> Date: Thu, 5 Nov 1998 13:20:37 +0800
> X-Sender: ngalwey@cyllene.uwa.edu.au
> Mime-Version: 1.0
> To: asreml@ram.chiswick.anprod.csiro.au
> From: "N.W. Galwey" <ngalwey@cyllene.uwa.edu.au>
> Subject: smoothing spline for crop density
>
> This is the continuing saga of an analysis on which Arthur Gilmour and Brian
> Cullis gave some advice a week or two ago. The data are from three lupin
> varieties sown at a range of target densities. Yield (tonnes/ha) (THA) and
> the realised density (plants/m2) (ESTAB) are measured.
>
> A smoothing spline is used to fit the response of THA to ESTAB. Brian
> pointed out that there are too many knots (49) in the resulting spline, and
> suggested that knot points should be chosen explicitly. However, I can't
> see how to do precisely this: the ASREML manual describes how to set the
> number of knot points (p. 51, version of 2 October 1998) but not their
> actual values.
>
ASREML does not let you choose the not points, just adjust the number.
There appears to have been 5 target densities.
You could make TDENS a factor (Add !I or !/25); it is not correctly at present
Maybe the current set are not optimum but the spl terms appear NS
so it may not matter.
> Brian recommended that Rep should not be fitted in combination with a
> spatial model, unless there was clear evidence that it was necessary. But
> there is: the two .asr files embedded below show an increase of max
> likelihood of about 10 from including Rep. Arthur suggested fitting COL as
> a random effect (the plots are laid out in two columns), and I hoped this
> might pick up the same variation as Rep, but it doesn't do much at all.
>
Was your layout 2 cols of 54 side by side?
I'm puzzled how you get the two AR structures on 54 points.
You probably only need 1 AR structure.
I would like to see the residual plots (you would have to send the .as and data
files). Usually, the REP term drops out when the spatial model is adequate.
Maybe there needs to be a spline over row or something.
The variety effects all appear NS leaving a strong -ve relationship with
ESTAB. Was ESTAB properly randomised. Fitting REP has reduced the
ESTAB regression !
Also, I assu7me the missing values for ESTAB occur where there are MV for THA.
If this -ve relationship is correct, the trend should be evident from fitting TDENS.
> Final puzzle (for the time being): the relationship between THA and ESTAB is
> negative and significant. Note that tonnes/ha, not yield/plant, is
> measured. A plot of the raw data is pretty flat, which is disappointing
> but okay - but how does one account for a significant negative relationship?
> Is it being tested against the wrong error?
>
What does a linear regression THA vs ESTAB say. Most other things other than
REPS and autocorrelation are NS so the linear regression should
show the same pattern. Otherwise something odd is happening.
Sorry to take so long to investigate this. Arthur
> Nick Galwey
>
> _______________________
>
> Analysis including Rep
>
0
> 2 TDENS 6 Factor 2 25 63.8889 125 0 0
> WARNING - More levels in factor than expected
*** CHange to TDENS 6 !I
>
> Source Model terms Gamma Component Compnt/StndErr
> Rep 5 5 0.573475 0.100567E-01 1.07 P
> spl(ESTAB) 4 4 0.503830E-01 0.883540E-03 0.30 P
> Variety.spl(ESTAB) 12 12 0.100000E-06 0.175365E-08 2.27 B
> Variance 108 82 1.00000 0.175365E-01 2.27 P
> Residual AR=AutoR 54 0.402072 0.402072 3.37 U
> Residual AR=AutoR 54 0.363720 0.363720 3.03 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 6 (X) for spl(ESTAB)
> 27.040 51.208 70.956 93.893 116.031 131.900
> Fitted Spline 6 (Y) for spl(ESTAB) 1
> 0.028978 -0.017173 -0.023585 -0.008760 0.007397 0.013143
> ' 0.03
> 0.02
> ,' 0.01
> 0.00
> ' -0.01
> ' -0.02
> ' -0.03
> -0.04
**** THESE are very small deviations from the straight line decline!
> Fitted Spline 6 (Y) for Variety.spl(ESTAB) 1
> Solution Standard Error T-value T-prev
> 12 c(Variety).ESTAB 2 3.41 3.41 [DF
> F_inc F_all]
> 1 0.571064E-03 0.386200E-03 1.48
> 2 -0.101010E-02 0.388844E-03 -2.60 -2.37
> 8 ESTAB 1 20.29 21.59 [DF
> F_inc F_all]
> 3 -0.190629E-02 0.410273E-03 -4.65
> 11 c(Variety) 2 0.49 1.90 0.5110E-01 [DF F_i
> F_a SED]
> MERRIT -0.291534E-01 0.301931E-01 -0.97
> 85SO46-37 0.580733E-01 0.298602E-01 1.94 1.65
> 10 mv_estimates 20 16.08 14.48 [DF
> F_inc F_all]
> 6 -0.899080 0.932293E-01 -9.64
> 7 -0.645952 0.948447E-01 -6.81 2.08
> 8 -1.10387 0.118815 -9.29 -2.92
> 9 -1.13570 0.124359 -9.13 -0.28
> 10 -1.13103 0.132515 -8.54 0.04
> 11 -1.14038 0.136347 -8.36 -0.08
> 12 -1.14252 0.139542 -8.19 -0.02
> 13 -1.14668 0.141591 -8.10 -0.04
> 14 -1.14913 0.143109 -8.03 -0.02
> 15 -1.15159 0.144174 -7.99 -0.02
> 16 -1.15344 0.144951 -7.96 -0.02
> 17 -1.15507 0.145517 -7.94 -0.01
> 18 -1.15638 0.145934 -7.92 -0.01
> 19 -1.15748 0.146244 -7.91 -0.01
> 20 -1.15839 0.146477 -7.91 -0.01
> 21 -1.15915 0.146653 -7.90 -0.01
> 22 -1.15978 0.146787 -7.90 -0.01
> 23 -1.16030 0.146891 -7.90 0.00
> 24 -1.16074 0.146971 -7.90 0.00
> 25 -1.16110 0.147035 -7.90 0.00
******** 20% missing is high. Are missing values related to TDENS?
> 9 mu 1 210.45 296.72 [DF
> F_inc F_all]
> 26 1.15333 0.669547E-01 17.23
> 3 Rep 5 effects fitted
> 13 spl(ESTAB) 4 effects fitted
> 14 Variety.spl(ESTAB) 12 effects fitted
> 1 possible outliers: see .res file
> Finished: 12:49:24.69 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
>
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Arthur Gilmour PhD email: Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics) fax: <61> 2 6391 3899
NSW Agriculture <61> 2 6391 3922
Orange Agricultural Institute telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA home: <61> 2 6362 0046
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