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

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4546 ✦ Chapter 56: The MIXED Procedure Table 56.4 continued Option Description DIFF Requests differences of LS-means OM Specifies weighting scheme for LS-mean computation SINGULAR= Tunes estimability checking SLICE= Partitions F tests (simple effects) Degrees of Freedom and p-values ADJDFE= Determines whether to compute row-wise denominator degrees of freedom with DDFM=SATTERTHWAITE or DDFM=KENWARDROGER ADJUST= Determines the method for multiple comparison adjustment of LSmean differences ALPHA=˛ Determines the confidence level (1 ˛) DF= Assigns specific value to degrees of freedom for tests and confidence limits Statistical Output CL Constructs confidence limits for means and or mean differences CORR Displays correlation matrix of LS-means COV Displays covariance matrix of LS-means E Prints the L matrix You can specify the following options in the LSMEANS statement after a slash (/). ADJDFE=SOURCE ADJDFE=ROW specifies how denominator degrees of freedom are determined when p-values and confidence limits are adjusted for multiple comparisons with the ADJUST= option. When you do not specify the ADJDFE= option, or when you specify ADJDFE=SOURCE, the denominator degrees of freedom for multiplicity-adjusted results are the denominator degrees of freedom for the LS-mean effect in the “Type 3 Tests of Fixed Effects” table. When you specify AD- JDFE=ROW, the denominator degrees of freedom for multiplicity-adjusted results correspond to the degrees of freedom displayed in the DF column of the “Differences of Least Squares Means” table. The ADJDFE=ROW setting is particularly useful if you want multiplicity adjustments to take into account that denominator degrees of freedom are not constant across LS-mean differences. This can be the case, for example, when the DDFM=SATTERTHWAITE or DDFM=KENWARDROGER degrees-of-freedom method is in effect. In one-way models with heterogeneous variance, combining certain ADJUST= options with the ADJDFE=ROW option corresponds to particular methods of performing multiplicity adjustments in the presence of heteroscedasticity. For example, the following statements fit a heteroscedastic one-way model and perform Dunnett’s T3 method (Dunnett 1980), which is based on the studentized maximum modulus (ADJUST=SMM):
ADJUST=BON proc mixed; class A; model y = A / ddfm=satterth; repeated / group=A; lsmeans A / adjust=smm adjdfe=row; run; LSMEANS Statement ✦ 4547 If you combine the ADJDFE=ROW option with ADJUST=SIDAK, the multiplicity adjustment corresponds to the T2 method of Tamhane (1979), while ADJUST=TUKEY corresponds to the method of Games-Howell (Games and Howell 1976). Note that ADJUST=TUKEY gives the exact results for the case of fractional degrees of freedom in the one-way model, but it does not take into account that the degrees of freedom are subject to variability. A more conservative method, such as ADJUST=SMM, might protect the overall error rate better. Unless the ADJUST= option of the LSMEANS statement is specified, the ADJDFE= option has no effect. ADJUST=DUNNETT ADJUST=SCHEFFE ADJUST=SIDAK ADJUST=SIMULATE< (sim-options) > ADJUST=SMM | GT2 ADJUST=TUKEY requests a multiple comparison adjustment for the p-values and confidence limits for the differences of LS-means. By default, PROC MIXED adjusts all pairwise differences unless you specify ADJUST=DUNNETT, in which case PROC MIXED analyzes all differences with a control level. The ADJUST= option implies the DIFF option. The BON (Bonferroni) and SIDAK adjustments involve correction factors described in Chapter 39, “The GLM Procedure,” and Chapter 58, “The MULTTEST Procedure;” also see Westfall and Young (1993) and Westfall et al. (1999). When you specify ADJUST=TUKEY and your data are unbalanced, PROC MIXED uses the approximation described in Kramer (1956). Similarly, when you specify ADJUST=DUNNETT and the LS-means are correlated, PROC MIXED uses the factor-analytic covariance approximation described in Hsu (1992). The preceding references also describe the SCHEFFE and SMM adjustments. The SIMULATE adjustment computes adjusted p-values and confidence limits from the simulated distribution of the maximum or maximum absolute value of a multivariate t random vector. All covariance parameters except the residual variance are fixed at their estimated values throughout the simulation, potentially resulting in some underdispersion. The simulation estimates q, the true .1 ˛/th quantile, where 1 ˛ is the confidence coefficient. The default ˛ is 0.05, and you can change this value with the ALPHA= option in the LSMEANS statement. The number of samples is set so that the tail area for the simulated q is within of 1 ˛ with 100.1 /% confidence. In equation form, P.jF .bq/ .1 ˛/j / D 1
Page 1 and 2: SAS/STAT ® 9.22 User’s Guide The
Page 3 and 4: Chapter 56 The MIXED Procedure Cont
Page 5 and 6: Basic Features ✦ 4515 Repeated me
Page 7 and 8: PROC MIXED Contrasted with Other SA
Page 9 and 10: proc mixed data=heights; class Fami
Page 11 and 12: Figure 56.6 Fit Statistics Fit Stat
Page 13 and 14: Figure 56.10 Dimensions and Number
Page 15 and 16: Syntax: MIXED Procedure The followi
Page 17 and 18: Table 56.1 continued Statement Desc
Page 19 and 20: PROC MIXED Statement ✦ 4529 CL< =
Page 21 and 22: INFO PROC MIXED Statement ✦ 4531
Page 23 and 24: ORD PROC MIXED Statement ✦ 4533 d
Page 25 and 26: PROC MIXED Statement ✦ 4535 RESID
Page 27 and 28: PROC MIXED Statement ✦ 4537 RANDO
Page 29 and 30: CLASS Statement ✦ 4539 Because so
Page 31 and 32: contrast 'A narrow' A 1 -1 0 A*B .5
Page 33 and 34: ESTIMATE Statement ESTIMATE ’labe
Page 35: ID Statement ID variables ; ID Stat
Page 39 and 40: LSMEANS Statement ✦ 4549 BYLEVEL
Page 41 and 42: SLICE= fixed-effect LSMESTIMATE Sta
Page 43 and 44: Table 56.6 Summary of Important MOD
Page 45 and 46: MODEL Statement ✦ 4555 DDFM=KENWA
Page 47 and 48: E E1 E2 E3 MODEL Statement ✦ 4557
Page 49 and 50: Table 56.8 continued Description Su
Page 51 and 52: SIZE=n MODEL Statement ✦ 4561 If
Page 53 and 54: MODEL Statement ✦ 4563 Table 56.1
Page 55 and 56: The estimated prediction variance i
Page 57 and 58: PARMS Statement PARMS (value-list)
Page 59 and 60: OLS PRIOR Statement ✦ 4569 By def
Page 61 and 62: PRIOR Statement ✦ 4571 JEFFREYS s
Page 63 and 64: RANDOM Statement ✦ 4573 TDATA= en
Page 65 and 66: RANDOM Statement ✦ 4575 GCORR dis
Page 67 and 68: RANDOM Statement ✦ 4577 component
Page 69 and 70: Table 56.12 continued Option Descri
Page 71 and 72: proc mixed; class a; model y = a x;
Page 73 and 74: REPEATED Statement ✦ 4583 assumed
Page 75 and 76: REPEATED Statement ✦ 4585 functio
Page 77 and 78: REPEATED Statement ✦ 4587 The fol
Page 79 and 80: TYPE=SP(EXPGA)(c1 c2) TYPE=SP(GAUGA
Page 81 and 82: TYPE=UN@AR(1) TYPE=UN@CS REPEATED S
Page 83 and 84: WEIGHT Statement WEIGHT variable ;
Page 85 and 86: 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
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Output 56.4.2 Model Dimensions and
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Example 56.4: Known G and R ✦ 466
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Example 56.5: Random Coefficients
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Example 56.5: Random Coefficients
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Output 56.5.7 Random Coefficients A
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Output 56.5.10 continued Covariance
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Example 56.6: Line-Source Sprinkler
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Output 56.6.3 Model Dimensions and
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Example 56.6: Line-Source Sprinkler
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Example 56.7: Influence in Heteroge
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Example 56.7: Influence in Heteroge
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Output 56.7.5 Covariance Parameter
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Output 56.7.7 Restricted Likelihood
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Output 56.7.9 Covariance Parameter
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Example 56.8: Influence Analysis fo
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Output 56.8.2 Restricted Likelihood
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Page 191 and 192:
Page 193 and 194:
Output 56.8.8 Distribution of Condi
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Output 56.9.2 Type 3 Tests in Split
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Output 56.9.5 Parameter Estimates i
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Output 56.10.1 Analysis of LS-Means
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References ✦ 4711 Cook, R. D. (19
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References ✦ 4713 Harville, D. A.
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References ✦ 4715 Matérn, B. (19
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Bulletin No. 343, Louisiana Agricul
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Subject Index 2D geometric anisotro
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graphics, influence diagnostics, 46
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matrix notation, theory (MIXED), 45
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parameter constraints, 4568, 4636 p
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subject effect MIXED procedure, 454
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INFLUENCE option, MODEL statement (
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NSAMPLE= option, 4572 NSEARCH= opti
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ESTIMATE statement (MIXED), 4544 LS
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