Tullibigeal trial linenum yield weed column 10 row 67 variety 532 # testlines 1:525, check lines 526:532 wheat.asd !skip 1 !DOPATH 1 !PATH 1 # AR1 x I y ~ mu weed mv !r variety 1 2 67 row AR1 0.1 10 column I 0 !PATH 2 # AR1 x AR1 y ~ mu weed mv !r variety 1 2 67 row AR1 0.1 10 column AR1 0.1 !PATH 3 # AR1 x AR1 + column trend y ~ mu weed pol(column,-1) mv !r variety 1 2 67 row AR1 0.1 10 column AR1 0.1 !PATH 4 # AR1 x AR1 + Nugget + column trend y ~ mu weed pol(column,-1) mv !r variety units 1 2 67 row AR1 0.1 10 column AR1 0.1 predict varThe data fields represent the factors variety, row and column, a covariate weed and the plot yield ( yield). There are three paths in the ASReml file. We begin with the one-dimensional spatial model, which assumes the variance model for the plot effects within columns is described by a first order autoregressive process. The abbreviated output file is
1 LogL=-4280.75 S2= 0.12850E+06 666 df 0.1000 1.000 0.1000
2 LogL=-4268.57 S2= 0.12138E+06 666 df 0.1516 1.000 0.1798
3 LogL=-4255.89 S2= 0.10968E+06 666 df 0.2977 1.000 0.2980
4 LogL=-4243.76 S2= 88033. 666 df 0.7398 1.000 0.4939
5 LogL=-4240.59 S2= 84420. 666 df 0.9125 1.000 0.6016
6 LogL=-4240.01 S2= 85617. 666 df 0.9344 1.000 0.6428
7 LogL=-4239.91 S2= 86032. 666 df 0.9474 1.000 0.6596
8 LogL=-4239.88 S2= 86189. 666 df 0.9540 1.000 0.6668
9 LogL=-4239.88 S2= 86253. 666 df 0.9571 1.000 0.6700
10 LogL=-4239.88 S2= 86280. 666 df 0.9585 1.000 0.6714
Final parameter values 0.95918 1.0000 0.67205
Source Model terms Gamma Component Comp/SE % C
variety 532 532 0.959184 82758.6 8.98 0 P
Variance 670 666 1.00000 86280.2 9.12 0 P
Residual AR=AutoR 67 0.672052 0.672052 16.04 1 U
Wald F statistics
Source of Variation NumDF DenDF F-inc Prob
7 mu 1 83.6 9799.18 <.001
3 weed 1 477.0 109.33 <.001
The iterative sequence converged, the REML estimate of the
autoregressive parameter indicating substantial within column
heterogeneity.
The abbreviated output from the two-dimensional AR1 cross AR1 spatial
model is
1 LogL=-4277.99 S2= 0.12850E+06 666 df
2 LogL=-4266.13 S2= 0.12097E+06 666 df
3 LogL=-4253.05 S2= 0.10777E+06 666 df
4 LogL=-4238.72 S2= 83156. 666 df
5 LogL=-4234.53 S2= 79868. 666 df
6 LogL=-4233.78 S2= 82024. 666 df
7 LogL=-4233.67 S2= 82725. 666 df
8 LogL=-4233.65 S2= 82975. 666 df
9 LogL=-4233.65 S2= 83065. 666 df
10 LogL=-4233.65 S2= 83100. 666 df
Source Model terms Gamma Component Comp/SE % C
variety 532 532 1.06038 88117.5 9.92 0 P
Variance 670 666 1.00000 83100.1 8.90 0 P
Residual AR=AutoR 67 0.685387 0.685387 16.65 0 U
Residual AR=AutoR 10 0.285909 0.285909 3.87 0 U
Wald F statistics
Source of Variation NumDF DenDF F-inc Prob
7 mu 1 41.7 6248.65 <.001
3 weed 1 491.2 85.84 <.001
The change in REML LogL is significant (χ21= 12.46, p<.001) with
the inclusion of the autoregressive parameter for
columns. The Figure presents the sample variogram of the
residuals for the AR1 cross AR1 model. There is an indication that
a linear drift from column 1 to column 10 is present. We include a
linear regression coefficient pol(column,-1) in the model to
account for this. Note we use the '-1' option in the pol term to
exclude the overall constant in the regression, as it is already
fitted. The linear regression of column number on yield is significant
(t=-2.96). The sample variogram (Figure 2 ) is more satisfactory,
though interpretation of variograms is often difficult, particularly
for unreplicated trials. This is an issue for further research.
#AR1xAR1 + pol(column,-1)
1 LogL=-4270.99 S2= 0.12730E+06 665 df
2 LogL=-4258.95 S2= 0.11961E+06 665 df
3 LogL=-4245.27 S2= 0.10545E+06 665 df
4 LogL=-4229.50 S2= 78387. 665 df
5 LogL=-4226.02 S2= 75375. 665 df
6 LogL=-4225.64 S2= 77373. 665 df
7 LogL=-4225.60 S2= 77710. 665 df
8 LogL=-4225.60 S2= 77786. 665 df
9 LogL=-4225.60 S2= 77806. 665 df
Source Model terms Gamma Component Comp/SE % C
variety 532 532 1.14370 88986.3 9.91 0 P
Variance 670 665 1.00000 77806.0 8.79 0 P
Residual AR=AutoR 67 0.671436 0.671436 15.66 0 U
Residual AR=AutoR 10 0.266088 0.266088 3.53 0 U
Wald F statistics
Source of Variation NumDF DenDF F-inc Prob
7 mu 1 42.5 7073.70 <.001
3 weed 1 457.4 91.91 <.001
8 pol(column,-1) 1 50.8 8.73 0.005
#
#AR1xAR1 + units + pol(column,-1)
#
1 LogL=-4272.74 S2= 0.11683E+06 665 df : 1 components constrained
2 LogL=-4266.07 S2= 50207. 665 df : 1 components constrained
3 LogL=-4228.96 S2= 76724. 665 df
4 LogL=-4220.63 S2= 55858. 665 df
5 LogL=-4220.19 S2= 54431. 665 df
6 LogL=-4220.18 S2= 54732. 665 df
7 LogL=-4220.18 S2= 54717. 665 df
8 LogL=-4220.18 S2= 54715. 665 df
Source Model terms Gamma Component Comp/SE % C
variety 532 532 1.34824 73769.0 7.08 0 P
units 670 670 0.556400 30443.6 3.77 0 P
Variance 670 665 1.00000 54715.2 5.15 0 P
Residual AR=AutoR 67 0.837503 0.837503 18.67 0 U
Residual AR=AutoR 10 0.375382 0.375382 3.26 0 U
Wald F statistics
Source of Variation NumDF DenDF F-inc Prob
7 mu 1 13.6 4241.53 <.001
3 weed 1 469.0 86.39 <.001
8 pol(column,-1) 1 18.5 4.84 0.040
The increase in REML LogL is significant. The predicted means for the varieties can be produced and printed in the .pvs file as
Warning: mvetimates is ignored for prediction
Warning: units is ignored for prediction
---- ---- ---- ---- ---- ---- ---- 1 ---- ---- ---- ---- ---- ---- ---- ----
column evaluated at 5.5000
weed is evaluated at average value of 0.4597
Predicted values of yield
variety PredictedVlue StandardEror Ecode
1.0000 2917.1782 179.2881 E
2.0000 2957.7405 178.7688 E
3.0000 2872.7615 176.9880 E
4.0000 2986.4725 178.7424 E
. . .
522.0000 2784.7683 179.1541 E
523.0000 2904.9421 179.5383 E
524.0000 2740.0330 178.8465 E
525.0000 2669.9565 179.2444 E
526.0000 2385.9806 44.2159 E
527.0000 2697.0670 133.4406 E
528.0000 2727.0324 112.2650 E
529.0000 2699.8243 103.9062 E
530.0000 3010.3907 112.3080 E
531.0000 3020.0720 112.2553 E
532.0000 3067.4479 112.6645 E
SED: Overall Standard Error of Difference 245.8
Note that the (replicated) check lines have lower SE than the (unreplicated)
test lines. There will also be large diffeneces in SEDs.
Rather than obtaining the large table of all SEDs, you could do the
prediction in parts