SAS/STAT 9.2 User's Guide: The MIXED Procedure (Book Excerpt)

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3914 ✦ Chapter 56: The MIXED Procedure SINGULAR=number tunes the estimability checking. If v is a vector, define ABS(v) to be the absolute value of the element of v with the largest absolute value. If ABS(K 0 K 0 T) is greater than C*number for any row of K 0 in the contrast, then K is declared nonestimable. Here T is the Hermite form matrix .X 0 X/ X 0 X, and C is ABS(K 0 ) except when it equals 0, and then C is 1. The value for number must be between 0 and 1; the default is 1E 4. SUBJECT coeffs SUB coeffs sets up random-effect contrasts between different subjects when a SUBJECT= variable appears in the RANDOM statement. By default, CONTRAST statement coefficients on random effects are distributed equally across subjects. ESTIMATE Statement ESTIMATE ’label’ < fixed-effect values . . . > < | random-effect values . . . >< / options > ; The ESTIMATE statement is exactly like a CONTRAST statement, except only one-row L matrices are permitted. The actual estimate, L 0 bp, is displayed along with its approximate standard error. An approximate t test that L 0 bp = 0 is also produced. PROC MIXED selects the degrees of freedom to match those displayed in the “Tests of Fixed Effects” table for the final effect you list in the ESTIMATE statement. You can modify the degrees of freedom by using the DF= option. If PROC MIXED finds the fixed-effects portion of the specified estimate to be nonestimable, then it displays “Non-est” for the estimate entries. The following examples of ESTIMATE statements compute the mean of the first level of A in the split-plot example (see Example 56.1) for various inference spaces: estimate ’A1 mean narrow’ intercept 1 A 1 B .5 .5 A*B .5 .5 | block .25 .25 .25 .25 A*Block .25 .25 .25 .25 0 0 0 0 0 0 0 0; estimate ’A1 mean intermed’ intercept 1 A 1 B .5 .5 A*B .5 .5 | Block .25 .25 .25 .25; estimate ’A1 mean broad’ intercept 1 A 1 B .5 .5 A*B .5 .5; The construction of the L vector for an ESTIMATE statement follows the same rules as listed under the CONTRAST statement. You can specify the following options in the ESTIMATE statement after a slash (/).
ESTIMATE Statement ✦ 3915 ALPHA=number requests that a t-type confidence interval be constructed with confidence level 1 number. The value of number must be between 0 and 1; the default is 0.05. CL requests that t-type confidence limits be constructed. The confidence level is 0.95 by default; this can be changed with the ALPHA= option. DF=number specifies the degrees of freedom for the t test and confidence limits. The default is the denominator degrees of freedom taken from the “Tests of Fixed Effects” table and corresponds to the final effect you list in the ESTIMATE statement. DIVISOR=number specifies a value by which to divide all coefficients so that fractional coefficients can be entered as integer numerators. E GROUP coeffs requests that the L matrix coefficients be displayed. For ODS purposes, the name of this “L Matrix Coefficients” table is “Coef.” GRP coeffs sets up random-effect contrasts between different groups when a GROUP= variable appears in the RANDOM statement. By default, ESTIMATE statement coefficients on random effects are distributed equally across groups. LOWER LOWERTAILED requests that the p-value for the t test be based only on values less than the t statistic. A two-tailed test is the default. A lower-tailed confidence limit is also produced if you specify the CL option. SINGULAR=number tunes the estimability checking as documented for the SINGULAR= option in the CONTRAST statement. SUBJECT coeffs SUB coeffs sets up random-effect contrasts between different subjects when a SUBJECT= variable appears in the RANDOM statement. By default, ESTIMATE statement coefficients on random effects are distributed equally across subjects. For example, the ESTIMATE statement in the following code from Example 56.5 constructs the difference between the random slopes of the first two batches. proc mixed data=rc; class batch; model y = month / s; random int month / type=un sub=batch s; estimate ’slope b1 - slope b2’ | month 1 / subject 1 -1; run;
Page 1 and 2: SAS/STAT ® 9.2 User’s Guide The
Page 3 and 4: Chapter 56 The MIXED Procedure Cont
Page 5 and 6: Basic Features ✦ 3887 clustered i
Page 7 and 8: variance components compound symmet
Page 9 and 10: Clustered Data Example ✦ 3891 The
Page 11 and 12: Clustered Data Example ✦ 3893 mat
Page 13 and 14: criterion of 1E 8. Figure 56.11 REM
Page 15 and 16: Syntax: MIXED Procedure ✦ 3897 Th
Page 17 and 18: Table 56.2 continued Option Descrip
Page 19 and 20: If H k is singular, then PROC MIXED
Page 21 and 22: MMEQ PROC MIXED Statement ✦ 3903
Page 23 and 24: PLOTS < (global-plot-options ) > <
Page 25 and 26: Residual Plot Options PROC MIXED St
Page 27 and 28: RATIO Multiple Plot Request PROC MI
Page 29 and 30: CONTRAST Statement ✦ 3911 TRUNCAT
Page 31: CONTRAST Statement ✦ 3913 differe
Page 35 and 36: Table 56.5 Summary of Important LSM
Page 37 and 38: LSMEANS Statement ✦ 3919 The numb
Page 39 and 40: E LSMEANS Statement ✦ 3921 are di
Page 41 and 42: Table 56.6 continued Option Descrip
Page 43 and 44: Table 56.7 Aliases for DDFM= Option
Page 45 and 46: E E1 E2 E3 FULLX MODEL Statement
Page 47 and 48: MODEL Statement ✦ 3929 The modifi
Page 49 and 50: SIZE=n MODEL Statement ✦ 3931 ins
Page 51 and 52: Table 56.10 continued Suboption Sta
Page 53 and 54: MODEL Statement ✦ 3935 where Vm i
Page 55 and 56: PARMS Statement PARMS (value-list)
Page 57 and 58: OLS PRIOR Statement ✦ 3939 approp
Page 59 and 60: PRIOR Statement ✦ 3941 JEFFREYS s
Page 61 and 62: RANDOM Statement ✦ 3943 TDATA= en
Page 63 and 64: RANDOM Statement ✦ 3945 GCORR dis
Page 65 and 66: RANDOM Statement ✦ 3947 available
Page 67 and 68: Table 56.12 continued Option Descri
Page 69 and 70: proc mixed; class a; model y = a x;
Page 71 and 72: REPEATED Statement ✦ 3953 TYPE=co
Page 73 and 74: Table 56.15 Covariance Structure Ex
Page 75 and 76: REPEATED Statement ✦ 3957 TYPE=AR
Page 77 and 78: TYPE=SP(EXPGA)(c1 c2) TYPE=SP(GAUGA
Page 79 and 80: TYPE=UN@AR(1) TYPE=UN@CS REPEATED S
Page 81 and 82: Mixed Models Theory ✦ 3963 where
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proc mixed; class indiv; model y =
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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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Mixed Models Theory ✦ 3969 In man
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Mixed Models Theory ✦ 3971 Finall
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Mixed Models Theory ✦ 3973 When L
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Parameterization of Mixed Models
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Interaction Effects Parameterizatio
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Table 56.20 Example of Continuous-b
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as ei ei p D pvi VarŒei and studen
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Residuals and Influence Diagnostics
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Default Output Default Output ✦ 3
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Default Output ✦ 3991 batch proce
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ODS Table Names ✦ 3993 You can us
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Table 56.22 continued ODS Table Nam
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Table 56.23 continued Table Name Va
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ODS Graphics ✦ 3999 The graphical
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ODS Graphics ✦ 4001 precision is
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Table 56.24 continued ODS Graph Nam
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Computational Issues ✦ 4005 For f
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Memory Computational Issues ✦ 400
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The following statements fit the sp
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Output 56.1.6 Split-Plot Analysis (
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proc mixed; class A B Block; model
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Example 56.2: Repeated Measures ✦
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Output 56.2.6 Repeated Measures Ana
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Output 56.2.9 Repeated Measures Ana
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Output 56.2.11 continued Dimensions
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Output 56.2.17 Analysis with Compou
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Example 56.2: Repeated Measures ✦
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The results from this analysis are
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Output 56.3.6 Estimated Covariance
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Output 56.3.10 Solutions of the Mix
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Output 56.3.14 Plot of Likelihood S
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Example 56.4: Known G and R ✦ 403
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Example 56.4: Known G and R ✦ 403
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Output 56.4.9 Solutions of the Mixe
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Example 56.5: Random Coefficients E
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Output 56.5.3 continued Number of O
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Output 56.5.9 Random Coefficients A
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Example 56.5: Random Coefficients
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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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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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References ✦ 4079 Carroll, R. J.
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References ✦ 4081 Hanks, R.J., Si
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References ✦ 4083 Littell, R. C.,
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References ✦ 4085 Smith, A. F. M.
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Subject Index 2D geometric anisotro
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graphics, residual panel, 3998 grap
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maximum likelihood estimation mixed
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parameterization, 3975 Pearson resi
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subject effect MIXED procedure, 391
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INFLUENCE option, MODEL statement (
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OUTG= option, 3942 OUTGT= option, 3
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INFLUENCE option, MODEL statement (
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