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

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4554 ✦ Chapter 56: The MIXED Procedure CHISQ CL requests that chi-square tests be performed for all specified effects in addition to the F tests. Type 3 tests are the default; you can produce the Type 1 and Type 2 tests by using the HTYPE= option. requests that t-type confidence limits be constructed for each of the fixed-effects parameter estimates. The confidence level is 0.95 by default; this can be changed with the ALPHA= option. CONTAIN has the same effect as the DDFM=CONTAIN option. CORRB produces the approximate correlation matrix of the fixed-effects parameter estimates. For ODS purposes, the name of this table is “CorrB.” COVB COVBI produces the approximate variance-covariance matrix of the fixed-effects parameter estimates bˇ. By default, this matrix equals .X 0bV 1 X/ and results from sweeping .X y/ 0bV 1 .X y/ on all but its last pivot and removing the y border. The EMPIRICAL option in the PROC MIXED statement changes this matrix into “empirical sandwich” form. For ODS purposes, the name of this table is “CovB.” If the degrees-of-freedom method of Kenward and Roger (1997) is in effect (DDFM=KENWARDROGER), the COVB matrix changes because the method entails an adjustment of the variance-covariance matrix of the fixed effects by the method proposed by Prasad and Rao (1990) and Harville and Jeske (1992); see also Kackar and Harville (1984). produces the inverse of the approximate variance-covariance matrix of the fixed-effects parameter estimates. For ODS purposes, the name of this table is “InvCovB.” DDF=value-list enables you to specify your own denominator degrees of freedom for the fixed effects. The value-list specification is a list of numbers or missing values (.) separated by commas. The degrees of freedom should be listed in the order in which the effects appear in the “Tests of Fixed Effects” table. If you want to retain the default degrees of freedom for a particular effect, use a missing value for its location in the list. For example, the following statement assigns 3 denominator degrees of freedom to A and 4.7 to A*B, while those for B remain the same: model Y = A B A*B / ddf=3,.,4.7; If you specify DDFM=SATTERTHWAITE or DDFM=KENWARDROGER, the DDF= option has no effect. DDFM=CONTAIN DDFM=BETWITHIN DDFM=RESIDUAL DDFM=SATTERTHWAITE
MODEL Statement ✦ 4555 DDFM=KENWARDROGER< (FIRSTORDER) > specifies the method for computing the denominator degrees of freedom for the tests of fixed effects resulting from the MODEL, CONTRAST, ESTIMATE, and LSMEANS statements. Table 56.7 lists syntax aliases for the degrees-of-freedom methods. Table 56.7 Aliases for DDFM= Option DDFM= Option Alias BETWITHIN BW CONTAIN CON KENWARDROGER KENROG, KR RESIDUAL RES SATTERTHWAITE SATTERTH, SAT The DDFM=CONTAIN option invokes the containment method to compute denominator degrees of freedom, and it is the default when you specify a RANDOM statement. The containment method is carried out as follows: Denote the fixed effect in question A, and search the RANDOM effect list for the effects that syntactically contain A. For example, the random effect B(A) contains A, but the random effect C does not, even if it has the same levels as B(A). Among the random effects that contain A, compute their rank contribution to the (X Z) matrix. The DDF assigned to A is the smallest of these rank contributions. If no effects are found, the DDF for A is set equal to the residual degrees of freedom, N rank.X Z/. This choice of DDF matches the tests performed for balanced split-plot designs and should be adequate for moderately unbalanced designs. CAUTION: If you have a Z matrix with a large number of columns, the overall memory requirements and the computing time after convergence can be substantial for the containment method. If it is too large, you might want to use the DDFM=BETWITHIN option. The DDFM=BETWITHIN option is the default for REPEATED statement specifications (with no RANDOM statements). It is computed by dividing the residual degrees of freedom into between-subject and within-subject portions. PROC MIXED then checks whether a fixed effect changes within any subject. If so, it assigns within-subject degrees of freedom to the effect; otherwise, it assigns the between-subject degrees of freedom to the effect (see Schluchter and Elashoff 1990). If there are multiple within-subject effects containing classification variables, the within-subject degrees of freedom are partitioned into components corresponding to the subject-by-effect interactions. One exception to the preceding method is the case where you have specified no RANDOM statements and a REPEATED statement with the TYPE=UN option. In this case, all effects are assigned the between-subject degrees of freedom to provide for better small-sample approximations to the relevant sampling distributions. DDFM=KENWARDROGER might be a better option to try for this case. The DDFM=RESIDUAL option performs all tests by using the residual degrees of freedom, n rank.X/, where n is the number of observations.
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 and 36: ID Statement ID variables ; ID Stat
Page 37 and 38: ADJUST=BON proc mixed; class A; mod
Page 39 and 40: LSMEANS Statement ✦ 4549 BYLEVEL
Page 41 and 42: SLICE= fixed-effect LSMESTIMATE Sta
Page 43: Table 56.6 Summary of Important MOD
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
Page 87 and 88: Mixed Models Theory ✦ 4597 Such a
Page 89 and 90: 2 6 Z D 6 4 2 6 G D 6 4 1 1 1 1 1 1
Page 91 and 92: Estimating Fixed and Random Effects
Page 93 and 94: Inference and Test Statistics Mixed
Page 95 and 96:
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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