 489factor analysis model, RAM statement, 485factor loadings, 528FACTOR procedure, 455, 460, 493, 566factor rotation, 494factor scores, 528, 530, 573fit function, 531goodness of fit, 531, 536, 538, 570gradient, 521, 551Hessian matrix, 508–509, 521, 534, 551–552

initial values, 438, 478, 482, 485, 489, 547input data set, 517kappa, 545kurtosis, 437, 471, 476, 544, 546latent variables, 437, 488, 512likelihood ratio test, 540, 561LINEQS model, 441, 488LISREL model, 442manifest variables, 437matrix inversion, 534matrix names, default, 494matrix properties, COSAN model, 479–480MODEL procedure, 566modification indices, 464, 472, 535, 560, 573optimization, 439, 465–469, 508, 551, 553, 558optimization history, 554optimization, initial values, 547, 552optimization, memory problems, 552optimization, termination criteria, 498, 502–507output data sets, 521output table names, 574predicted model matrix, 530–531, 549, 566, 570prefix name, 482, 485, 489–490PRINCOMP procedure, 455program statements, 515, 517program statements, differentiation, 476RAM model, 441, 484reciprocal causation, 473REG procedure, 566residuals, 536residuals, prefix, 488SCORE procedure, 459, 474, 530significance level, 475singularity criterion, 478singularity criterion, covariance matrix, 475, 477–

478skewness, 545squared multiple correlation, 543, 572step length, 469structural equation, 440, 473, 511, 544SYSLIN procedure, 566SYSNLIN procedure, 566t value, 535, 572test indices, constraints, 472variable selection, 548Wald test, probability limit, 478

CANALS methodTRANSREG procedure, 3397

CANCORR procedureanalyzing data in groups, 647canonical coefficients, 635canonical redundancy analysis, 635, 645computational resources, 651correction for means, 644correlation, 644eigenvalues and eigenvectors, 638, 652examples, 637, 656F statistics, Rao’s approximation, 649input data set, 644



missing values, 649OUT= data sets, 645, 649output data sets, 645, 649output table names, 654OUTSTAT= data sets, 650partial correlation, 645–646, 648regression coefficients, 643semipartial correlation, 646singularity checking, 646squared multiple correlation, 646squared partial correlation, 646squared semipartial correlation, 646statistical methods used, 636statistics computed, 635suppressing output, 645test criterion, 649weighted product-moment correlation coefficients,

649CANDISC procedure

computational details, 679computational resources, 683input data set, 680introductory example, 669Mahalanobis distance, 689MANOVA, 670memory requirements, 683missing values, 679multivariate analysis of variance, 670ODS table names, 686output data sets, 675, 681%PLOTIT macro, 669, 692time requirements, 683

canonical analysisANOVA procedure, 354GLM procedure, 1495repeated measurements, 364response surfaces, 3045

canonical coefficients, 667canonical component, 667canonical correlation

CANCORR procedure, 635definition, 636hypothesis tests, 635TRANSREG procedure, 3404, 3413

canonical discriminant analysis, 667, 1013canonical factor solution, 1128canonical redundancy analysis

CANCORR procedure, 635, 645canonical variables, 667

ANOVA procedure, 354TRANSREG procedure, 3404

canonical weights, 636, 667cascaded density estimates

MODECLUS procedure, 2247–2248case-control studies

odds ratio, 1301, 1316–1317PHREG procedure, 2573, 2583, 2617

casewise deletionPRINQUAL procedure, 2785

categorical data analysisSee CATMOD procedure

categorical variable, 66categorical variables

See classification variablesCATMOD procedure

analysis of variance, 699at sign (@) operator, 747AVERAGED models, 761bar (|) operator, 746cautions, 750–751, 766cell count data, 743classification variables, 745compared to other procedures, 699, 750–751, 1525computational method, 770–773continuous variables, 745continuous variables, caution, 750–751contrast examples, 797contrasts, comparing with GLM, 716convergence criterion, 726design matrix, 727, 729design matrix, REPEATED statement, 762effect specification, 745effective sample sizes, 766estimation methods, 701

–F– specification, 723hypothesis tests, 768input data sets, 697, 742interactive use, 702, 712introductory example, 703linear models, 698log-linear models, 698, 751, 793, 796, 1370logistic analysis, 699, 749, 810logistic regression, 698, 750, 789maximum likelihood estimation, 701, 726maximum likelihood estimation formulas, 774memory requirements, 775missing values, 742MODEL statement, examples, 724ordering of parameters, 761ordering of populations, 744ordering of responses, 744output data sets, 735, 747–748parameterization, comparing with GLM, 716positional requirements for statements, 712quasi-independence model, 796regression, 699repeated measures, 699, 731, 754, 803, 808, 810,

814repeated measures, MODEL statements, 756REPEATED statement, examples, 754response functions, 719, 723, 733, 735, 737–738,

740, 743, 780, 785, 821

–RESPONSE– keyword, 719, 722, 724–725, 731,745, 751, 754, 761–762, 764, 768, 776

–RESPONSE–= option, 721, 733restrictions on parameters, 741sample survey analysis, 700sampling zeros and log-linear analyses, 751



sensitivity, 818singular covariance matrix, 767specificity, 818time requirements, 775types of analysis, 698, 745underlying model, 700weighted least squares, 701, 727zeros, structural and sampling, 767, 796, 802

CDFSee cumulative distribution function

cell count data, 1277CATMOD procedure, 743example (FREQ), 1335

cell of a contingency table, 66cell-means coding

TRANSREG procedure, 3391, 3414, 3478censored

data (LIFEREG), 1761observations (PHREG), 2620survival times (PHREG), 2571–2572, 2617, 2619values (PHREG), 2574, 2608

censoring, 1761LIFEREG procedure, 1770, 1778right-, (LIFETEST), 1799variable (PHREG), 2574, 2582, 2590, 2619

center-point codingTRANSREG procedure, 3390, 3483, 3485

centroid component, 3595definition, 3593

centroid methodCLUSTER procedure, 844, 855

chaining, reducing when clustering, 850characteristic roots and vectors

ANOVA procedure, 353GLM procedure, 1493

chi-squareadjusted (CALIS), 541displaying (CALIS), 570–572indices (CALIS), 540reweighted (CALIS), 542

chi-square testsexamples (FREQ), 1337, 1342, 1345FREQ procedure, 1282–1283

choice experimentsTRANSREG procedure, 3476

Chromy’s methodSURVEYSELECT procedure, 3288, 3299, 3303

Cicchetti-Allison weights, 1310class level

MIXED procedure, 2102SURVEYMEANS procedure, 3203

classification criterionDISCRIM procedure, 1013error rate estimation (DISCRIM), 1037

classification levelSURVEYREG procedure, 3243

classification tableLOGISTIC procedure, 1928, 1956–1957, 2012

classification variables, 66

ANOVA procedure, 339, 366CATMOD procedure, 745GENMOD procedure, 1411GLM procedure, 1517MIXED procedure, 2105sort order of levels (GENMOD), 1379specifying (GENMOD), 1382SURVEYMEANS procedure, 3194, 3199, 3201SURVEYREG procedure, 3227TRANSREG procedure, 3383, 3391VARCOMP procedure, 3628

clustercenters, 1196, 1209definition (MODECLUS), 2252deletion, 1207elliptical, 303final, 1196initial, 1196–1197mean, 1209median, 1206, 1209midrange, 1209minimum distance separating, 1197plotting (MODECLUS), 2253seeds, 1196SURVEYMEANS procedure, 3195SURVEYREG procedure, 3228

cluster analysis (STDIZE)standardizing, 3140disjoint, 1195large data sets, 1195robust, 1195, 1209tree diagrams, 3533

CLUSTER procedureSee also TREE procedurealgorithms, 863association measure, 835average linkage, 835categorical data, 835centroid method, 835clustering methods, 835, 854complete linkage, 835computational resources, 864density linkage, 835, 845Euclidean distances, 835F statistics, 849, 862FASTCLUS procedure, compared, 835flexible-beta method, 835, 845–846, 859hierarchical clusters, 835input data sets, 847interval scale, 866kth-nearest-neighbor method, 835maximum likelihood, 835, 845McQuitty’s similarity analysis , 835median method, 835memory requirements, 864missing values, 865non-Euclidean distances, 835output data sets, 849, 867output table names, 872



pseudoF andt statistics, 849ratio scale, 866single linkage, 835size, shape, and correlation, 866test statistics, 846, 849, 851ties, 865time requirements, 864TREE procedure, compared, 835two-stage density linkage, 835types of data sets, 835using macros for many analyses, 890Ward’s minimum-variance method, 835Wong’s hybrid method, 835

cluster sampling, 153clustering, 835

See also CLUSTER procedureapproximate covariance estimation, 303average linkage, 844, 854centroid method, 844, 855complete linkage method, 844, 855density linkage methods, 844–845, 847–848, 850,

856, 858, 860disjoint, 3593Gower’s method, 845, 859hierarchical, 3593maximum-likelihood method, 849, 858–859McQuitty’s similarity analysis, 845, 859median method, 845, 859methods affected by frequencies, 852outliers in, 836, 850penalty coefficient, 849single linkage, 845, 859–860smoothing parameters, 857standardizing variables, 850transforming variables, 836two-stage density linkage, 845Ward’s method, 845, 861weighted average linkage, 845, 859

clustering and scalingMODECLUS procedure, 2230–2231, 2248STDIZE procedure, example, 3140

clustering criterionFASTCLUS procedure, 1195, 1208–1209

clustering methodsACECLUS procedure, 321FASTCLUS procedure, 1196–1197MODECLUS procedure, 2230, 2248

Cochran and Coxt approximation, 3569, 3574, 3579Cochran’sQ test, 1306, 1311, 1354Cochran-Armitage test for trend, 1302, 1349

continuity correction (MULTTEST), 2327MULTTEST procedure, 2324–2325, 2340permutation distribution (MULTTEST), 2327two-tailed test (MULTTEST), 2329

Cochran-Mantel-Haenszel statistics (FREQ), 1263,1312

See also chi-square testsANOVA (row mean scores) statistic, 1314correlation statistic, 1314

examples, 1347general association statistic, 1315

coefficientalpha (FACTOR), 1157of contrast (SURVEYREG), 3244of determination (CALIS), 473of estimate (SURVEYREG), 3244of relationship (INBREED), 1670of variation (SURVEYMEANS), 3201redundancy (TRANSREG), 3410

cohort studies, 1347relative risk, 1302, 1317–1318

collinearityREG procedure, 2967

combinationsgenerating with PLAN procedure, 2685

common factordefined for factor analysis, 1124

common factor analysiscommon factor rotation, 1125–1126compared with principal component analysis,

1125Harris component analysis, 1125image component analysis, 1125interpreting, 1125

comparinggroups (GLM), 1538means (TTEST), 3569, 3584variances (TTEST), 3569, 3578, 3584

comparisonwise error rate (GLM), 1543complete block design

example (ANOVA), 344example (GLM), 1580

complete linkageCLUSTER procedure, 844, 855

complete separationLOGISTIC procedure, 1944

completely randomized designexamples, 375

componentsPLS procedure, 2693

compound symmetry structureexample (MIXED), 2147, 2186, 2191MIXED procedure, 2137

computational detailsHessian matrix (CALIS), 477KDE procedure, 1698Lagrange multipliers (CALIS), 477LIFEREG procedure, 1778maximum likelihood method (VARCOMP), 3631MIVQUE0 method (VARCOMP), 3631MIXED procedure, 2171restricted maximum likelihood method (VAR-

COMP), 3632SIM2D procedure, 3107standard errors (CALIS), 477SURVEYREG procedure, 3237Type I method (VARCOMP), 3631VARCOMP procedure, 3631, 3634



computational problemsCALIS procedure, 564convergence (CALIS), 565convergence (FASTCLUS), 1207convergence (MIXED), 2172identification (CALIS), 556, 566, 610–611, 617,

625negative eigenvalues (CALIS), 567negative R-square (CALIS), 567NLMIXED procedure, 2472overflow (CALIS), 564singular predicted model (CALIS), 566time (CALIS), 567

computational resourcesACECLUS procedure, 326CANCORR procedure, 651CLUSTER procedure, 864FACTOR procedure, 1155FASTCLUS procedure, 1219LIFEREG procedure, 1784MODECLUS procedure, 2257MULTTEST procedure, 2337NLMIXED procedure, 2477PRINCOMP procedure, 2751VARCLUS procedure, 3610

concordant observations, 1287conditional and unconditional simulation

SIM2D procedure, 3087conditional data

MDS procedure, 2051conditional distributions of multivariate normal ran-

dom variablesSIM2D procedure, 3105

conditional logistic regressionPHREG procedure, 2573, 2619

confidence intervalsconfidence coefficient (GENMOD), 1389exact (FREQ), 1259fitted values of the mean (GENMOD), 1392, 1417individual observation (RSREG), 3040–3041means (ANOVA), 357means (RSREG), 3041model confidence interval (NLIN), 2403pairwise differences (ANOVA), 357parameter confidence interval (NLIN), 2403profile likelihood (GENMOD), 1391, 1415profile likelihood (LOGISTIC), 1928, 1950TTEST procedure, 3574Wald (GENMOD), 1394, 1416Wald (LOGISTIC), 1932, 1952

confidence levelbaseline survivor function (PHREG), 2580SURVEYMEANS procedure, 3190SURVEYREG procedure, 3225

confidence limitsbaseline survivor function (PHREG), 2579–2580,

2603LOGISTIC procedure, 1955MIXED procedure, 2098

SURVEYMEANS procedure, 3201–3202SURVEYREG procedure, 3232TRANSREG procedure, 3395, 3405–3406, 3408

configurationMDS procedure, 2045

conjoint analysisTRANSREG procedure, 3402, 3414, 3500, 3504

conjugatedescent (NLMIXED), 2448gradient (NLMIXED), 2446gradient algorithm (CALIS), 465, 467–469, 551

connectedness methodSee single linkage

constant transformationsavoiding (PRINQUAL), 2802avoiding (TRANSREG), 3422

constant variablesPRINQUAL procedure, 2803TRANSREG procedure, 3398, 3422

constrained estimationCALIS procedure, 453

constraintsboundary (CALIS), 453, 495, 562boundary (MIXED), 2123, 2125linear (CALIS), 453, 496, 562modification indices (CALIS), 472nonlinear (CALIS), 453, 497ordered (CALIS), 562program statements (CALIS), 453, 514, 517, 561test indices (CALIS), 472

containment methodMIXED procedure, 2117

contingency coefficient, 1282, 1286contingency tables, 66, 1247, 1266

CATMOD procedure, 700continuity-adjusted chi-square, 1282, 1284continuous variables, 366, 1517–1518

GENMOD procedure, 1411continuous-by-class effects

MIXED procedure, 2160model parameterization (GLM), 1523specifying (GLM), 1518

continuous-nesting-class effectsMIXED procedure, 2159model parameterization (GLM), 1523specifying (GLM), 1518

%CONTOUR macroDISCRIM procedure, 1076

contrasts, 2450comparing CATMOD and GLM, 716GENMOD procedure, 1384GLM procedure, 1483MIXED procedure, 2105, 2108repeated measurements (ANOVA), 363repeated measures (GLM), 1513specifying (CATMOD), 714SURVEYREG procedure, 3228, 3241

controlcomparing treatments to (GLM), 1541, 1546



control charts, 23control sorting

SURVEYSELECT procedure, 3294, 3296convergence criterion

ACECLUS procedure, 320CATMOD procedure, 726GENMOD procedure, 1389, 1398MDS procedure, 2052, 2054–2055MIXED procedure, 2098–2099, 2162, 2173profile likelihood (LOGISTIC), 1928

convergence problemsMIXED procedure, 2172NLMIXED procedure, 2474

convolutiondistribution (MULTTEST), 2328KDE procedure, 1702

Cook’sD influence statistic, 1508, 3040CORR procedure, 21correction for means

CANCORR procedure, 644correlated data

GEE (GENMOD), 1365, 1420correlation

CANCORR procedure, 644estimates (MIXED), 2130, 2133, 2137, 2188length (VARIOGRAM), 3652matrix (GENMOD), 1389, 1407matrix (REG), 2892matrix, estimated (CATMOD), 725principal components, 2750–2751range (KRIGE2D), 1710statistic (FREQ), 1314

CORRESP procedure, 947adjusted inertias, 981algorithm, 976analyse des correspondances, 947appropriate scoring, 947Best variables, 983binary design matrix, 962Burt table, 954, 962coding, 964COLUMN= option, use, 978computational resources, 975correspondence analysis, 947doubling, 964dual scaling, 947fuzzy coding, 964–965geometry of distance between points, 979, 990,

996homogeneity analysis, 947inertia, definition, 948input tables and variables, 950, 961matrix decompositions, 957, 979matrix formulas for statistics, 982memory requirements, 976missing values, 955, 966, 971multiple correspondence analysis (MCA), 954,

980, 1001optimal scaling, 947

optimal scoring, 947OUTC= data set, 973OUTF= data set, 974output data sets, 973output table names, 987partial contributions to inertia table, 982%PLOTIT macro, 948, 996, 1003PROFILE= option, use, 978quantification method, 947reciprocal averaging, 947ROW= option, use, 978scalogram analysis, 947supplementary rows and columns, 958, 981syntax, abbreviations, 951TABLES statement, use, 950, 959, 967time requirements, 976VAR statement, use, 951, 960, 970

correspondence analysisCORRESP procedure, 947

COSAN modelCALIS procedure, 440–441, 479specification, 448structural model example (CALIS), 449

counting processPHREG procedure, 2595

covarianceLATTICE procedure, 1753parameter estimates (MIXED), 2098–2099parameter estimates, ratio (MIXED), 2103parameters (MIXED), 2085principal components, 2750–2751regression coefficients (SURVEYREG), 3244

covariance coefficientsSee INBREED procedure

covariance matrixfor parameter estimates (CATMOD), 726for response functions (CATMOD), 725GENMOD procedure, 1389, 1407NLMIXED procedure, 2475, 2480PHREG procedure, 2578, 2587, 2597REG procedure, 2893singular (CATMOD), 767symmetric and positive definite (SIM2D), 3104

covariance parameter estimatesMIXED procedure, 2163

covariance structure analysis modelSee COSAN model

covariance structuresexamples (MIXED), 2139, 2180MIXED procedure, 2088, 2137

covariatesLIFETEST procedure, 1800MIXED procedure, 2157model parameterization (GLM), 1521

COVRATIO statistic, 2971Cox regression analysis

PHREG procedure, 2575semiparametric model (PHREG), 2571

Cramer’sV statistic, 1282, 1287



Cramer-von Mises statisticsNPAR1WAY procedure, 2531

Crime Rates Data, examplePRINCOMP procedure, 2753

cross validated density estimatesMODECLUS procedure, 2247

cross validationDISCRIM procedure, 1037PLS procedure, 2694, 2701, 2709–2710

crossed effectsdesign matrix (CATMOD), 758GENMOD procedure, 1411MIXED procedure, 2158model parameterization (GLM), 1522specifying (ANOVA), 366–367specifying (CATMOD), 746specifying (GLM), 1518

crossproducts matrixREG procedure, 2988

crosstabulation tables, 1247, 1266cubic clustering criterion, 848, 851

CLUSTER procedure, 846cumulative baseline hazard function

PHREG procedure, 2598cumulative distribution function, 1783, 1799, 2833

LIFEREG procedure, 1778LIFETEST procedure, 1799

cumulative logitsSee also response functionsexamples, (CATMOD), 750specifying in CATMOD procedure, 734using (CATMOD), 749

custom scoring coefficients, exampleSCORE procedure, 3083

DDATA step, 21Davidon-Fletcher-Powell update, 2447decomposition of the SSCP matrix

ACECLUS procedure, 303degrees of freedom

CALIS procedure, 461, 464, 478, 563FACTOR procedure, 1143models with class variables (GLM), 1525NLMIXED procedure, 2436SURVEYMEANS procedure, 3201SURVEYREG procedure, 3237TRANSREG procedure, 3434

delete variables (REG), 2896deleting observations

REG procedure, 2974dendritic method

See single linkagedendrogram, 3533density estimation

DISCRIM procedure, 1055, 1074MODECLUS procedure, 2245

density linkage

CLUSTER procedure, 844–845, 847–848, 850,856, 858, 860

dependent effect, definition, 366description field

LIFETEST procedure, 1811descriptive statistics

See also UNIVARIATE procedureLOGISTIC procedure, 1912PHREG procedure, 2579SURVEYMEANS procedure, 3204

design effectSURVEYREG procedure, 3240

design matrixformulas (CATMOD), 773generation in CATMOD procedure, 757GENMOD procedure, 1412GLMMOD procedure, 1639, 1647–1648linear dependence in (GENMOD), 1412TRANSREG procedure, 3406

design of experimentsSee experimental design

design points, TPSPLINE procedure,3325, 3343design summary

SURVEYREG procedure, 3242determination index

CALIS procedure, 543deviance

definition (GENMOD), 1369GENMOD procedure, 1389LOGISTIC procedure, 1922, 1930, 1959scaled (GENMOD), 1408

deviance residualsGENMOD procedure, 1418–1419LOGISTIC procedure, 1964PHREG procedure, 2589, 2599, 2640

deviations-from-means codingTRANSREG procedure, 3390, 3414, 3470, 3483,

3485DFBETA statistics

LOGISTIC procedure, 1965PHREG procedure, 2588, 2600

DFBETAS statistic (REG), 2972DFFITS statistic

GLM procedure, 1508REG procedure, 2971

diagnostic statisticsREG procedure, 2968, 2970

diameter methodSee complete linkage

difference between meansconfidence intervals, 357

dimension coefficientsMDS procedure, 2045–2046, 2051, 2056–2057,

2062–2063dimensions

MIXED procedure, 2102direct effects

design matrix (CATMOD), 759specifying (CATMOD), 746



direct product structureMIXED procedure, 2137

discordant observations, 1287discrete logistic model

likelihood (PHREG), 2594PHREG procedure, 2572, 2582, 2619

discrete variablesSee classification variables

DISCRIM procedurebackground, 1031Bayes’ theorem, 1031bivariate density estimation, 1074calibration data set, 1013, 1041classification criterion, 1013computational resources, 1048%CONTOUR macro, 1076cross validation, 1037density estimate, 1032, 1035, 1055, 1074error rate estimation, 1037, 1039input data sets, 1042, 1044introductory example, 1014kernel density estimates, 1066, 1087memory requirements, 1048missing values, 1031nonparametric methods, 1033ODS table names, 1052optimal bandwidth, selection, 1036output data sets, 1044–1045parametric methods, 1032%PLOT macro, 1057%PLOTIT macro, 1074posterior probability, 1032, 1035, 1055, 1074posterior probability error rate, 1038–1039quasi-inverse, 1038resubstitution, 1037squared distance, 1032test set classification, 1037time requirements, 1049training data set, 1013univariate density estimation, 1055

discriminant analysis, 1013canonical, 667, 1013error rate estimation, 1014misclassification probabilities, 1014nonparametric methods, 1033parametric methods, 1032stepwise selection, 3155

discriminant functions, 668disjoint clustering, 1195–1196, 1198, 3593dispersion parameter

estimation (GENMOD), 1368, 1409, 1413–1414GENMOD procedure, 1409LOGISTIC procedure, 1959weights (GENMOD), 1402

dissimilarity dataMDS procedure, 2045, 2052, 2058

distancebetween clusters (FASTCLUS), 1214classification (VARIOGRAM), 3666

data (FASTCLUS), 1195data (MDS), 2045Euclidean (FASTCLUS), 1196

distance dataMDS procedure, 2052, 2058

DISTANCE data setsCLUSTER procedure, 847

distance toleranceVARIOGRAM procedure, 3659

distributionsexponential, 1801Gompertz, 2833logistic, 2833normal, 2833Weibull, 1801

dollar-unit samplingSURVEYSELECT procedure, 3315

domain analysisSURVEYREG procedure, 3269

DOT product (SCORE), 3063double arcsine test

MULTTEST procedure, 2329double dogleg

algorithm (CALIS), 466–467, 469, 551method (NLMIXED), 2446

dual scalingCORRESP procedure, 947

Duncan’s multiple range test, 357, 1500, 1548Duncan-Waller test, 360, 1503, 1550

error seriousness ratio, 359, 1502multiple comparison (ANOVA), 378

Dunnett’s adjustmentGLM procedure, 1489MIXED procedure, 2111

Dunnett’s test, 1500, 1546one-tailed lower, 358, 1500one-tailed upper, 358two-tailed, 358

EEBLUP

MIXED procedure, 2120EDF statistics

NPAR1WAY procedure, 2529effect

coding (TRANSREG), 3372, 3390, 3470, 3483,3485

definition, 366, 745, 1517name length (MIXED), 2102specification (ANOVA), 366specification (CATMOD), 745specification (GENMOD), 1411specification (GLM), 1517testing (SURVEYREG), 3239, 3243

Efron methodlikelihood (PHREG), 2583, 2594

eigenvalues and eigenvectorsACECLUS procedure, 314–315, 322, 326–327CANCORR procedure, 638, 652



PRINCOMP procedure, 2737, 2750, 2752RSREG procedure, 3049

Einot and Gabriel’s multiple range testANOVA procedure, 360examples (GLM), 1583GLM procedure, 1502, 1549

Ekblom-Newton algorithmFASTCLUS procedure, 1209

elementary linkage analysisSee single linkage

empirical Bayes estimationNLMIXED procedure, 2458

empirical best linear unbiased predictionMIXED procedure, 2120

empirical distribution functionstatistics (NPAR1WAY), 2529

empirical sandwich estimatorMIXED procedure, 2100

Epanechnikov kernel (DISCRIM), 1034EQS program

CALIS procedure, 443equality

of means (TTEST), 3569, 3584of variances (TTEST), 3569, 3578, 3584

equamax method, 1123, 1142error rate estimation

DISCRIM procedure, 1037, 1039discriminant analysis, 1014

error seriousness ratioWaller-Duncan test, 359, 1502

error sum of squares clustering methodSee Ward’s method

estimabilityGLM procedure, 1484MIXED procedure, 2106

estimability checkingGENMOD procedure, 1383LOGISTIC procedure, 1919

estimable functions, 1484displaying (GLM), 1505example (GLM), 1526general form of, 1527GLM procedure, 1486–1487, 1493, 1507, 1526–

1528, 1530–1531, 1538printing (GLM), 1505SURVEYREG procedure, 3230, 3244

estimated population marginal meansSee least-squares means

estimationdispersion parameter (GENMOD), 1368maximum likelihood (GENMOD), 1406mixed model (MIXED), 2151regression parameters (GENMOD), 1368

estimation criteriaCALIS procedure, 533

estimation methodsCALIS procedure, 437, 462, 531–534MIXED procedure, 2101

Euclidean distances, 847, 849, 1033, 1196

clustering, 835MDS procedure, 2046, 2051, 2062

Euclidean lengthSTDIZE procedure, 3136

event times, 1799PHREG procedure, 2571, 2574

events/trials format for responseGENMOD procedure, 1388, 1405

exact methodlikelihood (PHREG), 2583, 2594

exact testscomputational algorithms (FREQ), 1319computational algorithms (NPAR1WAY), 2532computational resources (FREQ), 1321computational resources (NPAR1WAY), 2533confidence intervals, 1259examples (NPAR1WAY), 2548, 2550FREQ procedure, 1318, 1350MONTE Carlo estimates (NPAR1WAY), 2534NPAR1WAY procedure, 2531p-value, definitions, 1320, 2533permutation test (MULTTEST), 2327

excluded observationsPRINQUAL procedure, 2787, 2804TRANSREG procedure, 3424

exogenous variablesCALIS procedure, 549path diagram (CALIS), 550

expected mean squarescomputing, types (GLM), 1570random effects, 1568

expected trendMULTTEST procedure, 2329

experimental design, 23, 1631See also PLAN procedurealiasing structure (GLM), 1628

experimentwise error rate (GLM), 1543explicit intercept

TRANSREG procedure, 3423exploratory data analysis, 22exponential distribution, 1801

GENMOD procedure, 1448exponential semivariogram model

KRIGE2D procedure, 1724–1725external unfolding

MDS procedure, 2045extreme value distribution

PROBIT procedure, 2850

FF statistics

CLUSTER procedure, 849, 862GENMOD procedure, 1416Rao’s approximation (CANCORR) procedure, 649

factordefined for factor analysis, 1124

factor analysis, 3593compared to component analysis, 1123–1124

factor analysis model



CALIS procedure, 442–443, 493–494COSAN statement (CALIS), 480identification (CALIS), 493LINEQS statement (CALIS), 489MATRIX statement (CALIS), 483path diagram (CALIS), 486–487RAM statement (CALIS), 485specification (CALIS), 448structural model example (CALIS), 452

factor analytic structuresMIXED procedure, 2137

factor loadingsCALIS procedure, 528

FACTOR procedureCALIS procedure, 455, 460, 493computational resources, 1155degrees of freedom, 1143Heywood cases, 1153number of factors extracted, 1138OUT= data sets, 1141output data sets, 1129, 1141time requirements, 1151variances, 1143

factor rotation methods, 1123factor scores

CALIS procedure, 528, 530, 573displaying (CALIS), 573

factor scoring coefficientsFACTOR procedure, 3063SCORE procedure, 3063, 3073

factor structure, 1142factors

PLAN procedure, 2665–2666, 2675PLS procedure, 2693

failure time, 1799LIFEREG procedure, 1761

false discovery rate (MULTTEST)p-value adjustments, 2336adjustment (MULTTEST), 2336

false negative, false positive rateLOGISTIC procedure, 1928, 1957, 2013

fast Fourier transformKDE procedure, 1703MULTTEST procedure, 2328

FASTCLUS procedurealgorithm for updating cluster seeds, 1209bin-sort algorithm, 1206cluster deletion, 1207clustering criterion, 1195, 1208–1209clustering methods, 1196–1197compared to other procedures, 1219computational problems, convergence, 1207computational resources, 1219controlling iterations, 1210convergence criterion, 1207distance, 1195–1196, 1214DRIFT option, 1196Ekblom-Newton algorithm, 1209homotopy parameter, 1207

imputation of missing values, 1208incompatibilities, 1214iteratively reweighted least-squares, 1208Lp clustering, 1195, 1208MEAN= data sets, 1211memory requirements, 1219Merle-Spath algorithm, 1209missing values, 1196–1197, 1208, 1210, 1214Newton algorithm, 1209OUT= data sets, 1215outliers, 1195output data sets, 1210–1211, 1215output table names, 1224OUTSTAT= data set, 1211, 1217random number generator, 1211scale estimates, 1207, 1209, 1214, 1216seed replacement, 1197, 1211weighted cluster means, 1212

fiducial limits, 2840, 2851finite differencing

NLMIXED procedure, 2438, 2465finite population correction (fpc)

SURVEYMEANS procedure, 3196finite population correction factor, 154first canonical variable, 667first-order method

NLMIXED procedure, 2459first-stage sampling unit, 153Fisher exact test

FREQ procedure, 1282, 1285–1286MULTTEST procedure, 2322, 2324, 2331, 2349

Fisher information matrixexample (MIXED), 2192MIXED procedure, 2163

Fisher’s LSD test, 360, 1503Fisher’s scoring method

GENMOD procedure, 1394, 1407LOGISTIC procedure, 1930, 1932, 1942MIXED procedure, 2098, 2104, 2173

fit summarySURVEYREG procedure, 3242

fixed effectsMIXED procedure, 2087sum-to-zero assumptions, 1569VARCOMP procedure, 3623, 3629

fixed-effects modelVARCOMP procedure, 3630

fixed-effects parametersMIXED procedure, 2085, 2146

fixed-radius kernelsMODECLUS procedure, 2245

Fleiss-Cohen weights, 1310flexible-beta method

CLUSTER procedure, 835, 845–846, 859floating point errors

NLMIXED procedure, 2472folded formF statistic, 3569, 3578forward selection

LOGISTIC procedure, 1930, 1945



PHREG procedure, 2583, 2605REG procedure, 2876, 2947

Forward-Dolittle transformation, 1528fractional frequencies

PHREG procedure, 2581Freeman-Halton test, 1286Freeman-Tukey test

MULTTEST procedure, 2324, 2329, 2343FREQ procedure

alpha level, 1260, 1269binomial proportion, 1298, 1339Bowker’s test of symmetry, 1306Breslow-Day test, 1318cell count data, 1277, 1335chi-square tests, 1282–1284, 1337, 1342Cochran’sQ test, 1306Cochran-Mantel-Haenszel statistics, 1347computation time, limiting, 1261computational methods, 1319computational resources, 1321, 1323contingency coefficient, 1282contingency table, 1342continuity-adjusted chi-square, 1282, 1284correlation statistic, 1314Cramer’sV statistic, 1282default tables, 1266displayed output, 1327exactp-values, 1320EXACT statement, used with TABLES, 1261exact tests, 1259, 1318, 1350Fisher exact test, 1282Friedman’s chi-square statistic, 1352gamma statistic, 1287general association statistic, 1315grouping variables, 1278input data sets, 1257, 1277kappa coefficient, 1310–1311Kendall’s tau-b statistic, 1287lambda asymmetric, 1287lambda symmetric, 1287likelihood-ratio chi-square test, 1282Mantel-Haenszel chi-square test, 1282McNemar’s test, 1306measures of association, 1287missing values, 1279Monte Carlo estimation, 1259, 1261, 1322multiway tables, 1328–1329network algorithm, 1319odds ratio, 1301, 1315–1317ODS table names, 1332one-way frequency tables, 1283, 1327, 1337order of variables, 1258output data sets, 1262, 1324–1325, 1335, 1345output variable prefixes, 1326OUTPUT, used with TABLES or EXACT, 1265overall kappa coefficient, 1306Pearson chi-square test, 1282, 1284Pearson correlation coefficient, 1287phi coefficient, 1282

polychoric correlation coefficient, 1287relative risk, 1302, 1315, 1317–1318row mean scores statistic, 1314scores, 1281simple kappa coefficient, 1306Somers’D statistics, 1287Spearman rank correlation coefficient, 1287statistical computations, 1281stratified table, 1347Stuart’s tau-c statistic, 1287two-way frequency tables, 1283–1284, 1342uncertainty coefficients, 1287weighted kappa coefficient, 1306

FREQ statementand RMSSTD statement (CLUSTER), 852–853

frequency tables, 1247, 1266generating (CATMOD), 726–727input to CATMOD procedure, 743one-way (FREQ), 1283, 1327, 1337two-way (FREQ), 1283–1284, 1342

frequency variableLOGISTIC procedure, 1919PRINQUAL procedure, 2789programming statements (PHREG), 2590TRANSREG procedure, 3380value (PHREG), 2581

Friedman’s chi-square statistic, 1352full sibs mating

INBREED procedure, 1674full-rank coding

TRANSREG procedure, 3390furthest neighbor clustering

See complete linkagefuzzy coding

CORRESP procedure, 965

GG matrix

MIXED procedure, 2087, 2129, 2146–2147, 2212G-G epsilon, 1563G2 inverse

NLIN procedure, 2399Gabriel’s multiple-comparison procedure


gamma distribution, 1761, 1772, 1780GENMOD procedure, 1404

gamma statistic, 1287, 1289Gaussian assumption

SIM2D procedure, 3087Gaussian distribution

NLMIXED procedure, 2452Gaussian random field

SIM2D procedure, 3087Gaussian semivariogram model

KRIGE2D procedure, 1723–1724GCV function, TPSPLINE procedure,3323, 3325,

3340, 3347nonhomogeneous variance, 3340



GEESee Generalized Estimating Equations

general association statistic, 1315general distribution

NLMIXED procedure, 2452general linear structure

MIXED procedure, 2137generalized cross validation function (GCV), 3323,

3347generalized cyclic incomplete block design

generating with PLAN procedure, 2684Generalized Estimating Equations (GEE), 1375, 1398,

1420, 1452, 1457generalized inverse, 2154

MIXED procedure, 2107NLIN procedure, 2399NLMIXED procedure, 2439

generalized least squaresSee weighted least-squares estimation

generalized linear modelGENMOD procedure, 1366–1367theory (GENMOD), 1402

generalized logitsSee also response functionsexamples (CATMOD), 750formulas (CATMOD), 772specifying in CATMOD procedure, 734using (CATMOD), 749

generation (INBREED)nonoverlapping, 1659, 1662–1663number, 1666overlapping, 1659, 1661variable, 1666

GENMOD procedureadjusted residuals, 1419aliasing, 1374bar (|) operator, 1412binomial distribution, 1404built-in link function, 1368built-in probability distribution, 1368classification variables, 1411confidence intervals, 1389confidence limits, 1387continuous variables, 1411contrasts, 1384convergence criterion, 1389, 1398correlated data, 1365, 1420correlation matrix, 1389, 1407correlations, least-squares means, 1387covariance matrix, 1389, 1407covariances, least-squares means, 1387crossed effects, 1411design matrix, 1412deviance, 1389deviance definition, 1369deviance residuals, 1419dispersion parameter, 1409dispersion parameter estimation, 1368, 1413–1414dispersion parameter weights, 1402

effect specification, 1411estimability, 1386estimability checking, 1383events/trials format for response, 1388, 1405expected information matrix, 1407exponential distribution, 1448F statistics, 1416Fisher’s scoring method, 1394, 1407gamma distribution, 1404GEE, 1365, 1375, 1398, 1420, 1452, 1455, 1457Generalized Estimating Equations (GEE), 1365generalized linear model, 1366–1367goodness of fit, 1408gradient, 1406Hessian matrix, 1406information matrix, 1394initial values, 1390, 1399intercept, 1369, 1371, 1392inverse Gaussian distribution, 1403Lmatrices, 1386Lagrange multiplier statistics, 1417life data, 1445likelihood residuals, 1419linear model, 1366linear predictor, 1365–1366, 1372, 1412, 1433link function, 1365–1366, 1405log-likelihood functions, 1405log-linear models, 1370logistic regression, 1440main effects, 1411maximum likelihood estimation, 1406

–MEAN– automatic variable, 1397multinomial distribution, 1404multinomial models, 1419negative binomial distribution, 1404nested effects, 1411Newton-Raphson algorithm, 1406normal distribution, 1403observed information matrix, 1407offset, 1392, 1433offset variable, 1371ordinal data, 1448output table names, 1437overdispersion, 1410Pearson residuals, 1419Pearson’s chi-square, 1389, 1408Poisson distribution, 1404Poisson regression, 1370polynomial effects, 1411profile likelihood confidence intervals, 1391, 1415programming statements, 1396–1397quasi-likelihood, 1410raw residuals, 1418regression parameters estimation, 1368regressor effects, 1411repeated measures, 1365, 1420residuals, 1393, 1418–1419

–RESP– automatic variable, 1397scale parameter, 1405



scaled deviance, 1408score statistics, 1417singular contrast matrix, 1383specifying classification variables, 1382subpopulation, 1389suppressing output, 1381Type 1 analysis, 1369, 1413Type 3 analysis, 1369, 1414user-defined link function, 1385variance function, 1368Wald confidence intervals, 1394, 1416working correlation matrix, 1398–1400, 1421

–XBETA– automatic variable, 1397Gentleman-Givens computational method, 2555geometric anisotropy

KRIGE2D procedure, 1729–1732GLM procedure

absorption of effects, 1481, 1532aliasing structure, 1505, 1628alpha level, 1490, 1499, 1505, 1509at sign (@) operator, 1520bar (|) operator, 1519Bartlett’s test, 1501, 1553Bonferroni adjustment, 1489Brown and Forsythe’s test, 1501, 1554canonical analysis, 1495characteristic roots and vectors, 1493compared to other procedures, 1468, 1510, 1567,

1617, 1631, 2088, 2359, 2555, 3031comparing groups, 1538computational method, 1574computational resources, 1571contrasts, 1483, 1513covariate values for least-squares means, 1490disk space, 1480Dunnett’s adjustment, 1489effect specification, 1517error effect, 1494estimability, 1484, 1486–1487, 1493, 1507, 1527,

1538estimable functions, 1526ESTIMATE specification, 1536homogeneity of variance tests, 1501, 1553Hsu’s adjustment, 1489hypothesis tests, 1515, 1526interactive use, 1520interactivity and BY statement, 1482interactivity and missing values, 1521, 1571introductory example, 1469least-squares means (LS-means), 1488Levene’s test for homogeneity of variance, 1501,

1554means, 1497means versus least-squares means, 1538memory requirements, reduction of, 1481missing values, 1479, 1493, 1557, 1571model specification, 1517multiple comparisons, least-squares means, 1488,

1491, 1540, 1542

multiple comparisons, means, 1499–1503, 1540,1542

multiple comparisons, procedures, 1497multivariate analysis of variance, 1479, 1493,

1558nonstandard weights for least-squares means,

1491O’Brien’s test, 1501observed margins for least-squares means, 1491ODS table names, 1577output data sets, 1507, 1574–1575parameterization, 1521positional requirements for statements, 1477predicted population margins, 1488Q effects, 1568random effects, 1510, 1567–1568regression, quadratic, 1472relation to GLMMOD procedure, 1639repeated measures, 1511, 1560Sidak’s adjustment, 1489simple effects, 1492simulation-based adjustment, 1489singularity checking, 1484, 1487, 1493, 1506sphericity tests, 1514, 1563SSCP matrix for multivariate tests, 1493statistical assumptions, 1517summary of features, 1467tests, hypothesis, 1483transformations for MANOVA, 1494transformations for repeated measures, 1513Tukey’s adjustment, 1489types of least-squares means comparisons, 1491unbalanced analysis of variance, 1469, 1538, 1589unbalanced design, 1469, 1538, 1568, 1589, 1614weighted analysis, 1516weighted means, 1555Welch’s ANOVA, 1503WHERE statement, 1521

GLMMOD alternativeTRANSREG procedure, 3406, 3470

GLMMOD proceduredesign matrix, 1639, 1647–1648input data sets, 1644introductory example, 1639missing values, 1647–1648ODS table names, 1649output data sets, 1645, 1648relation to GLM procedure, 1639screening experiments, 1653

global influenceLD statistic (PHREG), 2589, 2601LMAX statistic (PHREG), 2589, 2601

global krigingKRIGE2D procedure, 1710

global null hypothesisPHREG procedure, 2574, 2597, 2607score test (PHREG), 2583, 2612

Gompertz distribution, 2833goodness of fit



GENMOD procedure, 1408Gower’s method

See also median methodCLUSTER procedure, 845, 859

gradientCALIS procedure, 521, 551GENMOD procedure, 1406LOGISTIC procedure, 1948MIXED procedure, 2099, 2162

Graeco-Latin squaregenerating with PLAN procedure, 2672

graphicsexamples (REG), 3015high resolution plots (REG), 2915keywords (REG), 2917options (REG), 2918saving output (LIFETEST), 1811

Greenhouse-Geisser epsilon, 1563grid search

example (MIXED), 2193group average clustering

See average linkagegrowth curve analysis

example (CATMOD), 810example (MIXED), 2147

GSK models, 701GT2 multiple-comparison method, 360, 1503, 1545

HH-F epsilon, 1564half-fraction design, analysis, 1626Harris component analysis, 1123, 1125, 1137Harris-Kaiser rotation, 1142hat matrix, 2971

LOGISTIC procedure, 1964hazard function, 1799

baseline (PHREG), 2572cumulative (PHREG), 2602definition (PHREG), 2593discrete (PHREG), 2582, 2593PHREG procedure, 2571rate (PHREG), 2620ratio (PHREG), 2574, 2576

hazards ratioconfidence interval (PHREG), 2587confidence limits (PHREG), 2587, 2598, 2607estimate (PHREG), 2598, 2607, 2620PHREG procedure, 2574

help system, 21Hertzsprung-Russell Plot, example

MODECLUS procedure, 2300Hessian matrix

CALIS procedure, 477, 508–509, 521, 534, 551–552

GENMOD procedure, 1406LOGISTIC procedure, 1930, 1948MIXED procedure, 2098–2099, 2104, 2123, 2162–

2163, 2172–2173, 2183, 2192NLMIXED procedure, 2440

Hessian scalingNLMIXED procedure, 2467

heterogeneityexample (MIXED), 2189MIXED procedure, 2130, 2133

heterogeneousAR(1) structure (MIXED), 2137compound-symmetry structure (MIXED), 2137covariance structures (MIXED), 2145Toeplitz structure (MIXED), 2137

heteroscedasticitytesting (REG), 2981

Heywood casesFACTOR procedure, 1153

hierarchical clustering, 845, 858, 3593hierarchical design

generating with PLAN procedure, 2680hierarchical model

example (MIXED), 2206hierarchy

LOGISTIC procedure, 1924Hochberg (MULTTEST)

p-value adjustments, 2335adjustment (MULTTEST), 2335

Hochberg’s GT2 multiple-comparison method, 360,1503, 1545

homogeneity analysisCORRESP procedure, 947

homogeneity of survival curvesLIFETEST procedure, 1799–1800

homogeneity of variance tests, 358, 1501, 1553Bartlett’s test (ANOVA), 358Bartlett’s test (GLM), 1501, 1553Brown and Forsythe’s test (ANOVA), 359Brown and Forsythe’s test (GLM), 1501, 1554

Cochran’s Q statistic (FREQ)Cochran’sQ statistic (FREQ), 1354

homogeneity of variance testsDISCRIM procedure, 1024examples, 1624Levene’s test (ANOVA), 359Levene’s test (GLM), 1501, 1554O’Brien’s test (ANOVA), 359O’Brien’s test (GLM), 1501Welch’s ANOVA, 1554

homotopy parameterFASTCLUS procedure, 1207

honestly significant difference test, 360, 1503, 1545–1546

Hosmer-Lemeshow testLOGISTIC procedure, 1926, 1961test statistic (LOGISTIC), 1962

Hotelling-Lawley trace, 353, 1493, 1563Hotelling-Lawley-McKeon statistic

MIXED procedure, 2134Hotelling-Lawley-Pillai-Samson statistic

MIXED procedure, 2134Howe’s solution, 1128HSD test, 360, 1503, 1545–1546



Hsu’s adjustmentGLM procedure, 1489MIXED procedure, 2111

Huynh-Feldtepsilon (GLM), 1564structure (GLM), 1563structure (MIXED), 2137

HYBRID optionand FREQ statement (CLUSTER), 852and other options (CLUSTER), 848, 850PROC CLUSTER statement, 856

hypergeometricdistribution (MULTTEST), 2331variance (MULTTEST), 2326

hypothesis testscomparing adjusted means (GLM), 1493contrasts (CATMOD), 714contrasts (GLM), 1483contrasts, examples (GLM), 1583, 1597, 1607custom tests (ANOVA), 365customized (GLM), 1515exact (FREQ), 1259for intercept (ANOVA), 361for intercept (GLM), 1505GLM procedure, 1526incorrect hypothesis (CATMOD), 768lack of fit (RSREG), 3044MANOVA (GLM), 1558mixed model (MIXED), 2156, 2165multivariate (REG), 2981nested design (NESTED), 2364parametric, comparing means (TTEST), 3569,

3584parametric, comparing variances (TTEST), 3569,

3584random effects (GLM), 1511, 1568REG procedure, 2907, 2933repeated measures (GLM), 1562TRANSREG procedure, 3433Type I sum of squares (GLM), 1528Type II sum of squares (GLM), 1530Type III sum of squares (GLM), 1531Type IV sum of squares (GLM), 1531

Iid variables

TRANSREG procedure, 3380ideal point model

TRANSREG procedure, 3413ideal points

TRANSREG procedure, 3523identification variables, 2451identity transformation

PRINQUAL procedure, 2793TRANSREG procedure, 3387

ill-conditioned dataORTHOREG procedure, 2555

image component analysis, 1123, 1125, 1137implicit intercept

TRANSREG procedure, 3423imputation of missing values

FASTCLUS procedure, 1208INBREED procedure

coancestry, computing, 1670coefficient of relationship, computing, 1670covariance coefficients, 1659, 1661, 1663, 1665,

1667, 1670covariance coefficients matrix, output, 1665first parent, 1667–1668full sibs mating, 1674generation number, 1666generation variable, 1666generation, nonoverlapping, 1659, 1662–1663generation, overlapping, 1659, 1661inbreeding coefficients, 1659, 1661, 1665, 1667,

1670inbreeding coefficients matrix, output, 1665individuals, outputting coefficients, 1665individuals, specifying, 1663, 1667–1668initial covariance value, 1668initial covariance value, assigning, 1665initial covariance value, specifying, 1661kinship coefficient, 1670last generation’s coefficients, output, 1665mating, offspring and parent, 1673mating, self, 1672matings, output, 1667memory requirements, 1677monoecious population analysis, example, 1679offspring, 1665, 1672ordering observations, 1660OUTCOV= data set, 1666, 1675output table names, 1677panels, 1675, 1684pedigree analysis, 1659–1660pedigree analysis, example, 1682, 1684population, monoecious, 1679population, multiparous, 1665, 1669population, nonoverlapping, 1666population, overlapping, 1660–1661, 1671progeny, 1668–1669, 1671–1673, 1682second parent, 1667–1668selective matings, output, 1667specifying gender, 1663theoretical correlation, 1670unknown or missing parents, 1674variables, unaddressed, 1668–1669

incomplete block designgenerating with PLAN procedure, 2681, 2684

incomplete principal componentsREG procedure, 2894, 2904

independent variabledefined (ANOVA), 339

individual difference modelsMDS procedure, 2045

INDSCAL modelMDS procedure, 2045, 2051

inertia, definition



CORRESP procedure, 948inference

mixed model (MIXED), 2155space, mixed model (MIXED), 2105–2106, 2109,

2179infinite likelihood

MIXED procedure, 2133, 2172–2173infinite parameter estimates

LOGISTIC procedure, 1927, 1944influence statistics

REG procedure, 2970information criteria

MIXED procedure, 2100information matrix, 2848

expected (GENMOD), 1407LIFEREG procedure, 1761–1762, 1778observed (GENMOD), 1407

initial covariance valueassigning (INBREED), 1665INBREED procedure, 1668specifying (INBREED), 1661

initial estimatesACECLUS procedure, 320LIFEREG procedure, 1778

initial seedsFASTCLUS procedure, 1196–1197, 1211

initial valuesCALIS procedure, 438, 476, 478, 482, 485, 489,

547GENMOD procedure, 1390, 1399LOGISTIC procedure, 1967MDS procedure, 2054–2058, 2065MIXED procedure, 2122

initializationrandom (PRINQUAL), 2803TRANSREG procedure, 3421

instantaneous failure ratePHREG procedure, 2593

integral approximationsNLMIXED procedure, 2444, 2458

interaction effectsMIXED procedure, 2158model parameterization (GLM), 1522quantitative (TRANSREG), 3415specifying (ANOVA), 366–367specifying (CATMOD), 746specifying (GLM), 1518TRANSREG procedure, 3381, 3414

interceptGENMOD procedure, 1369, 1371, 1392hypothesis tests for (ANOVA), 361hypothesis tests for (GLM), 1505MIXED procedure, 2157model parameterization (GLM), 1521no intercept (TRANSREG), 3398

interpretationfactor rotation, 1125

interpreting factors, elements to consider, 1126interpreting output

VARCLUS procedure, 3611interval determination

LIFETEST procedure, 1821interval variable, 66intraclass correlation coefficient

MIXED procedure, 2188inverse confidence limits

PROBIT procedure, 2840, 2852inverse Gaussian distribution

GENMOD procedure, 1403inverse matrix ofX0X

SURVEYREG procedure, 3243IPC analysis

REG procedure, 2894, 2904, 2987iterated factor analysis, 1123iteration history

NLMIXED procedure, 2441, 2479iterations

history (MIXED), 2162history (PHREG), 2587, 2606PRINQUAL procedure, 2797restarting (PRINQUAL), 2786, 2803restarting (TRANSREG), 3421

Jjoint selection probabilities

SURVEYSELECT procedure, 3286Jonckheere-Terpstra test, 1304

Kk-means clustering, 1195–1196k-th-nearest neighbor

See also density linkageSee also single linkage

k-th-nearest neighborestimation (CLUSTER), 848, 850, 856

K= optionand other options (CLUSTER), 847, 850

Kaplan-Meier estimatesSee product-limit estimatesdisplayed time points (LIFETEST), 1815

kappa coefficient, 1307, 1309tests, 1311weights, 1310

KDE procedurebandwidth selection, 1704binning, 1700computational details, 1698convolution, 1702fast Fourier transform, 1703options, 1695output table names, 1706references, 1706

Kendall’s tau-b statistic, 1287, 1290Kenward-Roger method

MIXED procedure, 2119kernel density estimates

DISCRIM procedure, 1033, 1066, 1087KDE procedure, 1689



Klotz scoresNPAR1WAY procedure, 2529

knotsPRINQUAL procedure, 2795–2796TRANSREG procedure, 3389–3390, 3392, 3431,

3491Kolmogorov-Smirnov statistics

NPAR1WAY procedure, 2530KRIGE2D procedure

anisotropic models, 1729–1732best linear unbiased prediction (BLUP), 1737correlation range, 1710discontinuity, 1727effective range, 1723–1725examples, 1739exponential semivariogram model, 1724–1725Gaussian semivariogram model, 1723–1724geometric anisotropy, 1729–1732global kriging, 1710input data set, 1715kriging with trend, 1735local kriging, 1709–1710nested models, 1726–1727nugget effect, 1720, 1727–1728ordinary kriging, 1709, 1733–1737OUTEST= data sets, 1737OUTNBHD= data set, 1737–1738output data sets, 1715, 1737–1738power semivariogram model, 1725range�, 1723sill, 1723spatial continuity, 1709spatial covariance, 1710spatial data, 1733spatial random fields, 1734spherical semivariogram model, 1723visual fit of the variogram, 1721zonal anisotropy, 1732

krigingordinary kriging (KRIGE2D), 1735ordinary kriging (VARIOGRAM), 3643with trend (KRIGE2D), 1735

kriging, ordinaryVARIOGRAM procedure, 3644

Kronecker product structureMIXED procedure, 2137

Kruskal-Wallis test, 2528Kuiper statistics

NPAR1WAY procedure, 2531kurtosis

CALIS procedure, 437, 471, 476, 544, 546displayed in CLUSTER procedure, 850

LL matrices

MIXED procedure, 2105, 2111, 2156lack of fit tests, 2840, 2851

RSREG procedure, 3044Lagrange multiplier

covariance matrix, 2404NLMIXED procedure, 2468statistics (GENMOD), 1417test statistics (LIFEREG), 1779test, modification indices (CALIS), 472, 560

lambda asymmetric, 1287, 1295lambda symmetric, 1287, 1296Lance-Williams flexible-beta method

See flexible-beta methodlatent variables

CALIS procedure, 437, 488, 512latent vectors

PLS procedure, 2693Latin square design

ANOVA procedure, 384generating with PLAN procedure, 2683

lattice designbalanced square lattice (LATTICE), 1747efficiency (LATTICE), 1749, 1752, 1756partially balanced square lattice (LATTICE), 1747,

1754rectangular lattice (LATTICE), 1747

LATTICE procedureadjusted treatment means, 1753ANOVA table, 1752Block variable, 1747, 1750–1751compared to MIXED procedure, 2089covariance, 1753Group variable, 1747, 1750–1751lattice design efficiency, 1749, 1752least significant differences, 1752missing values, 1752ODS table names, 1753Rep variable, 1747, 1750–1751response variable, 1750Treatmnt variable, 1747, 1750–1751variance of means, 1752

LD statisticPHREG procedure, 2589, 2601

leader algorithm, 1196least significant differences

LATTICE procedure, 1752least-significant-difference test, 360, 1503least-squares estimation

LIFEREG procedure, 1778least-squares means

Bonferroni adjustment (GLM), 1489Bonferroni adjustment (MIXED), 2111BYLEVEL processing (MIXED), 2113coefficient adjustment, 1557compared to means (GLM), 1538comparison types (GLM), 1491comparison types (MIXED), 2113construction of, 1555covariate values (GLM), 1490covariate values (MIXED), 2112Dunnett’s adjustment (GLM), 1489Dunnett’s adjustment (MIXED), 2111examples (GLM), 1592, 1598



examples (MIXED), 2193, 2215GLM procedure, 1488Hsu’s adjustment (GLM), 1489Hsu’s adjustment (MIXED), 2111mixed model (MIXED), 2110multiple comparisons adjustment (GLM), 1488,

1491multiple comparisons adjustment (MIXED), 2111nonstandard weights (GLM), 1491nonstandard weights (MIXED), 2114observed margins (GLM), 1491observed margins (MIXED), 2114Sidak’s adjustment (GLM), 1489Sidak’s adjustment (MIXED), 2111simple effects (GLM), 1492, 1551simple effects (MIXED), 2115simulation-based adjustment (GLM), 1489simulation-based adjustment (MIXED), 2111Tukey’s adjustment (GLM), 1489Tukey’s adjustment (MIXED), 2111

left truncation timePHREG procedure, 2583, 2604

less-than-full-rank modelTRANSREG procedure, 3391, 3487

level of measurementMDS procedure, 2046, 2055

levels, of class variable, 1518Levenberg-Marquardt algorithm

CALIS procedure, 466, 469, 551Levene’s test for homogeneity of variance

ANOVA procedure, 359GLM procedure, 1501, 1554, 1624

leverage, 1508TRANSREG procedure, 3408

life dataGENMOD procedure, 1445

life table estimates, 1819, 1845LIFEREG procedure, 1761

accelerated failure time models, 1761censoring, 1770, 1778computational details, 1778computational resources, 1784cumulative distribution function, 1778failure time, 1761information matrix, 1761–1762, 1778initial estimates, 1778Lagrange multiplier test statistics, 1779least-squares estimation, 1778log-likelihood function, 1762, 1778log-likelihood ratio tests, 1762main effects, 1777maximum likelihood estimates, 1761missing values, 1777model specification, 1778Newton-Raphson algorithm, 1761OUTEST= data sets, 1784output table names, 1786predicted values, 1783supported distributions, 1780

survival distribution function, 1761, 1778, 1780Tobit model, 1763, 1789

LIFETEST procedureannotations, 1810, 1812computational formulas, 1818confidence intervals: density, 1825confidence intervals: hazard function, 1825confidence intervals: survivor function, 1825confidence limits, 1821covariates, 1800covariates: and survival analysis, 1822effective sample size, 1819homogeneity of survival curves, 1799–1800interpreting plots, 1801interval determination, 1821INTERVALS= option, 1821Kaplan-Meier estimates, 1815life table estimates, 1845life table method, 1819likelihood ratio test, 1799, 1807, 1822log rank test, 1807log rank test for association, 1800, 1823log rank test for homogeneity, 1799, 1821mean survival time, 1814missing values, 1818NOTABLE option, 1807ODS table names, 1830output data sets, 1825OUTSURV= data set, 1814OUTTEST= data set, 1826product-limit estimates, 1831product-limit method, 1818proportional hazards model, 1801rank tests, 1821–1822saving graphics output, 1811suppressing output, 1813survival analysis, 1799tests of association, 1831time limit, 1814WIDTH= option, 1821Wilcoxon test, 1807Wilcoxon test for association, 1800, 1823Wilcoxon test for homogeneity, 1799, 1821

likelihood displacementPHREG procedure, 2589, 2601

likelihood function, 2848likelihood ratio test, 2178

Bartlett’s modification, 1024CALIS procedure, 540, 561chi-square (FREQ), 1282example (MIXED), 2191LIFETEST procedure, 1799mixed model (MIXED), 2155, 2157MIXED procedure, 2164PHREG procedure, 2597, 2607

likelihood residualsGENMOD procedure, 1419

likelihood-ratio testchi-square (FREQ), 1284



line printer plotsREG procedure, 2924, 2955

line-search methodsNLMIXED procedure, 2440, 2442, 2470

linear discriminant function, 1013linear equations model

See LINEQS modellinear hypotheses

PHREG procedure, 2573, 2592, 2598linear model

GENMOD procedure, 1366–1367linear models

CATMOD procedure, 698compared with log-linear models, 701

linear predictorGENMOD procedure, 1365–1366, 1372, 1412,

1433PHREG procedure, 2579, 2588–2589, 2640

linear regressionTRANSREG procedure, 3413

linear structural relationship modelSee LISREL model

linear structureMIXED procedure, 2137

linear transformationPRINQUAL procedure, 2792TRANSREG procedure, 3386, 3428

LINEQS modelCALIS procedure, 441, 488specification, 448structural model example (CALIS), 446, 450

link functionbuilt-in (GENMOD), 1368, 1391GENMOD procedure, 1365–1366, 1405LOGISTIC procedure, 1903, 1926, 1940, 1949user-defined (GENMOD), 1385

LISREL modelCALIS procedure, 442structural model example (CALIS), 447

LMAX statisticPHREG procedure, 2601

local influenceDFBETA statistics (PHREG), 2588, 2600score residuals (PHREG), 2589, 2600weighted score residuals (PHREG), 2600

local krigingKRIGE2D procedure, 1710

LOESS proceduredata scaling, 1873direct fitting method, 1874introductory example, 1856iterative reweighting, 1875kd trees and blending, 1874local polynomials, 1875local weighting, 1875missing values, 1871output data sets, 1871output table names, 1877scoring data sets, 1876

statistical inference, 1876log likelihood ratio chi-square test, 2849, 2851log odds

LOGISTIC procedure, 1952log rank test, 1831

LIFETEST procedure, 1799log-likelihood

functions (GENMOD), 1405output data sets (LOGISTIC), 1912

log-likelihood functionLIFEREG procedure, 1762, 1778PROBIT procedure, 2848

log-likelihood ratio testsLIFEREG procedure, 1762

log-linear modelsCATMOD procedure, 698, 751, 1370compared with linear models, 701design matrix (CATMOD), 764examples (CATMOD), 793, 796GENMOD procedure, 1370multiple populations (CATMOD), 752one population (CATMOD), 752

log-linear variance modelMIXED procedure, 2135

log-rank testPHREG procedure, 2575

logistic analysisCATMOD procedure, 699, 749caution (CATMOD), 751examples (CATMOD), 810ordinal data, 699

logistic distribution, 1761, 1772, 1780, 2833PROBIT procedure, 2850

LOGISTIC procedureAkaike’s information criterion, 1947Bayes’ theorem, 1928best subset selection, 1923branch and bound algorithm, 1946classification table, 1928, 1956–1957, 2012confidence intervals, 1928, 1932, 1950, 1952confidence limits, 1955convergence criterion, 1922customized odds ratio, 1938descriptive statistics, 1912deviance, 1922, 1930, 1959DFBETA diagnostic, 1965dispersion parameter, 1959displayed output, 1969estimability checking, 1919existence of MLEs, 1944Fisher’s scoring method, 1930, 1932, 1942goodness of fit, 1922, 1930gradient, 1948hat matrix, 1964Hessian matrix, 1930, 1948hierarchy, 1924Hosmer-Lemeshow test, 1926, 1961–1962infinite parameter estimates, 1927initial values, 1967



introductory example, 1906link function, 1903, 1926, 1940, 1949log odds, 1952maximum likelihood algorithms, 1942missing values, 1939model fitting criteria, 1947model hierarchy, 1905, 1924model selection, 1921, 1930, 1945multiple classifications, 1928Newton-Raphson algorithm, 1930, 1932, 1942–

1943odds ratio confidence limits, 1922–1923, 1929odds ratio estimation, 1952ODS table names, 1972output data sets, 1912, 1966–1967output ROC data sets, 1968overdispersion, 1929, 1958, 1960Pearson’s chi-square, 1922, 1930, 1959predicted probabilities, 1955prior event probability, 1928, 1958, 2012profile likelihood convergence criterion, 1928rank correlation, 1955regression diagnostics, 1963residuals, 1964reverse response level ordering, 1911, 1939ROC curve, 1927, 1962Schwarz criterion, 1947score statistics, 1948selection methods, 1921, 1930, 1945singular contrast matrix, 1919subpopulation, 1922, 1930, 1959testing linear hypotheses, 1937, 1963Williams’ method, 1960

logistic regression, 2833See also LOGISTIC procedureCATMOD procedure, 698, 750examples (CATMOD), 789GENMOD procedure, 1367, 1440

logitsSee adjacent-category logitsSee also cumulative logitsSee also generalized logits

loglogistic distribution, 1761, 1772, 1780lognormal distribution, 1761, 1772, 1780long run times

NLMIXED procedure, 2472Longley data set, 2555Lp clustering

FASTCLUS procedure, 1195, 1208LS-means

See least-squares meanslsd (least significant differences)

LATTICE procedure, 1752LSD test, 1503

MMAC method

PRINQUAL procedure, 2773, 2799macros

TRANSREG procedure, 3408Mahalanobis distance, 675, 1033

CANDISC procedure, 689main effects

design matrix (CATMOD), 757GENMOD procedure, 1411LIFEREG procedure, 1777MIXED procedure, 2158model parameterization (GLM), 1521specifying (ANOVA), 366–367specifying (CATMOD), 746specifying (GLM), 1518TRANSREG procedure, 3381, 3414

Mallows’ Cp selectionREG procedure, 2949

manifest variablesCALIS procedure, 437

Mann-Whitney-Wilcoxon test, 2528MANOVA

See multivariate analysis of varianceCANDISC procedure, 670

Mantel-Haenszel chi-square test, 1285Mantel-Haenszel test

chi-square test (FREQ), 1282log-rank test (PHREG), 2575

marginal probabilitiesSee also response functionsspecifying in CATMOD procedure, 734

martingale residualsPHREG procedure, 2589, 2598, 2640

matched comparisonsSee paired comparisons

matingoffspring and parent (INBREED), 1673self (INBREED), 1672

matrixdecompositions (CORRESP), 957, 979factor, defined for factor analysis (FACTOR), 1124inversion (CALIS), 534multiplication (SCORE), 3063names, default (CALIS), 494notation, theory (MIXED), 2145properties, COSAN model (CALIS), 479

matrix propertiesCOSAN model (CALIS), 480

MATRIX statement (CALIS)factor analysis model, 483

maximum average correlation methodPRINQUAL procedure, 2773, 2799

maximum likelihoodalgorithms (LOGISTIC), 1942estimates (LIFEREG), 1761estimates (LOGISTIC), 1944estimation (CATMOD), 701, 726, 774estimation (GENMOD), 1406hierarchical clustering (CLUSTER), 845, 849,

858–859NLMIXED procedure, 2422

maximum likelihood estimation



mixed model (MIXED), 2152maximum method

See complete linkagemaximum total variance method

PRINQUAL procedure, 2773maximum-likelihood factor analysis, 1123, 1137

with FACTOR procedure, 1128–1129McNemar’s test, 1306McQuitty’s similarity analysis

CLUSTER procedure, 845MDPREF analysis

PRINQUAL procedure, 2807MDS procedure

alternating least squares, 2050analyzing data in groups, 2059asymmetric data, 2058badness of fit, 2053, 2056–2057, 2063–2064conditional data, 2051configuration, 2045, 2056–2057, 2063convergence criterion, 2052, 2054–2055coordinates, 2056–2057, 2062–2063data weights, 2061dimension coefficients, 2045–2046, 2051, 2056–

2057, 2062–2063dissimilarity data, 2045, 2052, 2058distance data, 2045, 2052, 2058Euclidean distances, 2046, 2051, 2062external unfolding, 2045individual difference models, 2045INDSCAL model, 2045, 2051initial values, 2054–2058, 2065measurement level, 2046, 2055metric multidimensional scaling, 2045missing values, 2066multidimensional scaling, 2045nonmetric multidimensional scaling, 2045–2046normalization of the estimates, 2066optimal transformations, 2046, 2055output table names, 2071partitions, 2051, 2062plot of configuration, 2077–2078plot of dimension coefficients, 2078–2079plot of linear fit, 2076%PLOTIT macro, 2048plots, 2048proximity data, 2045, 2052, 2058residuals, 2057, 2061–2062, 2065, 2076similarity data, 2045, 2052, 2058stress formula, 2053–2054, 2063subject weights, 2045, 2051three-way multidimensional scaling, 2045ties, 2059transformations, 2046, 2055–2056, 2058, 2061–

2063transformed data, 2065transformed distances, 2065unfolding, 2045weighted Euclidean distance, 2046, 2051, 2062weighted Euclidean model, 2045, 2051

weighted least squares, 2061mean per element

SURVEYMEANS procedure, 3200mean separation tests

See multiple comparison proceduresmean survival time

LIFETEST procedure, 1814MEAN= data sets

FASTCLUS procedure, 1210–1211means

ANOVA procedure, 356compared to least-squares means (GLM), 1538displayed in CLUSTER procedure, 850GLM procedure, 1497SURVEYMEANS procedure, 3200weighted (GLM), 1555

MEANS procedure, 21means, difference between

independent samples, 3569, 3584paired observations, 3569

measurement levelMDS procedure, 2046, 2055

measures of agreement, 1306median

cluster, 1206, 1209method (CLUSTER), 845, 859scores (NPAR1WAY), 2528

Mehta and Patel, network algorithm, 1319, 2532memory requirements

ACECLUS procedure, 326CLUSTER procedure, 864FACTOR procedure, 1155FASTCLUS procedure, 1219INBREED procedure, 1677MIXED procedure, 2174reduction of (ANOVA), 350reduction of (GLM), 1481VARCLUS procedure, 3610

memory usageSIM2D procedure, 3107

Merle-Spath algorithmFASTCLUS procedure, 1209

METHOD= specificationPROC CLUSTER statement, 844

methods of estimationVARCOMP procedure, 3623, 3634

metric multidimensional scalingMDS procedure, 2045

MGV methodPRINQUAL procedure, 2773

minimum generalized variance methodPRINQUAL procedure, 2773

Minkowski metricSTDIZE procedure, 3136

misclassification probabilitiesdiscriminant analysis, 1014

missing level combinationsMIXED procedure, 2161

missing values



ACECLUS procedure, 325and interactivity (GLM), 1521CANCORR procedure, 649character (PRINQUAL), 2792CLUSTER procedure, 865FASTCLUS procedure, 1196–1197, 1208, 1210,

1214LIFEREG procedure, 1777LIFETEST procedure, 1818LOGISTIC procedure, 1939MDS procedure, 2066MODECLUS procedure, 2257MULTTEST procedure, 2336NPAR1WAY procedure, 2524PHREG procedure, 2582, 2591, 2623PRINCOMP procedure, 2748PRINQUAL procedure, 2785, 2797, 2804PROBIT procedure, 2847SCORE procedure, 3071STDIZE procedure, 3128, 3130strata variables (PHREG), 2592SURVEYMEANS procedure, 3191, 3197SURVEYREG procedure, 3235SURVEYSELECT procedure, 3296TRANSREG procedure, 3398, 3418–3419, 3424TREE procedure, 3548VARCOMP procedure, 3629

mixed model (MIXED)See also MIXED procedureestimation, 2151formulation, 2146hypothesis tests, 2156, 2165inference, 2155inference space, 2105–2106, 2109, 2179least-squares means, 2110likelihood ratio test, 2155, 2157linear model, 2085maximum likelihood estimation, 2152notation, 2087objective function, 2162parameterization, 2157predicted values, 2110restricted maximum likelihood, 2177theory, 2145Wald test, 2155, 2184unbalanced (GLM), 1614VARCOMP procedure, 3630

mixed model equationsexample (MIXED), 2192MIXED procedure, 2102, 2153

MIXED procedureSee also mixed modelAkaike’s information criterion, 2100, 2154, 2164ante-dependence structure, 2137ARIMA procedure, compared, 2089ARMA structure, 2137assumptions, 2085asymptotic covariance, 2098at sign (@) operator, 2158, 2214

AUTOREG procedure, compared, 2089autoregressive structure, 2137, 2186banded Toeplitz structure, 2137bar (|) operator, 2157–2158, 2214basic features, 2086Bayesian analysis, 2125between-within method, 2117BLUE, 2154BLUP, 2154, 2206Bonferroni adjustment, 2111boundary constraints, 2123, 2125, 2172BYLEVEL processing of LSMEANS, 2113CALIS procedure, compared, 2089Cholesky root, 2121, 2171class level, 2102classification variables, 2105compound symmetry structure, 2137, 2147, 2186,

2191computational details, 2171computational order, 2171confidence interval, 2110, 2129confidence limits, 2098, 2109, 2113, 2116, 2129containment method, 2117continuous effects, 2131, 2133, 2137continuous-by-class effects, 2160continuous-nesting-class effects, 2159contrasted SAS procedures, 1468, 1567, 1617,

2088–2089, 2359contrasts, 2105, 2108convergence criterion, 2098–2099, 2162, 2173convergence problems, 2172correlation estimates, 2130, 2133, 2137, 2188correlations of least-squares means, 2113covariance parameter estimates, 2098–2099, 2163covariance parameter estimates, ratio, 2103covariance parameters, 2085covariance structures, 2088, 2137, 2139, 2180covariances of least-squares means, 2113covariate values for LSMEANS, 2112covariates, 2157CPU requirements, 2174crossed effects, 2158degrees of freedom, 2106–2109, 2111, 2113, 2117,

2122, 2156, 2161, 2165, 2172, 2206dimensions, 2101–2102direct product structure, 2137Dunnett’s adjustment, 2111EBLUPs, 2131, 2154, 2198, 2213effect name length, 2102empirical best linear unbiased prediction, 2120empirical sandwich estimator, 2100estimability, 2106–2108, 2110–2111, 2114, 2121–

2122, 2156, 2161estimation methods, 2101factor analytic structures, 2137Fisher information matrix, 2163, 2192Fisher’s scoring method, 2098, 2104, 2173fitting information, 2163–2164fixed effects, 2087



fixed-effects parameters, 2085, 2122, 2146fixed-effects variance matrix, 2122function evaluations, 2101G matrix, 2129general linear structure, 2137generalized inverse, 2107, 2154gradient, 2099, 2162grid search, 2122, 2193growth curve analysis, 2147Hessian matrix, 2098–2099, 2104, 2123, 2162–

2163, 2172–2173, 2183, 2192heterogeneity, 2130, 2133, 2189heterogeneous AR(1) structure, 2137heterogeneous compound-symmetry structure,

2137heterogeneous covariance structures, 2145heterogeneous Toeplitz structure, 2137hierarchical model, 2206Hotelling-Lawley-McKeon statistic, 2134Hotelling-Lawley-Pillai-Sampson statistic, 2134Hsu’s adjustment, 2111Huynh-Feldt structure, 2137infinite likelihood, 2133, 2172–2173information criteria, 2100initial values, 2122input data sets, 2099interaction effects, 2158intercept, 2157intercept effect, 2120, 2129intraclass correlation coefficient, 2188introductory example, 2089iterations, 2101, 2162Kenward-Roger method, 2119Kronecker product structure, 2137L matrices, 2105, 2111, 2156LATTICE procedure, compared, 2089least-square means, 2193least-squares means, 2113, 2215likelihood ratio test, 2164linear structure, 2137log-linear variance model, 2135main effects, 2158matrix notation, 2145memory requirements, 2174missing level combinations, 2161mixed linear model, 2085mixed model, 2146mixed model equations, 2102, 2153, 2192mixed model theory, 2145model information, 2102model selection, 2154multilevel model, 2206multiple comparisons of least-squares means, 2111,

2113multiple tables, 2168multivariate tests, 2134nested effects, 2159nested error structure, 2210NESTED procedure, compared, 2089

Newton-Raphson algorithm, 2152nonfull-rank parameterization, 2088, 2135, 2161nonstandard weights for LSMEANS, 2114nugget effect, 2134observed margins for LSMEANS, 2114ordering of effects, 2103, 2160output changes, 2166output data sets, 2115over-parameterization, 2158parameter constraints, 2123, 2172parameterization, 2157pharmaceutical stability, example, 2206plotting the likelihood, 2198polynomial effects, 2157power-of-the-mean model, 2135predicted means, 2121predicted value confidence intervals, 2116predicted values, 2120, 2193prior density, 2126profiling residual variance, 2102, 2124, 2134, 2152,

2171Rmatrix, 2133, 2136random coefficients, 2186, 2206random effects, 2087, 2129random-effects parameter, 2131random-effects parameters, 2086, 2146regression effects, 2157rejection sampling, 2127repeated measures, 2086, 2133, 2180residual method, 2118residual variance tolerance, 2121restricted maximum likelihood (REML), 2086ridging, 2103, 2152sandwich estimator, 2100Satterthwaite method, 2118Schwarz’s Bayesian information criterion, 2100,

2154, 2164scoring, 2098, 2104, 2173Sidak’s adjustment, 2111simple effects, 2115simulation-based adjustment, 2111singularities, 2173spatial anisotropic exponential structure, 2137spatial covariance structures, 2138–2139, 2145,

2172split-plot design, 2149, 2175standard linear model, 2087statement positions, 2096subject effect, 2107, 2131, 2137, 2175, 2180summary of commands, 2097sweep operator, 2171table names, 2166tables, 2115Toeplitz structure, 2137, 2215TSCSREG procedure, compared, 2089Tukey’s adjustment, 2111Type 1 estimation, 2101Type 2 estimation, 2101Type 3 estimation, 2101



Type I testing, 2120Type II testing, 2120Type III testing, 2120, 2165unstructuredR matrix, 2137unstructured correlations, 2137unstructured covariance matrix, 2137VARCOMP procedure, example, 2192variance components, 2086, 2137variance ratios, 2123, 2131Wald test, 2163, 2165weighted LSMEANS, 2114weighting, 2145zero design columns, 2120zero variance component estimates, 2172

ML factor analysisand computer time, 1128and multivariate normal distribution, 1128

modal clustersdensity estimation (CLUSTER), 848

modal region, definition, 2253MODECLUS procedure

analyzing data in groups, 2231, 2248cascaded density estimates, 2247–2248clustering methods, 2230, 2248clusters, definition, 2252clusters, plotting, 2253compared with other procedures, 2230cross validated density estimates, 2247density estimation, 2245example using GPLOT procedure, 2294, 2300example using TRACE option, 2304example using TRANSPOSE procedure, 2287fixed-radius kernels, 2245functional summary, 2236Hertzsprung-Russell Plot, example, 2300JOIN option, discussion, 2254modal region, 2253neighborhood distribution function (NDF), defini-

tion, 2252nonparametric clustering methods, 2229output data sets, 2258p-value computation, 2251plotting samples from univariate distributions,

2264population clusters, risks of estimating, 2251saddle test, definition, 2253scaling variables, 2230significance tests, 2294standardizing, 2230summary of options, 2236variable-radius kernels, 2245

modelfit summary (REG), 2968–2969fitting criteria (LOGISTIC), 1947hierarchy (LOGISTIC), 1905, 1924information (MIXED), 2102parameterization (GLM), 1521specification (ANOVA), 366specification (GLM), 1517

specification (LIFEREG), 1778specification (NLMIXED, 2452

model selectionentry (PHREG), 2584examples (REG), 2993LOGISTIC procedure, 1921, 1930, 1945MIXED procedure, 2154PHREG procedure, 2573, 2583–2584, 2604REG procedure, 2876, 2947, 2949–2950removal (PHREG), 2585

modification indicesCALIS procedure, 464, 535, 560constraints (CALIS), 472displaying (CALIS), 573Lagrange multiplier test (CALIS), 472, 560Wald test (CALIS), 472, 560

modified ridit scores, 1282monoecious population analysis

example (INBREED), 1679monotone

regression function (TRANSREG), 3446transformations (TRANSREG), 3413

monotonictransformation (PRINQUAL), 2792–2793transformation (TRANSREG), 3386, 3428transformation, B-spline (PRINQUAL), 2792transformation, B-spline (TRANSREG), 3386,

3430Monte Carlo estimation

FREQ procedure, 1259, 1261, 1322NPAR1WAY procedure, 2534

Mood scoresNPAR1WAY procedure, 2529

MORALS methodTRANSREG procedure, 3397

mortality testMULTTEST procedure, 2329, 2347

MSESURVEYREG procedure, 3240

MTV methodPRINQUAL procedure, 2773

multicollinearityREG procedure, 2967

multidimensional preference analysisPRINQUAL procedure, 2807

multidimensional scalingMDS procedure, 2045metric (MDS), 2045nonmetric (MDS), 2045–2046three-way (MDS), 2045

multilevel modelexample (MIXED), 2206

multilevel response, 2850multinomial

distribution (GENMOD), 1404models (GENMOD), 1419

multiple classificationscutpoints (LOGISTIC), 1928

multiple comparison procedures, 1540



See also multiple comparisons of least-squaresmeans

See also multiple comparisons of meansGLM procedure, 1497multiple-stage tests, 1548pairwise (GLM), 1541–1542recommendations, 1550with a control (GLM), 1541, 1546

multiple comparisons adjustment (MIXED)least-squares means, 2111

multiple comparisons of least-squares meansSee also multiple comparison proceduresGLM procedure, 1488, 1491, 1542interpretation, 1551MIXED procedure, 2111, 2113

multiple comparisons of meansSee also multiple comparison proceduresANOVA procedure, 356Bonferronit test, 357, 1499Duncan’s multiple range test, 357, 1500Dunnett’s test, 358, 1500error mean square, 358, 1501examples, 1580Fisher�

Subject Index - WPI · 2000. 4. 11. · one-way layout, example, 340 one-way tests ... procedure,...

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Transcript of Subject Index - WPI · 2000. 4. 11. · one-way layout, example, 340 one-way tests ... procedure,...