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Weekend Workshop I

Weekend Workshop I. PROC MIXED. Random or Fixed ?. Twins: One gets SAS training method 1 , the other gets method 2 Response Y = programming times. PROC MIXED Model. Model ; Random ; Repeated ;.

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Weekend Workshop I

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  1. Weekend Workshop I PROC MIXED

  2. Random or Fixed ?

  3. Twins: One gets SAS training method 1, the other gets method 2 Response Y = programming times

  4. PROC MIXED Model Model ; Random ; Repeated ; Y = X b + Zg + e Variance of g is G = ,Variance of e is R =

  5. PROCMIXED DATA=TWINS; CLASS FAMILY METHOD; MODEL TIME = METHOD; * fixed; RANDOM FAMILY; *<- family ~ N(0, s2F) ; Covariance Parameter Estimates Cov Parm Estimate family 21.2184 Residual 40.8338 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F method 1 19 9.60 0.0059 Intraclass correlation (related to heritability) s2F /(s2F + s2) Estimated as 21.2/62 or about 1/3. Q: Why not usual (Pearson) correlation?

  6. Demo Get_Twins.sas Twins_MIXED.sas

  7. BLUP Yij = m + Fi + eij Di = Family mean – m = Fi + ei. best estimate of Fi = ? Variance of (Fi – b Di) is (1-b)2s2F + b2s2/2 Use b = s2F /(s2F + s2/2) Estimate: b = 21.2/(21.2 + 40.8/2) = 0.510 Overall mean + 0.510(Family i mean – Overall mean) PROCMIXED DATA=TWINS; CLASS FAMILY METHOD; MODEL TIME = METHOD; RANDOM FAMILY; ESTIMATE "1 " intercept 1 | family 1; ESTIMATE "2 " intercept 1 | family 01; PROCGLM DATA=TWINS; CLASS FAMILY METHOD; MODEL TIME = FAMILY METHOD; LSMEANS FAMILY;

  8. MEANS andBLUPs (GLM) (MIXED)

  9. Demo Twins_BLUP.sas Twins_TEST.sas

  10. ML Estimation Search over all (fixed and random) parameters Estimates of variances biased low!  • REML Estimation • Regress out fixed effects • Maximze likelihood of residuals (mean known: 0) • Variance estimates less biased (unbiased in some simple cases) 

  11. Unbalanced Data I vs. III free of subject effects for red data. Misses info in other data.

  12. procglm; class plug worker; model loss = worker plug; Random Worker; Estimate "I vs III - GLM" Plug -101; run; procmixed; class plug worker; model Loss=Plug; Random Worker; Estimate "I vs III - Mixed" Plug -101; run; Covariance Parameter Estimates Cov Parm Estimate worker 37.578 Residual 6.1674 GLM Source DF Type III SS F Value Pr > F worker 6 451.9062500 12.21 0.0074 plug 2 62.6562500 5.08 0.0625 Standard Parameter Estimate Error t Value Pr > |t| I vs III - GLM -4.8125 1.9635 -2.45 0.0579 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F plug 2 5 5.79 0.0499 Estimates Standard Label Estimate Error DF t Value Pr > |t| I vs III - Mixed -5.2448 1.9347 5 -2.71 0.0422

  13. Demo Earplugs.sas

  14. SPLIT PLOT 4 Aquariums, 2 aerated 2 not six dishes / aquarium one plant / dish soil x variety combinations ANOVA Source Air Error A V S VA VS AS AVS Error B Soil Variety 1 1 1 2 2 1 2 2 3 1 3 2

  15. Compare Air to No Air within soil 1 Variance of this contrast is hard to figure out: (1/3)[MS(A)+2 MS(B)] Need Satterthwaite df AUTOMATIC IN MIXED!!! PROCMIXED; CLASS VAR AQUARIUM SOIL AIR; MODEL YIELD = AIR SOIL VAR SOIL*VAR AIR*SOIL AIR*VAR AIR*SOIL*VAR / DDFM=SATTERTHWAITE; RANDOM AQUARIUM(AIR); ESTIMATE "SOIL 1: AIR EFFECT" AIR -11 AIR*SOIL -110000; RUN;

  16. Covariance Parameter Estimates Cov Parm Estimate AQUARIUM(AIR) 2.1833 Residual 7.7333 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F AIR 1 2 16.20 0.0565  SOIL 2 10 7.87 0.0088 VAR 1 10 24.91 0.0005 VAR*SOIL 2 10 0.04 0.9631 SOIL*AIR 2 10 1.08 0.3752 VAR*AIR 1 10 4.22 0.0669 VAR*SOIL*AIR 2 10 0.23 0.7973 Standard  Label Estimate Error DF t Value Pr > |t| SOIL 1: AIR EFFECT 5.2500 2.4597 5.47 2.13 0.0812

  17. Demo Aquarium.sas

  18. Random Coefficient Models the basic idea mistakes Dave Averageprogrammer a0 + b0 t Program writing time Line for individual j: (a0 + aj) + ( b0 + bj )t

  19. Hierarchial Models • Same as split plot - almost • Whole and split level continuous predictor variables (typically) • Aquarium level (level i): pHi • Dish level: Soil nitrogen test (Nij) • Yij = ai + biNij+eij • (3) Idea: ai = a0 + a1pHi + ai* • bi = b0 + b1pHi + bi* Yij = [a0 + a1pHi + b0Nij+ b1pHiNij] + [ai* +bi* Nij+eij] fixed random PROC MIXED DATA = UNDERWATER; MODEL GROWTH = N P N*P; RANDOM INTERCEPT N / SUBJECT = TANK TYPE=UN; Yij = ai + biNij+eij Yij = a0 + a1pHi + ai* + biNij+eij Yij = a0 + a1pHi + ai* + (b0 + b1pHi + bi* ) Nij+eij

  20. p aquarium N pH growth 1 2.21 5.5 27.05 1 1.25 5.5 25.92 1 4.36 5.5 30.09 1 7.14 5.5 33.66 1 8.61 5.5 36.13 1 6.53 5.5 33.00 2 6.58 4.7 35.72 2 3.12 4.7 31.17 2 5.28 4.7 34.35 2 1.09 4.7 28.34 2 4.83 4.7 33.56 2 9.61 4.7 40.25 3 7.99 4.2 47.04 3 7.79 4.2 46.56 3 8.32 4.2 48.27 3 2.53 4.2 34.20 3 6.85 4.2 44.59 3 4.73 4.2 39.29 4 0.95 5.1 24.94 4 2.00 5.1 27.33 4 9.99 5.1 43.84 4 0.23 5.1 23.54 4 0.13 5.1 23.56 4 1.17 5.1 25.68 Num Den Effect DF DF F Value Pr > F N 1 2 3.50 0.2018 pH 1 2.05 6.76 0.1186 N*pH 1 2 1.31 0.3702 Num Den Effect DF DF F Value Pr > F N 1 3 50.19 0.0058 pH 1 2.03 14.68 0.0603 Cov Parm Estimate UN(1,1) 1.8976 UN(2,1) -0.5563 UN(2,2) 0.2596 Residual 0.0286 N pH

  21. Demo Hierarchial.sas

  22. Next: Repeated Measures Notes in pdf from NCSU experimental design class (ST 711)

  23. Demo SURGERY.sas

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