Hi, i have a rather complex mulitvariate mixed model that has Y variables (traits) that do and do not have repeated measures. the aim is to look for across-individual correlations between traits. I have repeated measures of metabolism in relation to temperature, so that trait i wish to model as random intercepts and slopes. but, the other traits have only a single estimate (mass of internal organs, like liver, heart etc). i am interested mainly in whether intercepts and/or slopes of metabolism (smr) are correlated across individuals to growth (grow), and organ masses. i have standardised all variables to mean 0, variance 1. i understand i must fix residual variance to zero for those traits without repeated measures (see final line of parms parameters). i am able to do this for a bivariate situation, but the residual variances i request be held to zero are not all held at that ... SAS seems to fit something anyways! and for any model, even the bivariate models that converge and make sense, i get non positive definate errors. The Model: proc mixed maxiter=100 method=reml covtest; class id trait sex; where trait in ('smr' 'grow' 'stomach''liver''heart' ) ; model score = trait trait*mass trait*temp trait*sex / noint solution ; random trait trait*temp / subject=id type=un g gcorr ; repeated / subject=id group=trait type=vc ; parms 0.4 0.1 0.3 0.1 0.1 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0 0 0 0.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2 0 / hold=16-36,42-44,46-55,56-58,60; run; any help would be MUCH appreciated. Here is the output: Model Information Data Set WORK.SNAKE Dependent Variable score Covariance Structures Unstructured, Variance Components Subject Effects id, id Group Effect trait Estimation Method REML Residual Variance Method None Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values id 78 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 trait 5 grow heart liver smr stomach sex 2 f m Dimensions Covariance Parameters 60 Columns in X 25 Columns in Z Per Subject 10 Subjects 78 Max Obs Per Subject 7 Number of Observations Number of Observations Read 546 Number of Observations Used 543 Number of Observations Not Used 3 SNAKE gifford multivariate 993 14:02 Sunday, January 22, 2012 The Mixed Procedure Parameter Search CovP1 CovP2 CovP3 CovP4 CovP5 CovP6 CovP7 CovP8 CovP9 CovP10 0.4000 0.1000 0.3000 0.1000 0.1000 0.2000 0.1000 0.1000 0.1000 0.1000 Parameter Search CovP11 CovP12 CovP13 CovP14 CovP15 CovP16 CovP17 CovP18 CovP19 CovP20 0.1000 0.1000 0.1000 0.1000 0.1000 0 0 0 0 0 Parameter Search CovP21 CovP22 CovP23 CovP24 CovP25 CovP26 CovP27 CovP28 CovP29 CovP30 0 0 0 0 0 0 0 0 0 0 Parameter Search CovP31 CovP32 CovP33 CovP34 CovP35 CovP36 CovP37 CovP38 CovP39 CovP40 0 0 0 0 0 0 0.1000 0.1000 0.1000 0.1000 Parameter Search CovP41 CovP42 CovP43 CovP44 CovP45 CovP46 CovP47 CovP48 CovP49 CovP50 0.1000 0 0 0 0.2000 0 0 0 0 0 Parameter Search CovP51 CovP52 CovP53 CovP54 CovP55 CovP56 CovP57 CovP58 CovP59 CovP60 0 0 0 0 0 0 0 0 0.2000 0 Parameter Search Res Log Like -2 Res Log Like -1646.0444 3292.0888 Iteration History Iteration Evaluations -2 Res Log Like Criterion 1 2 3052.77234298 5076446.9586 2 1 3020.53129601 5396314.6003 SNAKE gifford multivariate 994 14:02 Sunday, January 22, 2012 The Mixed Procedure Iteration History Iteration Evaluations -2 Res Log Like Criterion 3 1 2623.03272815 3512091.3947 4 1 2239.29440240 2179422.9738 5 1 1955.97441629 1534676.7519 6 1 1857.64284936 1616514.1840 7 1 1753.59719832 1997053.3055 8 1 1602.83749339 3323477.4337 9 1 1493.10709367 5965459.3658 10 1 1432.24335881 10071334.555 11 3 1263.59574182 . 12 1 955.09012350 . 13 1 756.70827473 . 14 1 636.28480138 . 15 1 570.77910660 . 16 1 537.89890246 505.89610327 17 1 522.91363072 125.67368087 18 1 517.65753686 24.35200327 19 1 516.59637099 1.79963774 20 1 516.52797109 0.01407840 21 1 516.52755520 0.00000074 22 1 516.52755518 0.00000000 Convergence criteria met but final hessian is not positive definite. Estimated G Matrix Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6 1 trait grow 1 0.000751 -0.00107 -0.00363 -0.02785 0.006168 2 trait heart 1 -0.00107 0.5930 0.1582 -0.3107 0.3585 3 trait liver 1 -0.00363 0.1582 0.3993 -1.7961 0.2958 4 trait smr 1 -0.02785 -0.3107 -1.7961 3.4202 -1.4543 5 trait stomach 1 0.006168 0.3585 0.2958 -1.4543 0.9790 Estimated G Matrix Row Col7 Col8 Col9 Col10 1 0.01991 2 0.2445 3 1.2976 4 -3.0078 5 1.0739 SNAKE gifford multivariate 995 14:02 Sunday, January 22, 2012 The Mixed Procedure Estimated G Matrix Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6 6 temp*trait grow 1 7 temp*trait heart 1 8 temp*trait liver 1 9 temp*trait smr 1 0.01991 0.2445 1.2976 -3.0078 1.0739 10 temp*trait stomach 1 Estimated G Matrix Row Col7 Col8 Col9 Col10 6 7 8 9 2.5226 10 Estimated G Correlation Matrix Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6 1 trait grow 1 1.0000 -0.05076 -0.2097 -0.5496 0.2276 2 trait heart 1 -0.05076 1.0000 0.3251 -0.2181 0.4704 3 trait liver 1 -0.2097 0.3251 1.0000 -1.0000 0.4731 4 trait smr 1 -0.5496 -0.2181 -1.0000 1.0000 -0.7948 5 trait stomach 1 0.2276 0.4704 0.4731 -0.7948 1.0000 6 temp*trait grow 1 1.0000 7 temp*trait heart 1 8 temp*trait liver 1 9 temp*trait smr 1 0.4576 0.1999 1.0000 -1.0000 0.6834 Estimated G Correlation Matrix Row Col7 Col8 Col9 Col10 1 0.4576 2 0.1999 3 1.0000 4 -1.0000 5 0.6834 6 7 1.0000 8 1.0000 9 1.0000 SNAKE gifford multivariate 996 14:02 Sunday, January 22, 2012 The Mixed Procedure Estimated G Correlation Matrix Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6 10 temp*trait stomach 1 Estimated G Correlation Matrix Row Col7 Col8 Col9 Col10 10 1.0000 Covariance Parameter Estimates Standard Z Cov Parm Subject Group Estimate Error Value Pr Z UN(1,1) id 0.000751 0.000129 5.82 <.0001 UN(2,1) id -0.00107 0.003318 -0.32 0.7469 UN(2,2) id 0.5930 0.1577 3.76 <.0001 UN(3,1) id -0.00363 0.002722 -1.33 0.1823 UN(3,2) id 0.1582 0.09710 1.63 0.1033 UN(3,3) id 0.3993 0.1111 3.59 0.0002 UN(4,1) id -0.02785 0.02200 -1.27 0.2057 UN(4,2) id -0.3107 0.7639 -0.41 0.6842 UN(4,3) id -1.7961 0.6333 -2.84 0.0046 UN(4,4) id 3.4202 7.6157 0.45 0.3267 UN(5,1) id 0.006168 0.004053 1.52 0.1280 UN(5,2) id 0.3585 0.1483 2.42 0.0156 UN(5,3) id 0.2958 0.1174 2.52 0.0118 UN(5,4) id -1.4543 0.6873 -2.12 0.0343 UN(5,5) id 0.9790 0.1587 6.17 <.0001 UN(6,1) id 0 . . . UN(6,2) id 0 . . . UN(6,3) id 0 . . . UN(6,4) id 0 . . . UN(6,5) id 0 . . . UN(6,6) id 0 . . . UN(7,1) id 0 . . . UN(7,2) id 0 . . . UN(7,3) id 0 . . . UN(7,4) id 0 . . . UN(7,5) id 0 . . . UN(7,6) id 0 . . . UN(7,7) id 0 . . . UN(8,1) id 0 . . . UN(8,2) id 0 . . . UN(8,3) id 0 . . . UN(8,4) id 0 . . . SNAKE gifford multivariate 997 14:02 Sunday, January 22, 2012 The Mixed Procedure Covariance Parameter Estimates Standard Z Cov Parm Subject Group Estimate Error Value Pr Z UN(8,5) id 0 . . . UN(8,6) id 0 . . . UN(8,7) id 0 . . . UN(8,8) id 0 . . . UN(9,1) id 0.01991 0.01563 1.27 0.2026 UN(9,2) id 0.2445 0.5433 0.45 0.6527 UN(9,3) id 1.2976 0.4513 2.88 0.0040 UN(9,4) id -3.0078 5.3254 -0.56 0.5722 UN(9,5) id 1.0739 0.4884 2.20 0.0279 UN(9,6) id 0 . . . UN(9,7) id 0 . . . UN(9,8) id 0 . . . UN(9,9) id 2.5226 3.7309 0.68 0.2495 UN(10,1) id 0 . . . UN(10,2) id 0 . . . UN(10,3) id 0 . . . UN(10,4) id 0 . . . UN(10,5) id 0 . . . UN(10,6) id 0 . . . UN(10,7) id 0 . . . UN(10,8) id 0 . . . UN(10,9) id 0 . . . UN(10,10) id 0 . . . Residual id trait grow 0 . . . Residual id trait heart 0.2930 0 . . Residual id trait liver 0.1993 0 . . Residual id trait smr 0.2168 0.03502 6.19 <.0001 Residual id trait stomach 0 . . . Fit Statistics -2 Res Log Likelihood 516.5 AIC (smaller is better) 618.5 AICC (smaller is better) 629.7 BIC (smaller is better) 738.7 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 51 2775.56 <.0001 SNAKE gifford multivariate 998 14:02 Sunday, January 22, 2012 The Mixed Procedure Solution for Fixed Effects Standard Effect trait sex Estimate Error DF t Value Pr > |t| trait grow -0.3277 0.03308 378 -9.91 <.0001 trait heart -2.3197 1.0897 378 -2.13 0.0339 trait liver -4.7063 0.8233 378 -5.72 <.0001 trait smr -19.4215 0.7135 378 -27.22 <.0001 trait stomach -0.1774 0.1558 378 -1.14 0.2553 mass*trait grow 0.2982 0.02101 73 14.20 <.0001 mass*trait heart 1.3864 0.6801 73 2.04 0.0451 mass*trait liver 2.8763 0.5154 73 5.58 <.0001 mass*trait smr 1.8862 0.1671 73 11.29 <.0001 mass*trait stomach 0 . . . . temp*trait grow 0 . . . . temp*trait heart 0 . . . . temp*trait liver 0 . . . . temp*trait smr 11.3638 0.4747 77 23.94 <.0001 temp*trait stomach 0 . . . . trait*sex grow f -0.00298 0.006210 73 -0.48 0.6324 trait*sex grow m 0 . . . . trait*sex heart f 0.1831 0.2149 73 0.85 0.3971 trait*sex heart m 0 . . . . trait*sex liver f 0.2231 0.1625 73 1.37 0.1739 trait*sex liver m 0 . . . . trait*sex smr f -0.04568 0.04914 73 -0.93 0.3557 trait*sex smr m 0 . . . . trait*sex stomach f 0.3549 0.2164 73 1.64 0.1053 trait*sex stomach m 0 . . . . Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F trait 5 378 193.39 <.0001 mass*trait 4 73 105.26 <.0001 temp*trait 1 77 573.02 <.0001 trait*sex 5 73 1.27 0.2850
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