Index
A
ABSORB statement
ANOVA procedure 47
GLM procedure 47, 431-439
absorption 431-439
ADJUST= option, LSMEANS statement 80, 82, 109
adjusted R-square (Adj R-sq) 7, 13
adjusted treatment means, analysis of covariance 234-237
AIC, AICC (Akaike Information Criterion) 293
aliased effects 389
ALIASING option, MODEL statement 391-392, 396
ALPHA option
LSMEANS statement 80
MEANS statement 66-70
MODEL statement 36
ALPHA parameter, MEANS statement (ANOVA) 65-67
alphameric ordering 57
analysis of contrasts, repeated-measures data 266, 274-280
multivariate analysis 275-279
univariate ANOVA, contrast variables 279-280
univariate ANOVA, each measurement 274
analysis of covariance 229-263
adjusted and unadjusted means 235
adjusted treatment means 234-237
analysis-of-variance methods for 261-263
contrasts 237-238
equal slopes 349-352
fit regression techniques 261-263
homogeneity of slopes 240
logistic 347-352
multivariate analysis 317-320
one-way structure 230-238
orthogonal polynomials and covariance methods 256-263
two-way structure with interaction 249-255
two-way structure without interaction 247-249
Type III 296-303
unadjusted treatment means 234-237
unequal slopes models 239-246
analysis of variance 42-48
See also multivariate analysis of variance
absorbing nesting effects 433-439
analysis-of-covariance methods for 261-263
balanced incomplete-blocks (BIB) design 399
cross classification effects 44
crossed-nested classification 124
crossover design with residual effects 404-405
dummy-variable models 170-175
lack-of-fit analysis 397, 415-416
Latin square design 72-74
logistic 339-344
multiple comparisons 48, 55
nested classifications 45, 96-99
nested classifications, expected means squares 99-101
notation 42-44
one-way 49-62
one-way, dummy-variable models 170-179
one-way, multivariate 306-309
partitioning 42-44
planned comparisons 48, 56-58
preplanned comparisons 48
probit link with 344-346
random-location analysis of multi-location data 425
randomized-blocks design 64-65, 107-110
split-plot experiments 137-139
terminology 42-44
two-way factorial experiments 75-78
two-way mixed models 114-117
unbalanced data 144-146
unbalanced mixed-model data 222-225
unbalanced two-way classification 179-214
ANOVA method, univariate 266, 269-273
CONTRAST statement 272
ESTIMATE statement 272
GLM procedure 270
LSMEANS statement 272
repeated-measures data 266, 269-273
ANOVA procedure 42, 46
See also MEANS statement, ANOVA procedure
ABSORB statement 47
analysis of variance for nested classifications 96-97
ANOVA procedure (continued)
BY statement 47, 79
CLASS statement 46
computing one-way ANOVA table 54
ESTIMATE statement 60-62
FREQ statement 47
Hotelling’s T2 test 312
MANOVA statement 47
MODEL statement 46
multiple comparison methods 65-70
REPEATED statement 47
TEST statement 47
unbalanced two-way classification 180-181
ANOVA variance component estimates 154
ANTE(1) models (first-order ante dependence models) 283-284
approximate degrees of freedom, Satterthwaite’s formula for 129-131
AR(1) models (first-order autoregressive models) 283, 288
unstructured covariance models 294-295
arithmetic mean
difference, independent sample 39-41
difference, related samples 37-39
estimating, single sample 34-37
asthma drugs data set (example) 265, 267-269
CONTRAST statement 272-273
ESTIMATE statement 272-273
fixed-effects models 281-284
information criterion 284, 292-295
LSMEANS statement 272-273
MIXED procedure analysis 296-303
multivariate analysis 275-279
reassessing covariance structure 291
selecting covariance model 284-291
univariate ANOVA 270-271
AT MEANS option, LSMEANS statement 245
AUCTION and MARKET data sets (example)
fitting regression models 5-9, 12-14
restricted models 19-21
tests of subsets of coefficients 17
autoregressive models, first-order 283, 288
unstructured covariance models 294-295
B
bacterial inoculation of grasses data (example) 136-140
balanced incomplete-blocks (BIB) design 398-402
Bayesian Information Criterion (BIC) 293
beef data set (example) 45
analysis of variance 96-99
expected mean squares for hypothesis testing 99-101
overall mean and BLUP 104-106
variance component estimation 101-104
best linear unbiased predictions (BLUPs) 92
estimated BLUP 105
multi-location data 426-428
nested classifications 104-106
BIB (balanced incomplete-blocks) design 398-402
BIC (Bayesian Information Criterion) 293
binomial analysis models 339-352
See also negative binomial models
analysis of variance with probit link 344-346
logistic analysis of covariance 347-352
logistic analysis of variance 338-344
binomial clinical trial data (example) 339-352
analysis of variance with probit link 344-346
logistic analysis of variance 338-344
biological count data (example) 353-377
correcting for overdispersion 362-366
goodness-of-fit statistics 357-362
negative binomial models 366-377
blocks, confounding with 390-394
BLUPs
See best linear unbiased predictions
boll weight data set (example)
two-way analysis of covariance with interaction 249-255
two-way multivariate analysis 312-317
BULLET data set (example)
one-way analysis of variance 47-48
two-sample t-test 40
UNIVARIATE procedure to check assumptions 50-51
BY statement
ANOVA procedure 47, 79
GLM procedure 47, 79
MEANS procedure 34-35
BYLEVEL option, LSMEANS statement 237
C
calf feed rations (example) 188-190
canonical correlation 322
canonical link 330
canonical link functions 385
negative binomial model and GENMOD procedure 369-371
negative binomial model and user-supplied program 372-376
cattle data set (example)
fitting regression models 5-9
predicted values and confidence limits 10-11
cells
cell means 83
crossed classification 44
empty, unbalanced data 148-151, 158-161, 203-214
unbalanced data analysis 141
Challenger O-ring data set (example) 328-338
0-1 models 334-336
inverse link function 331-333
probit regression models 337-338
characteristic roots and vectors (eigenvalues, eigenvectors) 322
CHIPS data set (example) 122-135
analysis of variance 124
expected mean squares 124-129
MIXED procedure, analysis with 131-135
Satterthwaite’s formula 129-131
CL option, LSMEANS statement 80
CLASS statement
ANOVA procedure 46
GLM procedure 46
MEANS procedure 34-35
MIXED procedure 82
class variables 239
CLDIFF option, MEANS statement 69
CLI option, MODEL statement (REG procedure) 10-11
CLM option
MEANS statement 55-56
MODEL statement 10-11, 36
Coeff Var (C.V.) 7
coefficients, subsets of 17
collinearity 21
common slope models 230
common slopes analysis of covariance 349-352
comparisonwise error rate 48
complete factorial experiments 74
complete regression models 28
components of variance 96
compound symmetry (CS) models 274, 282
unstructured covariance models 294-295
confidence intervals 11, 29-31
multiple comparison results 69-70
one-way analysis of variance 55-56
simple effect differences 80-82
confidence limits, and predicted values 10-11
confounding in factorial experiments 389-398
blocks with 390-394
contrasts 390
CONTRAST statement, GENMOD procedure
correcting for overdispersion 364-366
GEE analysis of repeated measures 381-383
logistic analysis of variance 342
CONTRAST statement, GLM procedure 24-26, 47, 56-58
ABSORB statement and 436
comparing factor levels with other factor level subgroups 88
diagrammatic method for setting up 89
E= option 116
estimable functions, one-way analysis of variance 178-179
estimable functions, two-way classification 201-203
estimable functions, two-way classification, empty cells 210-214
expected mean squares, crossed-nested classification 124-129
INTERCEPT parameter 61-62
labels 25
main effect comparisons 85-86
mixed-model analysis 216
multivariate analysis 320-321
one-way analysis of variance, dummy-variable models 171
ORPOL function (IML) with 258
planned comparisons, two-way factorial experiments 82-84
simple effect comparisons 85-86
simultaneous contrasts, two-way classifications 86
testing several contrasts simultaneously 59
treatment differences, unequal slopes analysis of covariance 246
CONTRAST statement, GLM procedure (continued)
two-way mixed models 116
unbalanced data 146, 148
unbalanced data with empty cells 150
unbalanced mixed-model data 155-156
unbalanced mixed-model data with empty cells 159
unbalanced two-way classification 191-194
univariate ANOVA, repeated-measures data 272-273
CONTRAST statement, MIXED procedure
comparing factor levels with other factor level subgroups 88
diagrammatic method for setting up 89
expected mean squares, crossed-nested classification 124
main effect comparisons 85-86
ORPOL function (IML) with 258
planned comparisons, two-way factorial experiments 82-84
simple effect comparisons 85-86
simultaneous contrasts, two-way classifications 86
split-plot experiments 140
treatment differences, unequal slopes analysis of covariance 246
unbalanced data 146, 148
unbalanced data with empty cells 150
unbalanced mixed-model data 158
unbalanced mixed-model data with empty cells 160
univariate ANOVA, repeated-measures data 272-273
contrasts 256-263
See also contrasts of repeated measures
See also entries at CONTRAST statement
alternative multiple comparison methods 65-70
analysis of covariance 237-238
confounded effects 390
multivariate analysis 320-321
one-way analysis of variance 60
ORPOL function (IML) 259-261
orthogonal 60
planned comparisons 56-58
simultaneous, two-way classifications 86
testing several simultaneously 59
unbalanced two-way classification 192-193
contrasts of repeated measures 266, 274-280
multivariate analysis 275-279
univariate ANOVA, contrast variables 279-280
univariate ANOVA, each measurement 274
convergence problems 102
correction for the mean 15
CORRW option, REPEATED statement 380
cotton boll weight data set (example)
two-way analysis of covariance with interaction 249-255
two-way multivariate analysis 312-317
count data and overdispersion
See overdispersion and count data
covariables 239
covariance parameters 226
cross classification effects 44
nested effects, random-effects models 122-135
crossed-nested classification 122-135
analysis of variance 124
expected mean squares 124-129
MIXED procedure analysis 131-135
Satterthwaite’s formula 129-131
treatment differences 133-134
crossover design, with residual effects 402-409
CS (compound symmetry) models 274, 282
unstructured covariance models 294-295
cultivars of grasses (example) 136-140
D
DATA= option, PROC REG statement 6
DDFM option, MODEL statement 132, 427
degrees of freedom (DF)
Satterthwaite’s formula for approximating 129-131
variance partitioning 42-44
Delta Rule 331-332
logistic analysis of variance 341
probit regression models 338
dependent mean 7
dependent variables 3
DEPONLY option, MEANS statement 234
deviance 331
generalized linear models (GzLMs) 387
DF (degrees of freedom)
Satterthwaite’s formula for approximating 129-131, 134
variance partitioning 42-44
DIFF option, LSMEANS statement 134
DIST option, MODEL statement 329, 367
distribution of response variables 329
DIVISOR option, ESTIMATE statement 61
dosage-to-response data set (example) 256-263
DRUGS and FLUSH data sets (example) 142-144
analysis of variance 144-146
CONTRAST statement 146
empty cells 148-151
ESTIMATE statement 146
F-tests for fixed-effects unbalanced mixed models 222-225
LSMEANS statement 147
mixed-model methodology 151-161
DSCALE option, MODEL statement 363, 366
dummy-variable models 163
analysis of variance 170-175
estimable functions 175-179
LS mean 176-178
one-way 164-179
one-way analysis of variance 170-179
parameter estimates 167-170
DUNCAN option, MEANS statement 65-68
Duncan’s multiple-range test 48, 65-68
DUNNETT option, MEANS statement 70-71
Dunnett’s procedure 70-71
mixed-model random-blocks analysis 109
E
E option, LSMEANS statement 350
E= option
CONTRAST statement 116
ESTIMATE statement 117
LSMEANS statement 156, 176, 178, 210
TEST statement 100
EBLUP (estimated BLUP) 105
effect values 25
effects models 49-50
eigenvalues and eigenvectors 322
estimable functions, one-way analysis of variance 179
estimable functions, two-way classification 201-203
estimable functions, two-way classification, empty cells 210-214
estimating unequal slopes analysis of covariance 242-244
experiments with qualitative and quantitative variables 411
INTERCEPT parameter 61-62
main effect comparisons 85-86
one-way analysis of variance, dummy-variable models 170
random-location analysis of multi-location data 426-427
simple effect comparisons 85-86
unbalanced data 146
unbalanced data with empty cells 150
unbalanced mixed-model data 155-156
unbalanced mixed-model data with empty cells 159
unbalanced two-way classification 191-194
univariate ANOVA, repeated-measures data 272-273
ESTIMATE statement, MIXED procedure 82-84
crossed-nested classification 133
E= option 117
main effect comparisons 85-86
nested classifications, overall mean and BLUP 104-105
randomized-complete-blocks design 111
simple effect comparisons 85-86
split-plot experiments 140
unbalanced data 146
unbalanced data with empty cells 150
unbalanced mixed-model data 158
unbalanced mixed-model data with empty cells 160
univariate ANOVA, repeated-measures data 272-273
estimated BLUP 105
estimated standard errors 8, 11
See also t-statistic
two-way mixed models 117-120
estimated treatment differences, mixed-model random-blocks analysis 108-109
ETYPE= option, LSMEANS statement 176, 178
exact linear dependency 21
exam scores data (example) 164-179, 306-309
exam scores data (example) (continued)
analysis of variance 170-175
estimable functions 175
parameter estimates 167-170
EXP option, ESTIMATE statement 364-365
expected mean squares
analysis of variance with random effects 98
balanced incomplete-blocks (BIB) design 401
crossed-nested classification 124-129
crossover design with residual effects 405
F-tests for fixed-effects unbalanced mixed models 222-225
mixed-model analysis and split-plot design 216-222
nested classifications 99-101
quadratic forms 120-122
random-location analysis of multi-location data 425
split-plot experiments 138, 216-220
two-way mixed models 114-117, 120-122
unbalanced mixed-model data 153-154
unbalanced two-way classification 224-225
experiment design 74
experimentwise error rate 48
F
F-statistic 7, 13, 24, 29-31
See also contrasts
analysis of variance with random effects 98
ANOVA for two-way mixed models 115-117
crossed-nested classification 125
folded, computing with TTEST 40
generalized linear models (GzLMs) 387
NOINT option and 20
simple effects 79
two-way analysis of covariance with interaction 254
Type I and II sums of squares 16
unbalanced data, Type III sum of squares 147-148
unbalanced mixed-model data 152-155, 157
F-tests
for fixed-effects unbalanced mixed models 222-225
Type II, versus t-statistic 16-17
factor levels, comparing 88
factorial combinations, means of 79, 80, 134
factorial experiments
See also two-way factorial experiments
complete 74
fractional 389, 394-398
main effects 74-75
FEV1 data sets (example) 265, 267-269
CONTRAST statement 272-273
ESTIMATE statement 272-273
LSMEANS statement 272-273
MIXED procedure analysis 296-303
multivariate analysis, repeated-measures data 275-279
reassessing covariance structure 291
repeated measures, fixed-effects models 281-284
repeated measures, information criterion 284, 292-295
repeated measures, selecting covariance model 284-291
univariate ANOVA 270-271
first-order ante dependence models [ANTE(1)] 283-284
first-order autoregressive models [AR(1)] 283, 288
unstructured covariance models 294-295
fit regression, analysis-of-covariance techniques for 261-263
fitting models
with one independent variable 5-9
with several independent variables 12-14
fixed-blocks assumption, for randomized-complete- blocks designs 106, 110-113
fixed-effect quadratic forms, two-way mixed models 120-122
fixed effects, defined 91-92
fixed-effects models, repeated-measures data 281-284
fixed-effects unbalanced mixed models 222-225
fixed-location analysis of multi-location data 423-425
FLUSH and DRUGS data sets (example)
See DRUGS and FLUSH data sets (example)
folded F-statistic 40
fractional factorial experiments 389, 394-398
FREQ statement
ANOVA procedure 47
GLM procedure 47
MEANS procedure 34-35
FWDLINK statement, GENMOD procedure 370, 372
G
G-G (Greenhouse-Geisser) corrections 278
GARMENTS data set (example) 72-74
GEE analysis of repeated measures 377-384
GENMOD procedure for 379-384
GEE option, PROC GENMOD statement 377
generalized estimating equations (GEEs) 384
analysis of repeated measures 377-384
generalized inverse 31-32
for parameter estimation 167-170
generalized least squares (GLS) 225-227
generalized linear models (GzLMs) 325-388
binomial models 339-352
count data and overdispersion 353-377
deviance 387
errors 386-387
estimating equations 386
F-statistic 387
lack-of-fit analysis 387
likelihood ratio statistics 387
log likelihood 385
logistic and probit regression models 328-338
maximum likelihood estimator (MLE) 386
natural parameter 385
repeated measures 377-384, 388
repeated measures and GEEs 377-384, 388
scale parameter 385
statistical background 384-388
transformations versus 326
variance function 327
Wald statistics 387
GENMOD procedure 327, 329, 339-352
See also CONTRAST statement, GENMOD procedure
See also ESTIMATE statement, GENMOD procedure
See also MODEL statement, GENMOD procedure
analysis of variance with probit link 344-346
count data 355-356
count data, goodness of fit 357-362
FWDLINK statement 370, 372
GEE analysis of repeated measures 379-384
GEE option 377
INVLINK statement 370, 372
likelihood ratio statistics 331
logistic analysis of covariance 347-352
logistic analysis of variance 338-344
logistic regression models with 0-1 data 334-336
LSMEANS statement 341, 350
negative binomial models, canonical link with 369-376
negative binomial models, log link with 367-369
ODS statements 341
overdispersion correction 362-366
probit regression models 337-338
REPEATED statement 380-381
Wald statistics 331
Wald statistics, user-supplied distributions 373
GLIMMIX macro 384
“GLM,” as acronym 327-328
GLM procedure 22-27, 42, 46
See also CONTRAST statement, GLM procedure
See also ESTIMATE statement, GLM procedure
See also LSMEANS statement, GLM procedure
See also MANOVA statement, GLM procedure
See also MEANS statement, GLM procedure
See also MODEL statement, GLM procedure
See also RANDOM statement, GLM procedure
See also REPEATED statement, GLM procedure
ABSORB statement 47, 431-439
absorbing nesting effects 432-437
analysis of covariance 232
analysis of covariance, multivariate 317-320
analysis of covariance, two-way with interaction 251-255
analysis of covariance, two-way without interaction 247-249
analysis of covariance, unequal slopes 239-241
analysis of covariance, unequal slopes, treatment differences 244-246
analysis of variance, multivariate, repeated- measures data 275-279
analysis of variance, nested classifications 96-99
GLM procedure (continued)
analysis of variance, one-way, dummy-variable models 170-179
analysis of variance, one-way multivariate 306-309
analysis of variance, split-plot experiment 137-139
analysis of variance, two-way factorial experiment 77-78
analysis of variance, two-way multivariate 312-317
analysis of variance, two-way, unbalanced data 182-183
analysis of variance, unbalanced data 144-146
analysis of variance, univariate, repeated- measures data 270-271, 274, 279-280
balanced incomplete-blocks (BIB) design 399
BY statement 47, 79
CLASS statement 46
computing one-way ANOVA table 52-54
confounding with blocks 390-394
crossed-nested classification 124-127
crossover design with residual effects 403-409
dummy-variable models 163
empty cells in unbalanced data 158-161
expected mean squares, nested classification ANOVA 100-101
experiments with qualitative and quantitative variables 410-413
fractional factorial experiments 394-398
FREQ statement 47
generalized inverse 31-32
generalized inverse for parameter estimates 167-170
lack-of-fit analysis 415-416
mixed-model analysis 215
mixed-model analysis, repeated-measures data 284-285
multi-location data, fixed location with interaction 423-425
multi-location data, no interaction 422
multiple comparison methods 65-70
multiple linear regression 22-23
ORDER= option 57
orthogonal polynomial contrasts (example) 257-259
OUTPUT statement 170
randomized-complete-blocks design 110-113
TEST statement 47, 100, 115
two-way mixed models 113-122
unbalanced mixed-model data 152-156, 161
unbalanced mixed-model data with empty cells 158-161
unbalanced nested structure 417-420
unbalanced two-way classification 191-194
unbalanced two-way classification with empty cells 203-214
Wald and likelihood ratio statistics 103-104
WEIGHT statement 170
GLS (generalized least squares) 225-227
goodness-of-fit criteria, logistic analysis of variance 341
goodness-of-fit statistics 357-362
GPLOT procedure 77
grasses, bacterial inoculation of (example) 136-140
GRASSES data set (example) 75
analysis of variance 75-78
diagrammatic method for CONTRAST and ESTIMATE statements 89
multiple comparisons 78-80
planned comparisons 82-84
simultaneous contrasts, two-way classifications 86
two-way mixed models 113-122
Greenhouse-Geisser (G-G) corrections 278
ground beef data set (example) 45
analysis of variance 96-99
expected mean squares for hypothesis testing 99-101
overall mean and BLUP 104-106
variance component estimation 101-104
gunpowder data set (example)
one-way analysis of variance 47-48
two-sample t-test 40
UNIVARIATE procedure to check assumptions 50-51
GzLMs
See generalized linear models
H
H-F (Huynh-Feldt) condition 274, 276, 278
H= option, TEST statement 100
heterogeneity of slopes, analysis of covariance 240
homogeneity of slopes, analysis of covariance 240
Honest Significant Difference method 65, 68-70
Hotelling’s T2 test 309-312
HOVTEST option, MEANS statement (GLM procedure) 51, 53-54
HRTRATE data set (example) 402-409
Huynh-Feldt (H-F) condition 274, 276, 278
hypothesis tests 29-31, 99-101
I
ID statement, MEANS procedure 34-35
identity link 386
IML procedure, ORPOL function 259-261
incomplete-blocks designs 65
balanced 398-402
independent covariance models 282
independent variables 3
fitting models with one 5-9
fitting models with several 12-14
indicator variables 163
information criteria
comparing covariance models 284
log likelihood 292
mixed-model analysis, repeated-measures data 284, 292-295
insect control experiment data set (example) 353-377
correcting for overdispersion 362-366
goodness-of-fit statistics 357-362
negative binomial models 366-377
interaction effects
factorial experiments 74-75
sums of squares 44
INTERCEP parameter, RESTRICT statement 19
intercept 3, 83
INTERCEPT parameter, CONTRAST and ESTIMATE statements 61-62
intra-block and inter-block information (BIB design) 400
inverse link functions 331-333, 385
INVLINK statement, GENMOD procedure 370, 372
irrigating methods data set (example) 214-222
Dunnett’s procedure 70-71
expected mean squares 216-220
expected mean squares, model formulation and 221-222
proper error terms 214-216
randomized-blocks design 62-71
K
KR (Kenward-Roger) correction 132, 296
L
labels
CONTRAST statement 25
TEST statement 17
lack-of-fit analysis 413-416
generalized linear models (GzLMs) 387
lag 284
Latin square design 72-74
least significant difference (LSD) method 48, 55, 65-66
mixed-model random-blocks analysis 109
least squares, ordinary 6
least-squares (LS) mean 78-80
See also entries at LSMEANS statement
absorbing nesting effects 434
analysis of covariance 234-237
crossover design with residual effects 407
location index analysis for multi-location data 430
logistic analysis of variance 341, 350
mixed-model random-blocks analysis 108-109
multi-location data, no interaction 422
negative binomial models 374-376
one-way analysis of variance, dummy-variable models 176-178
random-location analysis of multi-location data 426
randomized-complete-blocks design 111-112
unbalanced data with empty cells 150
unbalanced mixed-model data 155-156
unbalanced nested structure 418
less-than-full-rank models
parameter estimates 167-170
reduction notation 185
restrictions on 167-170
Levene’s Test for Homogeneity 51, 53-54
likelihood methodology, mixed models 225-227
likelihood ratio statistics
generalized linear models (GzLMs) 387
likelihood ratio statistics (continued)
GENMOD procedure 331
nested classification ANOVA 102-104
overdispersion and 362
Type 3, logistic analysis of variance 343
linear dependency, exact 21
linear models 163-227
See also generalized linear models (GzLMs)
log-linear models 385
linear regression analysis 3-32
See also GLM procedure
See also multiple linear regression
See also REG procedure
See also simple linear regression
exact linear dependency 21
notation 27
one independent variable 5-9
predicted values and confidence limits 10-11
restricted models 18-21
several independent variables 12-14
simple versus multiple 3
statistical background 27-32
terminology 27
tests of subsets of coefficients 17
Types I and II sums of squares 14-17
link functions 327, 329, 385
location index analysis, for multi-location data 428-431
log likelihood
generalized linear models (GzLMs) 385
information criteria 292
log-linear models 385
log link, negative binomial models 367-369
log odds ratio 333
logistic analysis of covariance 347-352
logistic analysis of variance 339-344, 350
Delta Rule 341
goodness-of-fit criteria 341
Type 3 likelihood ratio statistics 343
logistic regression models 328-336, 385
0-1 models 334-336
inverse link function 331-333
logit 386
logit function 329
longitudinal data
See repeated measures
LS mean
See least-squares mean
LSD (least significant difference) method 48, 55, 65-67
mixed-model random-blocks analysis 109
LSD option, MEANS statement 55, 65-67
LSD parameter, MEANS statement (ANOVA) 65-67
LSMEANS statement, GENMOD procedure
E option 350
logistic analysis of variance 341, 350
LSMEANS statement, GLM procedure 47, 78-80
ABSORB statement and 436
ADJUST option 80
ALPHA option 80
analysis of covariance 234-237
AT MEANS option 245
BYLEVEL option 237
CL option 80
crossover design with residual effects 407
estimable functions, one-way analysis of variance 176-178
estimable functions, two-way classification 201-203
estimable functions, two-way classification, empty cells 210-214
multi-location data, no interaction 422
multiple comparisons for factorial experiment 78-80
one-way analysis of variance, dummy-variable models 170
PDIFF option 80, 176
SLICE option 79, 80
unbalanced data 147
unbalanced data with empty cells 150
unbalanced mixed-model data 155-156
unbalanced mixed-model data with empty cells 159
unbalanced nested structure 418
unbalanced two-way classification 191-194
univariate ANOVA, repeated-measures data 272-273
LSMEANS statement, MIXED procedure 78-80, 82
AT MEANS option 245
BYLEVEL option 237
crossed-nested classification 133
DIFF option 134
mixed-model random-blocks analysis 108-109
SLICE option 79, 80, 134
split-plot experiments 140
unbalanced data 147
unbalanced data with empty cells 150
unbalanced mixed-model data 158
unbalanced mixed-model data with empty cells 160
univariate ANOVA, repeated-measures data 272-273
M
M= option, MANOVA statement 310
main effects
factorial experiments 74-75
factorial experiments, two-way 85
sums of squares 43
MANOVA statement, ANOVA procedure 47
MANOVA statement, GLM procedure 47
Hotelling’s T2 test 309
M= option 310
one-way multivariate analysis 307-309
PRINTE and PRINTH options 308
SUMMARY and MNAMES= options 310
two-way multivariate analysis of variance 312-317
MARKET and AUCTION data sets (example)
See AUCTION and MARKET data sets (example)
Mauchly’s criterion 276
maximum likelihood 96
maximum likelihood estimator (MLE), GzLMs 386
mean
difference, independent sample 39-41
difference, related samples 37-39
estimating, single sample 34-37
MEAN option, MEANS procedure 35
mean squares (MS) 7, 43
See also expected mean squares
mean squares for error (MSE) 7, 28
means, ordinary
See entries at MEANS statement
means models 49-50
MEANS procedure 34-35, 36, 37
ANOVA for two-way factorial experiment 76-78
MEANS statement, ANOVA procedure 46, 55
ALPHA parameter 65-67
CLDIFF option 69
CLM option 55-56
DUNCAN option 65-67
DUNNETT option 70-71
LSD option 55, 65-67
LSD parameter 65-67
multiple comparisons for factorial experiments 78-80
TUKEY option 65-67
WALLER option 65-67
MEANS statement, GLM procedure 46, 55, 177
ALPHA parameter 65-67
analysis of covariance 234-237
CLDIFF option 69
CLM option 55-56
DEPONLY option 234
DUNCAN option 65-67
DUNNETT option 70-71
HOVTEST option 51, 53-54
LSD option 55, 65-67
LSD parameter 65-67
multi-location data, fixed location with interaction 424
multi-location data, no interaction 422
multiple comparisons for factorial experiments 78-80
TUKEY option 65-67
two-way multivariate analysis 315
unbalanced nested structure 418
unbalanced two-way classification 191-194
WALLER option 65-67
METHOD= parameter, CLASS statement 118-119
METHODS data set (example)
Dunnett’s procedure 70-71
randomized-blocks design 62-71
microbial counts data set (example) 45
analysis of variance 96-99
expected mean squares for hypothesis testing 99-101
overall mean and BLUP 104-106
variance component estimation 101-104
mixed-model analysis 214-222
See also entries at MIXED procedure
See also mixed-model analysis of repeated- measures data
See also two-way mixed models
mixed-model analysis (continued)
absorbing nesting effects 437-439
balanced incomplete-blocks (BIB) design 401
expected mean squares 216-220
expected mean squares, and model formulation 221-222
GLS and likelihood methodology 225-227
proper error terms 214-216
random-blocks design 107-110
unbalanced data 151-161
unbalanced models, analysis of variance 222-225
mixed-model analysis of repeated-measures data 266, 280-303
covariance models, list of 281-284
covariance models, selecting 284-291
information criteria 284, 292-295
MIXED procedure analysis 296-298
regression comparisons 301-303
treatment and time effects 298-303
MIXED procedure 42, 80-82
See also CONTRAST statement, MIXED procedure
See also ESTIMATE statement, MIXED procedure
See also LSMEANS statement, MIXED procedure
See also MODEL statement, MIXED procedure
See also RANDOM statement, MIXED procedure
absorbing nesting effects 437-439
analysis of variance, nested classifications 96-97
analysis of variance, split-plot experiment 139-140
asthma drugs (example) 296-303
balanced incomplete-blocks (BIB) design 401
CLASS statement 82
crossed-nested classification 124, 127, 131-135
crossover design with residual effects 408
dummy-variable models 163
fit regression, analysis-of-covariance techniques for 262-263
GLS and likelihood methodology mixed models 225-227
mixed-model random-blocks analysis 107-110
mixed-model repeated-measures analysis 296-298
NOBOUND option 118-119
NOPROFILE option 302
ODS statements 82, 300
ORDER= option 109
overall mean and BLUP, nested classifications 104-106
PARMS statement 301-302
random-location analysis of multi-location data 425-428
randomized-complete-blocks design 110-113
repeated measures, information criterion 284, 292-295
repeated measures, selecting covariance model 284-291
repeated-measures data 281-284
REPEATED statement 226, 294-295
two-way analysis of covariance with interaction 251-255
two-way mixed models 113-122
unbalanced mixed-model data 156-158, 161
unbalanced mixed-model data with empty cells 159-161
unequal slopes analysis of covariance, treatment differences 244-246
VAR statement 82
variance component estimation, nested classification 101-104
Wald and likelihood ratio statistics 103-104
MLE (maximum likelihood estimator), GzLMs 386
MLOC data set (example) 420-431
MNAMES= option, MANOVA statement 310
model fitting, one independent variable 5-9
model-fitting criteria
See information criteria
model parameters 83
linear combinations of 59
MODEL statement, ANOVA procedure 46
MODEL statement, GENMOD procedure
DIST option 329, 367
DSCALE option 363, 366
OBSTATS option 358
probit regression models 337-338
PSCALE option 363, 366
TYPE1 and TYPE3 options 330
WALD option 330
MODEL statement, GLM procedure 46, 101
ALIASING option 391-392, 396
NOUNI option 310
one-way analysis of variance, dummy-variable models 171-173
two-way analysis of variance, unbalanced data 183
MODEL statement, MEANS procedure 36
MODEL statement, MIXED procedure 82, 101-104
crossed-nested classification 132
DDFM option 132, 427
split-plot experiments 139-140
versus GLM procedure 101
MODEL statement, REG procedure 4
CLI option 10-11
CLM option 10-11, 36
NOINT option 6, 20
P option 10-11
SS1, SS2 options 14-17
model (regression) sums of squares 7, 28
MONOFIL data set (example) 409-413
monofilament fiber tensile strength data set (example) 409-413
MS (mean squares) 7, 43
MSE (mean square error) 7, 28
μ -model notation, sums of squares 185-187
multi-location data 420-431
BLUPs 426-428
fixed-location analysis with interaction 423-425
location index analysis 428-431
no LOC HTRT interaction 421-423
random-location analysis 425-428
multiple comparisons, analysis of variance 48, 55
ANOVA procedure 65-70
confidence intervals 69-70
factorial experiments 78-80
GLM procedure 65-70
multiple covariates 238
multiple linear regression 3, 12-14
estimating combinations of parameters 26
exact linear dependency 21
GLM procedure 22-23
restricted models 18-21
statistical background 27-32
tests of subsets of coefficients 17
Types I and II sums of squares 14-17
multivariate analysis of variance 305-323
analysis of covariance 317-320
asthma drugs (example) 275-279
contrasts 320-321
Hotelling’s T2 test 309-312
notation 321-323
one-way 306-309
repeated measures 280-281
statistical background 321-323
two-factor factorial 312-317
two-way 312-317
muzzle velocity data set (example)
one-way analysis of variance 47-48
two-sample t-test 40
UNIVARIATE procedure to check assumptions 50-51
N
natural parameter, GzLMs 385
negative binomial models 366-377
canonical link, GENMOD procedure for 369-371
canonical link, user-supplied program for 372-376
log link, GENMOD procedure for 367-369
nested classifications 45, 93-106
See also crossed-nested classification
analysis of variance 45, 96-99
expected means squares 99-101
overall mean and BLUP 104-106
variance component estimation 101-104
variances of means and sampling plans 99
Wald statistics 102-104
nested effects, absorbing 431-439
NESTED procedure 96-97
nested structure, unbalanced 416-420
nested sums of squares 45
NOBOUND option, PROC MIXED statement 118-119
NOINT option, MODEL statement 6, 20-21
NOITER option, PROC MIXED statement 302
NOPROFILE option, PROC MIXED statement 302
notation
See also statistical background
analysis of variance 42-44
“GLM,” as acronym 327-328
linear regression analysis 27
multivariate analysis 321-323
notation (continued)
reduction notation for sums of squares 183-185
NOUNI option, MODEL statement 310
O
O-ring data set (example) 328-338
0-1 models 334-336
inverse link function 331-333
probit regression models 337-338
OBSTATS option, MODEL statement 358
odds 333
ODS statements
GENMOD procedure 341
MIXED procedure 82, 300
OLS estimates 6
one-sample analysis 34-37
paired-difference analysis 37-39
one-way analysis of covariance 230-238
adjusted and unadjusted means 234-237
contrasts 237-238
multiple covariates 238
one-way analysis of variance 49-62
BULLET data set 47-48
computing ANOVA table 52-54
confidence intervals 55-56
estimating linear combinations of parameters 60-62
means and confidence intervals 55
model parameters 59
orthogonal contrasts 60
testing several contrasts simultaneously 59
one-way dummy-variable models 164-179
analysis of variance 170-179
estimable functions 175-179
parameter estimates 167-170
one-way multivariate analysis 306-309
optimum sampling plans, nested classifications 99
orange sales data set (example)
estimating regression slopes 241-246
multivariate analysis of covariance 317-320
two-way analysis of covariance without interaction 247-249
orange tree irrigation data set (example) 214-222
Dunnett’s procedure 70-71
expected mean squares 216-220
expected mean squares, and model formulation 221-222
mixed-model random-blocks analysis 107-110
proper error terms 214-216
randomized-blocks design 62-71
ORDER= option
PROC GLM statement 57
PROC MIXED statement 109
ordinary least squares 6
ordinary means
See entries at MEANS statement
ORPOL function, IML procedure 259-261
orthogonal contrasts 60
See also contrasts
orthogonal polynomial contrasts 257-259
orthogonal polynomials, and covariance methods 256-263
OUTPUT statement
GLM procedure 170
MEANS procedure 34-35, 37
overall mean, nested classifications 104-106
overdispersion and count data 353-377
correcting for overdispersion 362-366
goodness-of-fit statistics 357-362
likelihood ratio statistics 362
negative binomial models 366-377
overdispersion parameter 362
Wald statistics 362
overspecified models 165
oyster growth data set (example) 231
adjusted and unadjusted means 234-237
contrasts 237-238
testing homogeneity of slopes 240
P
P option, MODEL statement (REG procedure) 10-11
p-value 13
paired-difference analysis 37-39
parameter estimates 14
crossover design with residual effects 406
generalized inverse for 167-170
less-than-full-rank models 167-170
one-way dummy-variable models 167-170
unbalanced two-way classification 193
PARMS statement, MIXED procedure 301-302
partial sum of squares
See Type II (partial) sum of squares
partitioning
analysis of variance 42-44
sums of squares 28, 208
PDIFF option, LSMEANS statement 80, 176
unbalanced data 147
Pearson Chi-Square 331
planned comparisons
one-way analysis of variance 48, 56-58
two-way factorial experiments 82-84
PLOT procedure 76-77
Poisson distribution as appropriate
See overdispersion and count data
pooled variance estimate 39
population models 5
predicted values 10
confidence limits and 10-11
preplanned comparisons, analysis of variance 48
PRINTE option
MANOVA statement 308
REPEATED statement 275
PRINTH option, MANOVA statement 308
probit function 329
probit link 386
analysis of variance with 344-346
probit regression models 336-338
proper error terms 214-216
PRT option, MEANS procedure 35
PSCALE option, MODEL statement 363, 366
PULSE data set (example)
paired-difference analysis 37-39
randomized-complete-blocks design 62
Q
Q option, RANDOM statement 116, 120-122
crossed-nested classification 126
quadratic forms, expected mean squares 120-122
qualitative and quantitative variables, experiments with 409-413
quasi-likelihood theory 384, 387-388
R
R-square 7, 13
NOINT option and (MODEL statement) 20-21
random-effects models 91-140
crossed-nested classification 122-135
nested classification effects 45, 93-106
random-blocks analysis 106-113
Satterthwaite’s formula 129-131
split-plot experiments 135-140
two-way mixed models 113-122
random-location analysis of multi-location data 425-428
RANDOM statement, GLM procedure 97
ANOVA for two-way mixed models 115
expected mean squares, crossed-nested classification 124-129
one-way analysis of variance, dummy-variable models 170
Q option 116, 120-122, 126
TEST option 113-122, 128
unbalanced mixed-model data 153-154, 158
RANDOM statement, MIXED procedure
crossed-nested classification 133
expected mean squares, crossed-nested classification 124
GLS and likelihood methodology mixed models 226
Q option 116, 120-122, 126
random-blocks analysis 107-108
split-plot experiments 139-140
TEST option 113-122, 128
randomized-blocks design 62-71
analysis of variance 64-65, 107-110
Dunnett’s procedure 70-71
GLM versus MIXED procedures 110-113
mixed-model analysis 107-110
multiple comparison methods with 65-70
randomized-complete-blocks design 62
analysis of variance 64-65
fixed-blocks assumption 106, 110-113
GLM versus MIXED procedures 110-113
random-blocks analysis 106-113
sums of squares 65
treatment differences 112
treatment means 111
rat weight-gain data set (example) 309-312
reduced regression models 17-18, 28
reduction in sum of squares 29
reduction notation, for sums of squares 183-185
REG procedure 4-22
See also MODEL statement, REG procedure
DATA= option, 6
exact linear dependency 21
fitting models 5-9, 12-14
generalized inverse 31-32
labels 17
multiple linear regression 12-14
NOINT option 6
RESTRICT statement 18-21
TEST statement 17-18
regression analysis 3
See also linear regression analysis
regression coefficients 3
regression comparisons, mixed-model repeated measures 301-303
regression models
complete 28
fit regression, analysis-of-covariance techniques for 261-263
fitting 5-9, 12-14
lack-of-fit analysis 414-416
probit 336-338
reduced 17-18, 28
restricted 18-21
regression parameters 24-26
See also F-statistic
See also t-statistic
regression sums of squares 7, 28
REML (restricted maximum likelihood) 96, 102, 301
two-way mixed models 118
unbalanced mixed-model data 157
repeated measures 265-303
See also mixed-model analysis
analysis of contrasts 266, 274-280
fixed-effects models 281-284
GEE analysis of 377-384
generalized linear models (GzLMs) 377-384, 388
information criterion 284, 292-295
selecting covariance model 284-291
univariate ANOVA method 266, 269-273
REPEATED statement, ANOVA procedure 47
REPEATED statement, GENMOD procedure 380-381
CORRW and TYPE options 380
REPEATED statement, GLM procedure 47
multivariate analysis, repeated-measures data 275-279
PRINTE option 275
SUMMARY option 279-280
REPEATED statement, MIXED procedure
GLS and likelihood methodology mixed models 226
unstructured covariance models 294-295
residual DF (degrees of freedom) 43
residual effects, crossover design with 402-409
residual log likelihood 102
residual mean squares 43
residual sums of squares 7, 28, 42
response variables 329
RESTRICT statement, REG procedure 18-21
INTERCEP parameter 19
restricted maximum likelihood (REML) 96, 102, 301
two-way mixed models 118
unbalanced mixed-model data 157
restricted regression models 18-21
restrictions, on less-than-full-rank models 167-170
root MSE 7
S
sampling plans, nested classifications 99
Satterthwaite’s formula for approximate DF 129-131, 134
saturated models 343
SBC (Schwartz’s Bayesian Information Criterion) 293
scale parameter, GzLMs 385
Schwartz’s Bayesian Information Criterion (SBC) 293
SEIZURE data set (example) 377-384
semiconductor resistance data set (example) 122-135
analysis of variance 124
expected mean squares 124-129
MIXED procedure analysis 131-135
Satterthwaite’s formula 129-131
separate slopes models 230
sequential sum of squares
See Type I (sequential) sum of squares
shrinkage estimator 105
simple effects 44
comparisons 85-86
confidence limits on differences 80-82
F-statistic 79
factorial experiments 74-75
factorial experiments, two-way 84
simple linear regression 3
fitting models with REG procedure 5-9
fitting regression models with GLM procedure 22-23
predicted values and confidence limits 10-11
testing hypotheses on regression parameters 24-26
simultaneous contrasts, two-way classifications 86
single-sample analysis 34-37
paired-difference analysis 37-39
SINGULAR= option, LSMEANS statement 176
sires data set (example) 431-439
SLICE option, LSMEANS statement 79, 80, 134
slope 3
common slope models 230
common slopes analysis of covariance 349-352
equal slopes analysis of covariance 349-352
heterogeneity of 240
homogeneity of 240
regression slopes 241-246
separate slopes models 230
unequal slopes analysis of covariance 239-246
SOLUTION option, MODEL statement 104-105
estimating estimable functions, two-way classification 201
one-way analysis of variance, dummy-variable models 171-173
split-plot experiments 135-140, 214-222
analysis of variance 137-139
expected mean squares 138, 216-220
expected mean squares, model formulation and 221-222
proper error terms 214-216
split-plot in time ANOVA 266
SS1, SS2 options, MODEL statement 14-17
standard errors
See estimated standard errors
statistical background
generalized linear models (GzLMs) 384-388
linear regression 27-32
multiple linear regression 27-32
multivariate analysis 321-323
statistical models 4
STD option, MEANS procedure 35
STDERR option
LSMEANS statement 176
MEANS procedure 35
steer sires data set (example) 431-439
student exam scores data (example) 164-179, 306-309
analysis of variance 170-175
estimable functions 175
parameter estimates 167-170
subsets of coefficients 17
SUMMARY option
MANOVA statement 310
REPEATED statement 279-280
sums of squares
See also Type I (sequential) sum of squares
See also Type II (partial) sum of squares
See also Type III sum of squares
See also Type IV sum of squares
estimable functions, two-way classification 196-201
interaction effect 44
main effect 43
μ -model notation 185-187
nested 45
NOINT option and (MODEL statement) 20-21
partitioning 28, 208
randomized-complete-blocks design 65
reduction in 29
reduction notation 183-185
regression (model) 7, 28
residual (error) 7, 28, 42
total 28, 42
unadjusted treatment 233-234, 400
unbalanced two-way classification 189-190, 223
T
T option, MEANS procedure 35
t-statistic 14, 24, 29-31
See also estimated standard errors
t-statistic (continued)
Hotelling’s T2 test versus 309
LSD (least significant difference) method 48
single sample 34-37
two independent samples 39-41
two related samples 37-39
Type II F-tests versus 16-17
T2 test 309-312
tensile strength of fiber (example) 409-413
terminology
analysis of variance 42-44
linear regression analysis 27
TEST option, RANDOM statement 97, 100
crossed-nested classification 128
two-way mixed models 113-122
TEST statement
ANOVA procedure 47
GLM procedure 47, 100, 115
REG procedure 17-18
tests of subsets of coefficients 17
time-to-event variables 326
Toeplitz models 283, 288
unstructured covariance models 294-295
total DF (degrees of freedom) 43
total sums of squares 28, 42
transformations versus generalized linear models 326
treatment design 74
treatment differences
crossed-nested classification 133-134
randomized-complete-blocks design 112
unequal slopes analysis-of-covariance models 244-246
treatment-dose bioassay data (example) 347-352
treatment means, randomized-complete-blocks design 111
TTEST procedure 38-39
folded F-statistic 40
TUKEY option, MEANS statement 65, 68-70
Tukey’s Honest Significant Difference method 65, 68-70
turf grasses data
See GRASSES data set (example)
two-cube factorial data (example) 390-394
two-way analysis of covariance
with interaction 249-255
without interaction 247-249
two-way classification of unbalanced data
See unbalanced data, two-way classification
two-way factorial experiments 74-90
analysis of variance 75-78
confidence limits on simple effect differences 80-82
confounding in 389-398
factor levels with other factor level subgroups 87-88
interaction effects 74-75
main effects 85
multiple comparisons 78-80
planned comparisons 82-84
simple effects 84
simultaneous contrasts 86
two-way mixed models 113-122
analysis of variance 114-117
quadratic forms and fixed-effects hypotheses 120-122
standard errors 117-120
two-way multivariate analysis 312-317
type-dose data set (example) 256-263
analysis of covariance 261-263
Type I error
CONTRAST statements and (GLM procedure) 58
multiple comparison tests 65-66
multiple comparisons and 48
simultaneous contrasts, two-way classifications 87
Type I (sequential) sum of squares 14-17
balanced incomplete-blocks (BIB) design 400
empty cells, effect of 149-150
estimable functions, two-way classification 196-201
F-statistic 16
μ -model notation 185-187
randomized-complete-blocks design 65
reduction notation 183-185
two-way mixed models 118-119
unbalanced mixed-model data 152-153
unbalanced two-way classification 182-183, 189-190
Type II error
multiple comparison tests 65-66
simultaneous contrasts, two-way classifications 87
Type II F-tests versus t-statistic 16-17
Type II (partial) sum of squares 14-17, 23
empty cells, effect of 149-150
estimable functions, two-way classification 196-201
F-statistic 16
μ -model notation 185-187
reduction notation 183-185
two-way mixed models 118-119
unbalanced mixed-model data 152-153
unbalanced two-way classification 182-183
Type III analysis of covariance 296-303
Type 3 likelihood ratio statistics, logistic analysis of variance 343
Type III sum of squares 23
balanced incomplete-blocks (BIB) design 400
empty cells, effect of 149-150
empty cells, unbalanced two-way classification 203-214
estimable functions, two-way classification
μ -model notation 185-187
randomized-complete-blocks design 65
reduction notation 183-185
two-way mixed models 118-119
unbalanced data 147-148
unbalanced mixed-model data 152-153
unbalanced two-way classification 182-183, 189-190
Type IV sum of squares 23
empty cells, effect of 149-150
empty cells, unbalanced two-way classification 203-214
estimable functions, two-way classification 196-201
μ -model notation 185-187
reduction notation 183-185
unbalanced two-way classification 182-183, 189-190
TYPE option, REPEATED statement 380
TYPE1 and TYPE3 options, MODEL statement 330
U
unadjusted treatment means, analysis of covariance 234-237
unadjusted treatment sum of squares 233-234
balanced incomplete-blocks (BIB) design 400
unbalanced data 141-161
See also unbalanced data, two-way classification
See also unbalanced mixed-model data
analysis of variance 144-146
CONTRAST statement 146, 148, 150
empty cells in 148-151
ESTIMATE statement 146, 150
LSMEANS statement 150
Type III sum of squares, F-statistic 147-148
weighted hypothesis 148
unbalanced data, two-way classification 179-214
CONTRAST statement 191-194
contrasts 192-193
empty cells 203-214
estimable functions 194-203
ESTIMATE statement 191-194
example of (calf feed rations) 188-190
GLM procedure for sums of squares 182
LSMEANS statement 191-194
MEANS statement 191-194
μ -model notation for sums of squares 185-187
parameter estimates 193
reduction notation for sums of squares 183-185
sums of squares 189-190, 223
unbalanced mixed-model data 151-161
See also unbalanced data
analysis of variance 222-225
CONTRAST statement 155-156
empty cells 158-161
ESTIMATE statement 155-156
F-statistic 152-155, 157
fixed effects 222-225
GLM procedure with 152-156, 161
LSMEANS statement 155-156
MIXED procedure with 156-158, 161
variance component estimation 154
unbalanced nested structure 416-420
underdispersion 373
unequal slopes analysis-of-covariance models 239-246
estimating slopes 241-244
testing treatment differences 244-246
univariate ANOVA, repeated-measures data 266, 269-273
UNIVARIATE procedure, checking ANOVA assumptions 50-51
unstructured covariance models 282, 294-295
unstructured models and compound symmetry 294-295
V
Valencia orange data set (example) 214-222
Dunnett’s procedure 70-71
expected mean squares 216-220
expected mean squares, and model formulation 221-222
proper error terms 214-216
randomized-blocks design 62-71
VAR statement
MEANS procedure 34-35
MIXED procedure 82
VARCOMP procedure 96-97
variables
See also dummy-variable models
class variables 239
covariables 239
dependent variables 3
independent variables 3, 5-9, 12-14
indicator variables 163
qualitative and quantitative together 409-413
response variables 329
time-to-event variables 326
variance, components of 96
variance component estimation
nested classification 101-104
unbalanced mixed-model data 154
variance function 327
generalized linear models (GzLMs) 385
variance partitioning 42-44
variances of means, nested classifications 99
VENEER data set (example)
ANOVA table 52-54
means and confidence intervals 55
orthogonal contrasts 60
planned comparisons 56-58
W
WALD option, MODEL statement 330
Wald statistics
generalized linear models (GzLMs) 387
GENMOD procedure 331
nested classification ANOVA 102-104
overdispersion and 362
user-supplied distributions, GENMOD procedure 373
Waller-Duncan method 65-67
WALLER option, MEANS statement 65-67
weight gain in rats (example) 309-312
WEIGHT statement
GLM procedure 170
MEANS procedure 34-35
weighted hypothesis, unbalanced data 148
weighted squares of means analysis 48
WHERE statement, MEANS procedure 34-35
working correlation matrix 388
WTGAIN data set (example) 309-312
Y
Yates’s weighted squares of means analysis 48
Numbers
0-1 models
fractional factorial data 397
logistic regression 334-336