I would be grateful for feedback on the ASREML command file and output
embedded below. The objective is to determine the relationship between
field establishment (plants/m2) and grain yield (t/ha) in three varieties of
lupin.
I'd like to know whether the output indicates that the model I am fitting is
appropriate. In particular:
i. I put two starting values after the codeword AR with the intention of
getting first- and second-lag autocorrelations. Is this the correct method?
ii. If so, does the output indicate that the inclusion of second-lag
autocorrelation gives a significantly better fit? I am assuming that it
does because the Compnt/StndErr values for both AR terms are quite large
(>3).
iii. Why are the gamma and component values for these two terms so
similar? Is this just coincidence?
iv. I don't want to fit any column effects. So is the codeword IDEN
okay? How should I decide whether the identify matrix should be scaled?
v. Is it okay to fit a linear effect of the variate ESTAB (and its
interaction with Variety), to account for any overall trend, before
including the spline in the model?
vi. Should the spline (and its interaction with Variety) be put in the
random effects model? If so, will the variance explained by the spline be
included in the error against which the linear trend is tested?
vii. Am I right in thinking that it makes no difference to the fitted value
of a data point whether a term (e.g. spl(ESTAB)) is fitted as a fixed or a
random effect?
The desired outcome is a curve relating yield to establishment in each
variety, and it is therefore necessary to obtain predicted values. I would
like to avoid the complexities of setting up a .pin file, and the ASREML
manual suggests adding some "missing data" and fitting them with "missing
values" (p 86, version of 2 October 1998). However, it seems to me that
this approach won't work for a spatial analysis, as each observation must be
allocated to a row and column. I had hoped that the row and column values
would not influence the fitted value (just as the variogram is not
influenced by whether AR terms are fitted), but it turns out that they do
have an effect. Any suggestions?
__________________
96wh14.as
Restricted branching lupin - density trials
Variety 3 !A
TDENS 6
Rep 5
PLOT 90
COL 2
ROW 101
THA
ESTAB
C:\DOCS\Dracup_M\96WH14\96WH14.dat !skip 1 !maxit 20
THA ~ mu mv c(Variety) ESTAB c(Variety).ESTAB,
!r Rep spl(ESTAB) c(Variety).spl(ESTAB)
1 2
ROW ROW AR .1 .1
COL COL IDEN
______________________
96wh14.asr
ASREML [30 Sep 1998] Restricted branching lupin - density trials
10/29/98 12:09:43.22 8.00 Mbyte c:\DOCS\Dracup_M\96WH14\96wh14.as
QUALIFIERS: !skip 1
Reading C:\DOCS\Dracup_M\96WH14\96WH14.dat FREE FORMAT skipping 1
lines
Univariate analysis of THA
Using 108 records [of 108 read from 108 lines of
C:\DOCS\Dracup_M\96W]
Model term Size Type COL Minimum Mean Maximum #zero #miss
1 Variety 3 Factor 1 1 2.0000 3 0 18
2 TDENS 6 Factor 2 25 71.6667 125 0 18
WARNING - More levels in factor than expected
3 Rep 5 Factor 3 1 3.0000 5 0 18
4 PLOT 90 Factor 4 1 45.5000 90 0 18
5 COL 2 Factor 5 1 1.5000 2 0 0
6 ROW 54 Factor 6 1 27.5000 54 0 0
7 THA 1 Variate 7 0.7530 1.014 1.428 0 20
8 ESTAB 1 Covariat 8 19.60 71.19 137.6 0 18
9 mu 1 Constant Term
10 mv_estimates 20 Missing value
11 c(Variety) 2 Factor 1 1 2.0000 3 0 18
12 c(Variety).E 2 Interaction 11 c(Vari: 2 8 ESTAB : 1
13 spl(ESTAB) 47 Spline 8 19.60 71.19 137.6 0 18
14 c(Variety).s 94 Interaction 11 c(Vari: 2 13 spl(ESTAB) : 47
54 AR=AutoR 0.10 0.10
2 identity
Forming 173 equations: 27 dense
Initial updates will be shrunk by factor 0.548
LogL= 80.6926 S2= 0.11703E-01 82 df 0.10000 0.10000 0.10000
1.0000 0.10000 0.10000
LogL= 104.813 S2= 0.11911E-01 82 df 0.16662 0.10000E-010.10000E-01
1.0000 0.21445 0.27837
LogL= 116.546 S2= 0.13897E-01 82 df 0.30356 0.10000E-020.10000E-02
1.0000 0.30181 0.35295
LogL= 121.136 S2= 0.15483E-01 82 df 0.40011 0.10000E-030.10000E-03
1.0000 0.35163 0.34838
LogL= 122.124 S2= 0.14720E-01 82 df 0.44461 0.58089E-040.10000E-04
1.0000 0.35465 0.31151
LogL= 122.722 S2= 0.18048E-01 82 df 0.42452 0.49216E-040.10000E-06
1.0000 0.34659 0.41749
LogL= 122.719 S2= 0.20917E-01 82 df 0.36671 0.45774E-040.10000E-06
1.0000 0.40451 0.39840
Final parameter values 0.56309 0.65929E-040.10000E-06
1.0000 0.37353 0.37798
Source Model terms Gamma Component Compnt/StndErr
Rep 5 5 0.563094 0.117781E-01 1.77 P
spl(ESTAB) 47 47 0.659291E-04 0.137902E-05 0.75 P
c(Variety).spl(ESTAB 94 94 0.100000E-06 0.209167E-08 1.86 B
Variance 108 82 1.00000 0.209167E-01 1.86 P
Residual AR=AutoR 54 0.373534 0.373534 3.20 U
Residual AR=AutoR 54 0.377980 0.377980 3.20 U
WARNING: Code B - fixed at a boundary (!GP)
C - Constrained by user (!CON)
S - Singular Information matrix
S means there is no information in the data for this parameter.
Very small components with Comp/SE ratios of zero sometimes indicate poor
scaling. Consider rescaling the design matrix in such cases
Fitted Spline 49 (X) for spl(ESTAB)
19.600 21.800 24.400 27.050 28.200 29.800 32.800 37.400
41.200 42.900 44.000 45.200 46.600 48.400 50.350 52.400
54.200 56.000 57.700 59.000 60.600 63.350 64.733 69.900
71.400 72.800 76.000 79.500 80.800 82.400 85.000 87.267
89.400 91.600 93.400 95.600 98.600 100.000 103.800 105.800
111.000 115.267 116.900 118.800 121.000 122.700 128.400 130.800
137.600
Fitted Spline 49 (Y) for spl(ESTAB) 1
0.028825 0.025985 0.022633 0.019228 0.017760 0.015734 0.011984 0.006362
0.001891 -0.000024 -0.001228 -0.002504 -0.003938 -0.005686 -0.007444 -0.009122
-0.010445 -0.011620 -0.012588 -0.013231 -0.013901 -0.014735 -0.015003 -0.015187
-0.015038 -0.014829 -0.014125 -0.013057 -0.012588 -0.011960 -0.010830 -0.009747
-0.008657 -0.007466 -0.006443 -0.005138 -0.003267 -0.002361 0.000183 0.001561
0.005231 0.008293 0.009465 0.010819 0.012369 0.013552 0.017448 0.019085
0.023756
', , 0.03
'',, ,' 0.02
' ,,,'' 0.01
',, ,,' 0.00
''',, ,,,'' 0.00
''',,,,,,,,,,,'''' -0.01
-0.02
-0.03
Fitted Spline 49 (Y) for c(Variety).spl(ESTAB 1
-0.74E-06 -0.58E-06 -0.40E-06 -0.23E-06 -0.16E-06 -0.58E-07 0.14E-06 0.50E-06
0.89E-06 0.11E-05 0.13E-05 0.15E-05 0.17E-05 0.20E-05 0.24E-05 0.29E-05
0.32E-05 0.35E-05 0.38E-05 0.39E-05 0.39E-05 0.37E-05 0.35E-05 0.20E-05
0.14E-05 0.73E-06 -0.97E-06 -0.30E-05 -0.37E-05 -0.45E-05 -0.57E-05 -0.65E-05
-0.70E-05 -0.74E-05 -0.76E-05 -0.76E-05 -0.72E-05 -0.69E-05 -0.59E-05 -0.51E-05
-0.26E-05 -0.24E-06 0.73E-06 0.19E-05 0.32E-05 0.42E-05 0.76E-05 0.91E-05
0.13E-04
''''''''''''''''''''''''''''''''''''''''''''''''' 0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.01
Fitted Spline 49 (Y) for c(Variety).spl(ESTAB 2
-0.61E-05 -0.52E-05 -0.41E-05 -0.31E-05 -0.26E-05 -0.20E-05 -0.93E-06 0.40E-06
0.11E-05 0.13E-05 0.14E-05 0.16E-05 0.17E-05 0.17E-05 0.18E-05 0.17E-05
0.16E-05 0.15E-05 0.13E-05 0.12E-05 0.94E-06 0.53E-06 0.33E-06 -0.14E-06
-0.18E-06 -0.17E-06 0.13E-07 0.44E-06 0.65E-06 0.93E-06 0.14E-05 0.19E-05
0.22E-05 0.26E-05 0.28E-05 0.29E-05 0.30E-05 0.30E-05 0.27E-05 0.24E-05
0.13E-05 0.12E-06 -0.38E-06 -0.10E-05 -0.18E-05 -0.24E-05 -0.46E-05 -0.55E-05
-0.82E-05
''''''''''''''''''''''''''''''''''''''''''''''''' 0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.01
-0.01
Solution Standard Error T-value T-prev
12 c(Variety).ESTAB 2 3.46 3.46 [DF
F_inc F_all]
1 0.582442E-03 0.385741E-03 1.51
2 -0.101474E-02 0.388952E-03 -2.61 -2.41
8 ESTAB 1 23.84 24.87 [DF
F_inc F_all]
3 -0.196641E-02 0.394323E-03 -4.99
11 c(Variety) 2 0.37 2.08 0.5136E-01 [DF F_i
F_a SED]
MERRIT -0.305525E-01 0.302952E-01 -1.01
85SO46-37 0.607833E-01 0.298523E-01 2.04 1.73
10 mv_estimates 20 13.49 14.01 [DF
F_inc F_all]
6 -0.882628 0.916597E-01 -9.63
7 -0.647879 0.941482E-01 -6.88 1.92
8 -1.07879 0.116429 -9.27 -2.83
9 -1.11726 0.122686 -9.11 -0.34
10 -1.10920 0.133636 -8.30 0.07
11 -1.12127 0.138845 -8.08 -0.10
12 -1.12293 0.143739 -7.81 -0.01
13 -1.12842 0.147031 -7.67 -0.05
14 -1.13130 0.149708 -7.56 -0.02
15 -1.13465 0.151712 -7.48 -0.03
16 -1.13715 0.153298 -7.42 -0.02
17 -1.13950 0.154532 -7.37 -0.02
18 -1.14145 0.155512 -7.34 -0.02
19 -1.14317 0.156290 -7.31 -0.01
20 -1.14464 0.156913 -7.29 -0.01
21 -1.14592 0.157416 -7.28 -0.01
22 -1.14703 0.157823 -7.27 -0.01
23 -1.14799 0.158154 -7.26 -0.01
24 -1.14882 0.158426 -7.25 -0.01
25 -1.14953 0.158650 -7.25 -0.01
9 mu 1 157.88 287.57 [DF
F_inc F_all]
26 1.15412 0.680586E-01 16.96
3 Rep 5 effects fitted
13 spl(ESTAB) 47 effects fitted
14 c(Variety).spl(ESTAB 94 effects fitted
Finished: 12:10:59.39 LogL Converged
_____________________________________________________________________
N.W. Galwey,
Faculty of Agriculture,
University of Western Australia,
Nedlands, WA 6709, Australia.
Tel.: +61 9 380 1959 (direct line)
+61 9 380 2554 (switchboard)
Fax: +61 9 380 1108