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

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4572 ✦ Chapter 56: The MIXED Procedure WARNING: The log ratio bound of LL was violated at sample XX. When this occurs, PROC MIXED reruns an optimization algorithm to determine a new log upper bound and then restarts the rejection sampling. The resulting OUT= data set contains all observations that have been generated; therefore, assuming that you have requested N samples, you should retain only the final N observations in this data set for analysis purposes. NSAMPLE=number specifies the number of posterior samples to generate. The default is 1000, but more accurate results are obtained with larger samples such as 10000. NSEARCH=number specifies the number of posterior evaluations PROC MIXED makes for each transformed parameter in determining the parameters for the inverted gamma densities. The default is 20. OUT=SAS-data-set creates an output data set containing the sample from the posterior density. OUTG=SAS-data-set creates an output data set from the grid evaluations specified in the GRID= option. OUTGT=SAS-data-set creates an output data set from the transformed grid evaluations specified in the GRIDT= option. PSEARCH displays the search used to determine the parameters for the inverted gamma densities. For ODS purposes, the name of the table is “Search.” PTRANS displays the transformation of the variance components. For ODS purposes, the name of the table is “Trans.” SEED=number specifies an integer used to start the pseudo-random number generator for the simulation. If you do not specify a seed, or if you specify a value less than or equal to zero, the seed is by default generated from reading the time of day from the computer clock. You should use a positive seed (less than 2 31 1) whenever you want to duplicate the sample in another run of PROC MIXED. SFACTOR=number enables you to adjust the range over which PROC MIXED searches the transformed parameters in order to determine the parameters for the inverted gamma densities. PROC MIXED determines the range by first transforming the estimates from the standard PROC MIXED analysis (REML, ML, or MIVQUE0, depending upon which estimation method you select). It then multiplies and divides the transformed estimates by 2 number to obtain upper and lower bounds, respectively. Transformed values that produce negative variance components in the original scale are not included in the search. The default value is 1; number must be greater than 0.5.
RANDOM Statement ✦ 4573 TDATA= enables you to input the transformation of the covariance parameters used by the sampling algorithm. This data set should contain the CovP1–CovPn variables. The format of the TDATA= data set matches that created by PROC MIXED in the “Trans” table, so you can output the transformation from one run and use it as input for a subsequent run. TRANS=EXPECTED | MIVQUE0 | OBSERVED specifies the particular algorithm used to determine the transformation of the covariance parameters. The default is MIVQUE0, indicating a transformation based on the MIVQUE(0) equations. The other two options indicate the type of Hessian matrix used in constructing the transformation via a Cholesky root. UPDATE=number is an alias for the LOGNOTE= option. RANDOM Statement RANDOM random-effects < / options > ; The RANDOM statement defines the random effects constituting the vector in the mixed model. It can be used to specify traditional variance component models (as in the VARCOMP procedure) and to specify random coefficients. The random effects can be classification or continuous, and multiple RANDOM statements are possible. Using notation from the section “Mixed Models Theory” on page 4593, the purpose of the RANDOM statement is to define the Z matrix of the mixed model, the random effects in the vector, and the structure of G. The Z matrix is constructed exactly as the X matrix for the fixed effects, and the G matrix is constructed to correspond with the effects constituting Z. The structure of G is defined by using the TYPE= option. You can specify INTERCEPT (or INT) as a random effect to indicate the intercept. PROC MIXED does not include the intercept in the RANDOM statement by default as it does in the MODEL statement. Table 56.11 summarizes important options in the RANDOM statement. All options are subsequently discussed in alphabetical order. Table 56.11 Summary of Important RANDOM Statement Options Option Description Construction of Covariance Structure GDATA= Requests that the G matrix be read from a SAS data set GROUP= Varies covariance parameters by groups LDATA= Specifies data set with coefficient matrices for TYPE=LIN NOFULLZ Eliminates columns in Z corresponding to missing values RATIOS Indicates that ratios are specified in the GDATA= data set SUBJECT= Identifies the subjects in the model
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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
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 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: PRIOR Statement ✦ 4571 JEFFREYS s
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,
Page 97 and 98: Intercept Parameterization of Mixed
Page 99 and 100: Table 56.18 continued Data I A B(A)
Page 101 and 102: Residuals and Influence Diagnostics
Page 103 and 104: Scaled Residuals Residuals and Infl
Page 105 and 106: Predicted Values, PRESS Residual, a
Page 107 and 108: When ITER=0 and 2 is profiled, then
Page 109 and 110: Using results in Cook and Weisberg
Page 111 and 112: 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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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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