Variance estimates
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Variance estimates

I am trying to interpret some output from a variance component
estimation attempt with asreml.  I have run a random regression model
for fat depth in beef cattle and I am modelling fat depth on weight.

The .as file is

Random regression of rib fat dpeth on weight
 animal 3220 !I #Animal
 bdate 731 !A # in format 22/07/69 etc
 sire  199 !A #example 'NBBK090' with the quotes
 breed   4 !A #!DHHHH !DMGMG !DSSSS #4 of these
 herd   23 !A #
 nut     8 !A #nutritional treatment imposed during grow out
 fin     2 !A #finish, pasture or feedlot
 mk1     3 !A #market, Domestic, Korean or Japanese
 mk2     2 !A #market, Domestic or Export
 cohort 12 !A #Taurus, steer, 1993, 1st intake TS931
 dtwt   #date of weight eg   34491
 wt !-422.5 !/237.5  #weight in kg standardized to -1 to 1 
 dtp8  !M-1 #date of p8 fat measure
 p8 !M-1 !*100 #p8 fat measure (mm)
 dtrib !M-1 #date of rib measure
 rib !M-1 !*100 #rib fat 12/13 measure (mm)
 dtema !M-1 #date of eye-muscle area measure (sqcm)
 ema  !M-1 #eye muscle area measure (sqcm)
 bdate2 !M25406  #birth date in days like dtrib etc above
 cg    41 !A #cohort.fin.mk2
 n2    28 !A #cohort.nut

../../../Data/data4.dat  !maxit 1000 # reading data file 
rib ~ mu wt wt.wt cg cg.wt cg.wt.wt n2 n2.wt n2.wt.wt,
  br br.wt br.wt.wt !r he he.wt s s.wt an an.wt 

1 2 3 !STEP 0.1
3 0 DIAG 9804.57 9761.96 9214.61 !GUUU

he 2
2 0 US 4702.17 4214.69 5946.26 !GUUU
s 2
2 0 US 4702.17 4214.69 5946.26 !GUUU

an 2
2 0 US 17854 18000 46610 !GUUU

The output for my variance components is

   Source       Model  terms     Gamma     Component    Compnt/StndErr
   Residual   DIAG=Dia     1   328.423       9805.47         25.01
   Residual   DIAG=Dia     2   326.861       9758.85         25.16
   Residual   DIAG=Dia     3   308.629       9214.49         24.81
  sire        US=UnStr     1   157.896       4714.19          7.31
  sire        US=UnStr     1   142.277       4247.86          5.86
  sire        US=UnStr     2   201.654       6020.64          5.98
  animal      US=UnStr     1   583.459       17419.9         29.40
  animal      US=UnStr     1   771.300       23028.1         29.85
  animal      US=UnStr     2   867.785       25908.8         19.29

'Component' are the variance components I am interested in.  What are
the 'Gamma' components and how sould I be using these?  I have three
residuals.. the data is sorted by weight.  So there will be three
residuals, one for each of three weight classes.

Also I have a problem that if I expand out the variances over the
range of weights, in this case from -1 to 1 for the standardized
weights some are negative... or sometimes the correlation between
measures at different weights could be greater than 1.  How can I
constrain the acceptable solutions to consider the parameter space
where variances are not neagtive for example.

Take the component for animal above ... the variance at weight -1
would be 17419.9 - 2 * 23028.1 + 25908.8 = -2727.5.  This is a
negative variance... the problem exists in this case at the low
weights.  I saw in the manual that placing some constraints on a
function of the variance components is possible.  However, I can't see
how to make it work for my example.  Hopefully someone out there can
be of some help.

The problem appears to be for my animal or permanent environmental
effects.  I have three measures per animal.

Steve Miller

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