Dear SAS-Community, i want to calculate coefficients of variance (CV) for grain dry matter data with 12 variants and 4 replicates. I want then to test differences of CV-Values between the treatments and the fertiliser levels. Here is a table containing the variants with the corresponding treatment and fertiliser level:
Variant
treatment
fertiliser level
1
1
0
2
1
1
3
2
0
4
2
1
5
3
0
6
3
1
7
4
0
8
4
1
9
5
0
10
6
0
11
7
0
12
7
1
13
8
0
14
8
1
When i run my code i get the following warning in the Log:
The final Hessian matrix is not positive definite, and therefore the estimated covariance matrix is not full rank and may be unreliable. The variance of some parameter estimates is zero or some parameters are linearly related to other parameters.
Could someone of you help me with finding a solution to this problem? Here comes my code with sample data (similar to my own data):
data Total_Grain_DM_Sample;
input Block Variant Total_Grain_DM_kg_ha;
datalines;
2 1 4016.79
1 1 3904.58
3 1 3857.5
3 1 3962.11
4 2 3777.43
2 2 3857.63
1 2 4053.94
3 2 3902.49
4 3 4494.53
3 3 4607.35
1 3 4616.06
2 3 4660.09
2 4 4580.31
4 4 5225.37
1 4 4666.99
4 4 4782.53
1 5 5271.92
4 5 5302.86
4 5 5056.13
2 5 5033.14
2 6 5213.04
3 6 5477.23
4 6 5173.18
1 6 5482.44
3 7 5389.63
2 7 5482.13
1 7 5764.17
4 7 4824.41
1 8 5662.74
3 8 5906.35
3 8 5904.86
2 8 5693.09
2 9 5821.93
3 9 5989.53
1 9 6351.82
4 9 5813.85
4 10 6210.08
1 10 6257.52
3 10 6125.38
2 10 5959
1 11 6225.87
2 11 6236.02
3 11 6328.76
4 11 6395.25
3 12 6677.88
4 12 6447.28
1 12 6274.82
2 12 6341.02
;run;
;
/* Dummy-Variables for NLMixed */
data Total_Grain_DM_Sample;set Total_Grain_DM_Sample;
if Variant=1 then trt1=1;else trt1=0;
trt2=0;if Variant=2 then trt2=1;
trt3=0;if Variant=3 then trt3=1;
trt4=0;if Variant=4 then trt4=1;
trt5=0;if Variant=5 then trt5=1;
trt6=0;if Variant=6 then trt6=1;
trt7=0;if Variant=7 then trt7=1;
trt8=0;if Variant=8 then trt8=1;
trt9=0;if Variant=9 then trt9=1;
trt10=0;if Variant=10 then trt10=1;
trt11=0;if Variant=11 then trt11=1;
trt12=0;if Variant=12 then trt12=1;
run;
;
/* Berechnung und Vergleich der Variationskoeffizienten */
Proc nlmixed data=Total_Grain_DM_Sample;
parameters t1=3200 t2=4500.00 t3=3700.00 t4=5800 t5=4200.00 t6=4000.00 t7=3250.00 t8=4600.99 t9=4500.00 t10=3200.00 t11=3800.00 t12=4800.00 v1=26000.00 v2=27000.00 v3=262133.76 v4=2120000.00 v5=275000 v6=140500.00 v7=261000.00 v8=280000.00 v9=262500.00 v10=250000.00 v11=108000.00 v12=111000.00;
mu=trt1*t1+trt2*t2+trt3*t3+trt4*t4+trt5*t5+trt6*t6+trt7*t7+trt8*t8+trt9*t9+trt10*t10+trt11*t11+trt12*t12+u1*trt1+u2*trt2+u3*trt3+u4*trt4+u5*trt5+u6*trt6+u7*trt7+u8*trt8+u9*trt9+u10*trt10+u11*trt11+u12*trt12;
model Total_Grain_DM_kg_ha ~ normal (mu,0.0000001);
random u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12 ~ normal([0,0,0,0,0,0,0,0,0,0,0,0],
[v1,
0, v2,
0, 0, v3,
0, 0, 0, v4,
0, 0, 0, 0, v5,
0, 0, 0, 0, 0, v6,
0, 0, 0, 0, 0, 0, v7,
0, 0, 0, 0, 0, 0, 0, v8,
0, 0, 0, 0, 0, 0, 0, 0, v9,
0, 0, 0, 0, 0, 0, 0, 0, 0, v10,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, v11,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, v12]) SUBJECT = block OUT = ausgabe;
/* Calculation of CV-values */
predict ((v1)**(1/2)/(t1))*100 out=cv_t1;
predict ((v2)**(1/2)/(t2))*100 out=cv_t2;
predict ((v3)**(1/2)/(t3))*100 out=cv_t3;
predict ((v4)**(1/2)/(t4))*100 out=cv_t4;
predict ((v5)**(1/2)/(t5))*100 out=cv_t5;
predict ((v6)**(1/2)/(t6))*100 out=cv_t6;
predict ((v7)**(1/2)/(t7))*100 out=cv_t7;
predict ((v8)**(1/2)/(t8))*100 out=cv_t8;
predict ((v9)**(1/2)/(t9))*100 out=cv_t9;
predict ((v10)**(1/2)/(t10))*100 out=cv_t10;
predict ((v11)**(1/2)/(t11))*100 out=cv_t11;
predict ((v12)**(1/2)/(t12))*100 out=cv_t12;
/* Comparison of the CV-values */
/* Between the treatments */
/* with fertiliser level 0 */
predict ((v1)**(1/2)/(t1))*100-((v3)**(1/2)/(t3))*100 out=cv_t1_vs_cv_t3;
predict ((v5)**(1/2)/(t5))*100-((v1)**(1/2)/(t1))*100 out=cv_t5_vs_cv_t1;
predict ((v5)**(1/2)/(t5))*100-((v3)**(1/2)/(t3))*100 out=cv_t5_vs_cv_t3;
predict ((v5)**(1/2)/(t5))*100-((v7)**(1/2)/(t7))*100 out=cv_t5_vs_cv_t7;
predict ((v5)**(1/2)/(t5))*100-((v9)**(1/2)/(t9))*100 out=cv_t5_vs_cv_t9;
predict ((v5)**(1/2)/(t5))*100-((v10)**(1/2)/(t10))*100 out=cv_t5_vs_cv_t10;
predict ((v5)**(1/2)/(t5))*100-((v11)**(1/2)/(t11))*100 out=cv_t5_vs_cv_t11;
predict ((v7)**(1/2)/(t7))*100-((v1)**(1/2)/(t1))*100 out=cv_t7_vs_cv_t1;
predict ((v7)**(1/2)/(t7))*100-((v9)**(1/2)/(t9))*100 out=cv_t7_vs_cv_t9;
predict ((v7)**(1/2)/(t7))*100-((v10)**(1/2)/(t10))*100 out=cv_t7_vs_cv_t10;
predict ((v7)**(1/2)/(t7))*100-((v11)**(1/2)/(t11))*100 out=cv_t7_vs_cv_t11;
predict ((v9)**(1/2)/(t9))*100-((v1)**(1/2)/(t1))*100 out=cv_t9_vs_cv_t1;
predict ((v9)**(1/2)/(t9))*100-((v3)**(1/2)/(t3))*100 out=cv_t9_vs_cv_t3;
predict ((v9)**(1/2)/(t9))*100-((v10)**(1/2)/(t10))*100 out=cv_t9_vs_cv_t10;
predict ((v9)**(1/2)/(t9))*100-((v11)**(1/2)/(t11))*100 out=cv_t9_vs_cv_t11;
predict ((v10)**(1/2)/(t10))*100-((v1)**(1/2)/(t1))*100 out=cv_t10_vs_cv_t1;
predict ((v10)**(1/2)/(t10))*100-((v3)**(1/2)/(t3))*100 out=cv_t10_vs_cv_t3;
predict ((v10)**(1/2)/(t10))*100-((v11)**(1/2)/(t11))*100 out=cv_t10_vs_cv_t11;
/* with fertiliser 1evel 1 */
predict ((v2)**(1/2)/(t2))*100-((v4)**(1/2)/(t4))*100 out=cv_t2_vs_cv_t4;
predict ((v6)**(1/2)/(t6))*100-((v2)**(1/2)/(t2))*100 out=cv_t6_vs_cv_t2;
predict ((v6)**(1/2)/(t6))*100-((v4)**(1/2)/(t4))*100 out=cv_t6_vs_cv_t4;
predict ((v6)**(1/2)/(t6))*100-((v8)**(1/2)/(t8))*100 out=cv_t6_vs_cv_t8;
predict ((v6)**(1/2)/(t6))*100-((v12)**(1/2)/(t12))*100 out=cv_t6_vs_cv_t12;
predict ((v8)**(1/2)/(t8))*100-((v2)**(1/2)/(t2))*100 out=cv_t8_vs_cv_t2;
predict ((v8)**(1/2)/(t8))*100-((v4)**(1/2)/(t4))*100 out=cv_t8_vs_cv_t4;
predict ((v8)**(1/2)/(t8))*100-((v12)**(1/2)/(t12))*100 out=cv_t8_vs_cv_t12;
predict ((v12)**(1/2)/(t12))*100-((v2)**(1/2)/(t2))*100 out=cv_t12_vs_cv_t2;
predict ((v12)**(1/2)/(t12))*100-((v4)**(1/2)/(t4))*100 out=cv_t12_vs_cv_t4;
/* Between the fertiliser levels */
predict ((v2)**(1/2)/(t2))*100-((v1)**(1/2)/(t1))*100 out=cv_t2_vs_cv_t1;
predict ((v4)**(1/2)/(t4))*100-((v3)**(1/2)/(t3))*100 out=cv_t4_vs_cv_t3;
predict ((v6)**(1/2)/(t6))*100-((v5)**(1/2)/(t5))*100 out=cv_t6_vs_cv_t5;
predict ((v8)**(1/2)/(t8))*100-((v7)**(1/2)/(t7))*100 out=cv_t8_vs_cv_t7;
predict ((v12)**(1/2)/(t12))*100-((v11)**(1/2)/(t11))*100 out=cv_t12_vs_cv_t11;
run;
;
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