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

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4694 ✦ Chapter 56: The MIXED Procedure Output 56.7.10 Influence Diagnostics Observations 6, 9, 14, and 21 have considerable impact on estimates and precision of fixed effects and covariance parameters. This is not necessarily the case. Observations can be influential on only some aspects of the analysis, as shown in the next example. Example 56.8: Influence Analysis for Repeated Measures Data This example revisits the repeated measures data of Pothoff and Roy (1964) that were analyzed in Example 56.2. Recall that the data consist of growth measurements at ages 8, 10, 12, and 14 for 11 girls and 16 boys. The model being fit contains fixed effects for Gender and Age and their interaction. The earlier analysis of these data indicated some unusual observations in this data set. Because of the clustered data structure, it is of interest to study the influence of clusters (children) on the analysis rather than the influence of individual observations. A cluster comprises the repeated measurements for each child. The repeated measures are first modeled with an unstructured within-child variance-covariance matrix. A residual variance is not profiled in this model. A noniterative influence analysis will
Example 56.8: Influence Analysis for Repeated Measures Data ✦ 4695 update the fixed effects only. The following statements request this noniterative maximum likelihood analysis and produce Output 56.8.1: proc mixed data=pr method=ml; class person gender; model y = gender age gender*age / influence(effect=person); repeated / type=un subject=person; ods select influence; run; Output 56.8.1 Default Influence Statistics in Noniterative Analysis The Mixed Procedure Influence Diagnostics for Levels of Person Number of Observations PRESS Cook's Person in Level Statistic D 1 4 10.1716 0.01539 2 4 3.8187 0.03988 3 4 10.8448 0.02891 4 4 24.0339 0.04515 5 4 1.6900 0.01613 6 4 11.8592 0.01634 7 4 1.1887 0.00521 8 4 4.6717 0.02742 9 4 13.4244 0.03949 10 4 85.1195 0.13848 11 4 67.9397 0.09728 12 4 40.6467 0.04438 13 4 13.0304 0.00924 14 4 6.1712 0.00411 15 4 24.5702 0.12727 16 4 20.5266 0.01026 17 4 9.9917 0.01526 18 4 7.9355 0.01070 19 4 15.5955 0.01982 20 4 42.6845 0.01973 21 4 95.3282 0.10075 22 4 13.9649 0.03778 23 4 4.9656 0.01245 24 4 37.2494 0.15094 25 4 4.3756 0.03375 26 4 8.1448 0.03470 27 4 20.2913 0.02523 Each observation in the “Influence Diagnostics for Levels of Person” table in Output 56.8.1 represents the removal of four observations. The subjects 10, 15, and 24 have the greatest impact on the fixed effects (Cook’s D), and subject 10 and 21 have large PRESS statistics. The 21st child has a large PRESS statistic, and its D statistic is not that extreme. This is an indication that the model fits rather poorly for this child, whether it is part of the data or not.
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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 ✦
Page 133 and 134: Example 56.1: Split-Plot Design ✦
Page 135 and 136: 4 F 23.5 24.5 25.0 26.5 5 F 21.5 23
Page 137 and 138: Output 56.2.4 Repeated Measures Ana
Page 139 and 140: Output 56.2.7 Repeated Measures Ana
Page 141 and 142: Example 56.2: Repeated Measures ✦
Page 143 and 144: Output 56.2.14 Analysis with Compou
Page 145 and 146: Example 56.2: Repeated Measures ✦
Page 147 and 148: Example 56.3: Plotting the Likeliho
Page 149 and 150: Output 56.3.3 continued Number of O
Page 151 and 152: Output 56.3.8 Fit Statistics and Li
Page 153 and 154: Output 56.3.12 Least Squares Means
Page 155 and 156: 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: Output 56.7.9 Covariance Parameter
Page 187 and 188: Output 56.8.2 Restricted Likelihood
Page 189 and 190: Example 56.8: Influence Analysis fo
Page 191 and 192: Example 56.8: Influence Analysis fo
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 and 208: Bulletin No. 343, Louisiana Agricul
Page 209 and 210: Subject Index 2D geometric anisotro
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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SAS/STAT 922 User's Guide: The MIXED Procedure (Book Excerpt)

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