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

More documents

Recommendations

Info

4530 ✦ Chapter 56: The MIXED Procedure If H k is singular, then PROC MIXED uses the following relative criterion: g 0 k g k jf kj number To prevent the division by jf kj, use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E 8. COVTEST produces asymptotic standard errors and Wald Z-tests for the covariance parameter estimates. DATA=SAS-data-set names the SAS data set to be used by PROC MIXED. The default is the most recently created data set. DFBW has the same effect as the DDFM=BW option in the MODEL statement. EMPIRICAL computes the estimated variance-covariance matrix of the fixed-effects parameters by using the asymptotically consistent estimator described in Huber (1967), White (1980), Liang and Zeger (1986), and Diggle, Liang, and Zeger (1994). This estimator is commonly referred to as the “sandwich” estimator, and it is computed as follows: IC .X 0bV 1 X/ SX iD1 X 0 i cVi 1 bi bi 0cVi 1 Xi ! .X 0bV 1 X/ Here, bi D yi Xi bˇ, S is the number of subjects, and matrices with an i subscript are those for the ith subject. You must include the SUBJECT= option in either a RANDOM or REPEATED statement for this option to take effect. When you specify the EMPIRICAL option, PROC MIXED adjusts all standard errors and test statistics involving the fixed-effects parameters. This changes output in the following tables (listed in Table 56.22): Contrast, CorrB, CovB, Diffs, Estimates, InvCovB, LSMeans, Slices, SolutionF, Tests1–Tests3. The OUTP= and OUTPM= data sets are also affected. Finally, the Satterthwaite and Kenward-Roger degrees of freedom methods are not available if you specify the EMPIRICAL option. displays a table of various information criteria. The criteria are all in smaller-is-better form, and are described in Table 56.3. Table 56.3 Information Criteria Criterion Formula Reference AIC 2` C 2d Akaike (1974) AICC 2` C 2dn =.n d 1/ Hurvich and Tsai (1989) Burnham and Anderson (1998) HQIC 2` C 2d log log n Hannan and Quinn (1979) BIC 2` C d log n Schwarz (1978) CAIC 2` C d.log n C 1/ Bozdogan (1987)
INFO PROC MIXED Statement ✦ 4531 Here ` denotes the maximum value of the (possibly restricted) log likelihood, d the dimension of the model, and n the number of observations. In SAS 6 of SAS/STAT software, n equals the number of valid observations for maximum likelihood estimation and n p for restricted maximum likelihood estimation, where p equals the rank of X. In later versions, n equals the number of effective subjects as displayed in the “Dimensions” table, unless this value equals 1, in which case n equals the number of levels of the first random effect you specify in a RANDOM statement. If the number of effective subjects equals 1 and you have no RANDOM statements, then n reverts to the SAS 6 values. For AICC (a finite-sample corrected version of AIC), n equals the SAS 6 values of n, unless this number is less than d C 2, in which case it equals d C 2. For restricted likelihood estimation, d equals q, the effective number of estimated covariance parameters. In SAS 6, when a parameter estimate lies on a boundary constraint, then it is still included in the calculation of d, but in later versions it is not. The most common example of this behavior is when a variance component is estimated to equal zero. For maximum likelihood estimation, d equals q Cp. The value of d is displayed in the “Information Criteria” table as the value of Parms variable; see Table 56.23. For ODS purposes, the name of the “Information Criteria” table is “InfoCrit.” is a default option. The creation of the “Model Information,” “Dimensions,” and “Number of Observations” tables can be suppressed by using the NOINFO option. Note that in SAS 6 this option displays the “Model Information” and “Dimensions” tables. ITDETAILS displays the parameter values at each iteration and enables the writing of notes to the SAS log pertaining to “infinite likelihood” and “singularities” during Newton-Raphson iterations. LOGNOTE writes periodic notes to the log describing the current status of computations. It is designed for use with analyses requiring extensive CPU resources. MAXFUNC=number specifies the maximum number of likelihood evaluations in the optimization process. The default is 150. MAXITER=number specifies the maximum number of iterations. The default is 50. METHOD=REML | ML | MIVQUE0 | TYPE1 | TYPE2 | TYPE3 specifies the estimation method for the covariance parameters. The REML specification performs residual (restricted) maximum likelihood, and it is the default method. The ML specification performs maximum likelihood, and the MIVQUE0 specification performs minimum variance quadratic unbiased estimation of the covariance parameters. The METHOD=TYPEn specifications apply only to variance component models with no SUBJECT= effects and no REPEATED statement. An analysis of variance table is included in the output, and the expected mean squares are used to estimate the variance components
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: PROC MIXED Statement ✦ 4529 CL< =
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 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,
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
Page 113 and 114:
Null Model Likelihood Ratio Test De
Page 115 and 116:
Table 56.22 continued ODS Table Nam
Page 117 and 118:
ODS Table Names ✦ 4627 CAUTION: T
Page 119 and 120:
ODS Graphics ✦ 4629 Some of the v
Page 121 and 122:
Figure 56.16 Panel of the Condition
Page 123 and 124:
Figure 56.18 Deletion Estimates ODS
Page 125 and 126:
Computational Issues Computational
Page 127 and 128:
Memory Computational Issues ✦ 463
Page 129 and 130:
Examples: MIXED Procedure Examples:
Page 131 and 132:
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 and 184:
Output 56.7.9 Covariance Parameter
Page 185 and 186:
Example 56.8: Influence Analysis fo
Page 187 and 188:
Output 56.8.2 Restricted Likelihood
Page 189 and 190:
Page 191 and 192:
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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?