SAS/STAT 922 User's Guide: The MIXED Procedure (Book Excerpt)

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4718 ✦ Chapter 56: The MIXED Procedure Wolfinger, R. D. and Chang, M. (1995), “Comparing the SAS GLM and MIXED Procedures for Repeated Measures,” Proceedings of the Twentieth Annual SAS Users Group Conference. Wolfinger, R. D., Tobias, R. D., and Sall, J. (1991), “Mixed Models: A Future Direction,” Proceedings of the Sixteenth Annual SAS Users Group Conference, 1380–1388. Wolfinger, R. D., Tobias, R. D., and Sall, J. (1994), “Computing Gaussian Likelihoods and Their Derivatives for General Linear Mixed Models,” SIAM Journal on Scientific Computing, 15(6), 1294–1310. Wright, P. S. (1994), “Adjusted F Tests for Repeated Measures with the MIXED Procedure,” 328 SMC-Statistics Department, University of Tennessee. Zimmerman, D. L. and Harville, D. A. (1991), “A Random Field Approach to the Analysis of Field-Plot Experiments and Other Spatial Experiments,” Biometrics, 47, 223–239.
Subject Index 2D geometric anisotropic structure MIXED procedure, 4583 Akaike’s information criterion example (MIXED), 4642, 4656, 4684 MIXED procedure, 4530, 4601, 4622 Akaike’s information criterion (finite sample corrected version) MIXED procedure, 4530, 4622 alpha level MIXED procedure, 4528, 4543, 4548, 4553, 4574 anisotropic power covariance structure MIXED procedure, 4584 anisotropic spatial power structure MIXED procedure, 4584 ANTE(1) structure MIXED procedure, 4583 ante-dependence structure MIXED procedure, 4583 AR(1) structure MIXED procedure, 4583 asymptotic covariance MIXED procedure, 4528 at sign (@) operator MIXED procedure, 4608, 4680 autoregressive moving-average structure MIXED procedure, 4583 autoregressive structure example (MIXED), 4650 MIXED procedure, 4583 banded Toeplitz structure MIXED procedure, 4583 bar (|) operator MIXED procedure, 4607, 4608, 4680 Bayesian analysis MIXED procedure, 4569 BLUE MIXED procedure, 4602 BLUP MIXED procedure, 4602 Bonferroni adjustment MIXED procedure, 4547 boundary constraints MIXED procedure, 4568, 4569, 4636 CALIS procedure compared to MIXED procedure, 4518 chi-square test MIXED procedure, 4542, 4554 class level MIXED procedure, 4532, 4620 compound symmetry structure example (MIXED), 4595, 4650, 4656 MIXED procedure, 4583 computational details MIXED procedure, 4635 computational problems convergence (MIXED), 4636 conditional residuals MIXED procedure, 4612 confidence limits adjusted (MIXED), 4708 and isotronic contrasts (MIXED), 4708 MIXED procedure, 4529 constraints boundary (MIXED), 4568, 4569 containment method MIXED procedure, 4554, 4555 continuous-by-class effects MIXED procedure, 4609 continuous-nesting-class effects MIXED procedure, 4609 contrasts MIXED procedure, 4539, 4543 convergence criterion MIXED procedure, 4528, 4529, 4621, 4637 convergence problems MIXED procedure, 4636 convergence status MIXED procedure, 4621 Cook’s D MIXED procedure, 4616 Cook’s D for covariance parameters MIXED procedure, 4616 correlation estimates (MIXED), 4575, 4577, 4582, 4652 covariance parameter estimates (MIXED), 4529, 4530 parameter estimates, ratio (MIXED), 4538 parameters (MIXED), 4514 covariance parameter estimates MIXED procedure, 4622 covariance structure anisotropic power (MIXED), 4590 ante-dependence (MIXED), 4587
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SAS/STAT ® 9.22 User’s Guide The
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Chapter 56 The MIXED Procedure Cont
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Basic Features ✦ 4515 Repeated me
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PROC MIXED Contrasted with Other SA
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proc mixed data=heights; class Fami
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Figure 56.6 Fit Statistics Fit Stat
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Figure 56.10 Dimensions and Number
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Syntax: MIXED Procedure The followi
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Table 56.1 continued Statement Desc
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PROC MIXED Statement ✦ 4529 CL< =
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INFO PROC MIXED Statement ✦ 4531
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ORD PROC MIXED Statement ✦ 4533 d
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PROC MIXED Statement ✦ 4535 RESID
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PROC MIXED Statement ✦ 4537 RANDO
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CLASS Statement ✦ 4539 Because so
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contrast 'A narrow' A 1 -1 0 A*B .5
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ESTIMATE Statement ESTIMATE ’labe
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ID Statement ID variables ; ID Stat
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ADJUST=BON proc mixed; class A; mod
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LSMEANS Statement ✦ 4549 BYLEVEL
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SLICE= fixed-effect LSMESTIMATE Sta
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Table 56.6 Summary of Important MOD
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MODEL Statement ✦ 4555 DDFM=KENWA
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E E1 E2 E3 MODEL Statement ✦ 4557
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Table 56.8 continued Description Su
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SIZE=n MODEL Statement ✦ 4561 If
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MODEL Statement ✦ 4563 Table 56.1
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The estimated prediction variance i
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PARMS Statement PARMS (value-list)
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OLS PRIOR Statement ✦ 4569 By def
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PRIOR Statement ✦ 4571 JEFFREYS s
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RANDOM Statement ✦ 4573 TDATA= en
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RANDOM Statement ✦ 4575 GCORR dis
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RANDOM Statement ✦ 4577 component
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Table 56.12 continued Option Descri
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proc mixed; class a; model y = a x;
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REPEATED Statement ✦ 4583 assumed
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REPEATED Statement ✦ 4585 functio
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REPEATED Statement ✦ 4587 The fol
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TYPE=SP(EXPGA)(c1 c2) TYPE=SP(GAUGA
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TYPE=UN@AR(1) TYPE=UN@CS REPEATED S
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WEIGHT Statement WEIGHT variable ;
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Example: Growth Curve with Compound
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Mixed Models Theory ✦ 4597 Such a
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2 6 Z D 6 4 2 6 G D 6 4 1 1 1 1 1 1
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Estimating Fixed and Random Effects
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Inference and Test Statistics Mixed
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Mixed Models Theory ✦ 4605 (2002,
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Intercept Parameterization of Mixed
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Table 56.18 continued Data I A B(A)
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Residuals and Influence Diagnostics
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Scaled Residuals Residuals and Infl
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Predicted Values, PRESS Residual, a
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When ITER=0 and 2 is profiled, then
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Using results in Cook and Weisberg
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Default Output ✦ 4621 The Evaluat
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Null Model Likelihood Ratio Test De
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Table 56.22 continued ODS Table Nam
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ODS Table Names ✦ 4627 CAUTION: T
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ODS Graphics ✦ 4629 Some of the v
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Figure 56.16 Panel of the Condition
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Figure 56.18 Deletion Estimates ODS
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Computational Issues Computational
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Memory Computational Issues ✦ 463
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Examples: MIXED Procedure Examples:
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Example 56.1: Split-Plot Design ✦
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Example 56.1: Split-Plot Design ✦
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4 F 23.5 24.5 25.0 26.5 5 F 21.5 23
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Output 56.2.4 Repeated Measures Ana
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Output 56.2.7 Repeated Measures Ana
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Example 56.2: Repeated Measures ✦
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Output 56.2.14 Analysis with Compou
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Example 56.2: Repeated Measures ✦
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Example 56.3: Plotting the Likeliho
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Output 56.3.3 continued Number of O
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Output 56.3.8 Fit Statistics and Li
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Output 56.3.12 Least Squares Means
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Both G and R are known. 2 2 1 1 2 1
Page 157 and 158: Output 56.4.2 Model Dimensions and
Page 159 and 160: Example 56.4: Known G and R ✦ 466
Page 161 and 162: Example 56.5: Random Coefficients
Page 163 and 164: Example 56.5: Random Coefficients
Page 165 and 166: Output 56.5.7 Random Coefficients A
Page 167 and 168: Output 56.5.10 continued Covariance
Page 169 and 170: Example 56.6: Line-Source Sprinkler
Page 171 and 172: Output 56.6.3 Model Dimensions and
Page 173 and 174: Example 56.6: Line-Source Sprinkler
Page 175 and 176: Example 56.7: Influence in Heteroge
Page 177 and 178: Example 56.7: Influence in Heteroge
Page 179 and 180: Output 56.7.5 Covariance Parameter
Page 181 and 182: Output 56.7.7 Restricted Likelihood
Page 183 and 184: Output 56.7.9 Covariance Parameter
Page 185 and 186: Example 56.8: Influence Analysis fo
Page 187 and 188: Output 56.8.2 Restricted Likelihood
Page 193 and 194: Output 56.8.8 Distribution of Condi
Page 195 and 196: Output 56.9.2 Type 3 Tests in Split
Page 197 and 198: Output 56.9.5 Parameter Estimates i
Page 199 and 200: Output 56.10.1 Analysis of LS-Means
Page 201 and 202: References ✦ 4711 Cook, R. D. (19
Page 203 and 204: References ✦ 4713 Harville, D. A.
Page 205 and 206: References ✦ 4715 Matérn, B. (19
Page 207: Bulletin No. 343, Louisiana Agricul
Page 211 and 212: graphics, influence diagnostics, 46
Page 213 and 214: matrix notation, theory (MIXED), 45
Page 215 and 216: parameter constraints, 4568, 4636 p
Page 217: subject effect MIXED procedure, 454
Page 220 and 221: INFLUENCE option, MODEL statement (
Page 222 and 223: NSAMPLE= option, 4572 NSEARCH= opti
Page 224 and 225: ESTIMATE statement (MIXED), 4544 LS
Page 227: SAS® Publishing Delivers! Whether
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