Re: Parameters at the boundary

Dear Denis,

The estimated variance parameters need to be treated with caustion as
follows.

First, the ? means that when ASReml calculates an AI update, the
result is not positive defiite so must be rejected. ASReml then
performs an EM type of update but EM updates take a long time to
converge.

In this case, it is the SIRE term that is having trouble.
But the final parameters are

Covariance/Variance/Correlation Matrix UnStructured Trait.sire
0.6037E-01 0.8908
0.3931 3.225

which does not reveal a correaltion of almost 1, or a variance almost
zero, so it has not converged to a boundary condition.
[In general (for more than 2 traits, check the eigen values in the .res
file)]

Often, you could specify the !PXEM qualifier and it might converge
faster.
Since you are using a pedigree for SIRE though, this may not work.

The problem is like trying to climb mount Everest when you are not
allowed into Nepal. REML wants to locate the maximum REML likelihood
associated with the data and model, but you have said the SIRE matrix
must be positive definite and the highest REML LogL is associated with a
sire matrix that is not positive definite.

So, all you can do, is try and find the highest point along the
boundary.

Since it is a small data set, (512 individuals), the sire variance
matrix may not be well estimated (how many actual sires are there).

So, in this case, the SIRE matrix is not almost singular (on the
boundary of the parameter space) so (much) more iteration is required.

 
On Tue, 2009-05-26 at 12:50 -0600, fmujibi_at_UALBERTA.CA wrote:
> Hello All.
> I am wondering about the validity of the variance components obtained
> when parameters converge at the boundary. (ASreml gives a warning
> message "? - liable to change from P to B"). Despite the fact that
> standard errors are not obtained, do the estimates still stand?
>
> Attached is a truncated version of the .asr file that I get
>
> Folder: C:\Documents and Settings\User\Desktop\Final_Formats
> id !P
> sire !P
> dam !P
> breed 4 !I
> group 3 !I
> A-inverse retrieved from ainverse.bin
> PEDIGREE [testdata.csv ] has 1014 identities, 2433 Non zero elements
> QUALIFIERS: !SKIP 1 !EXTRA 90 !MAXIT 100 !MVINCLUDE
> Reading testdata.csv FREE FORMAT skipping 1 lines
>
> Bivariate analysis of vfa and fwd100
> Using 512 records of 512 read
>
> Model term Size #miss #zero MinNon0 Mean MaxNon0
> 1 id !P 1014 0 0 1.000 491.3 1014.
> 2 sire !P 1014 33 0 1.000 235.3 1013.
> 3 dam !P 1014 40 0 34.00 438.9 1010.
> 4 breed 4 33 0 1 2.6931 4
> 5 group 3 33 0 1 2.1315 3
> 6 age 33 0 161.0 240.5 332.0
> Warning: Fewer levels found in vfa than specified
> 7 vfa 50 33 2 -3 0.0082 3
> 8 stpws50 0 0 -2.486 0.9287 5.230
> 9 fwd100 Variate 0 0 -3.493 1.972 9.896
> 10 bwd50 17 0 -1.833 0.2840 2.468
> 11 st50blp 17 0 -2.578 0.2707 3.205
> 12 Trait 2
> 13 at(Trait,1) 1
> 14 at(Trait,1).age 1 13 at(Trait,1: 1 6 age : 1
> 15 at(Trait,1).breed 4 13 at(Trait,1: 1 4 breed : 4
> 16 at(Trait,1).group 3 13 at(Trait,1: 1 5 group : 3
> 17 Trait.sire 2028 12 Trait : 2 2 sire : 1014
> Warning: 330 missing values were detected in the design variables
> Missing values are treated as zeros
> Consider deleting the records in which they occur
> 512 identity
> 2 UnStructure 0.7900 0.4000 2.1000
> 1024 records assumed pre-sorted 2 within 512
> 2 UnStructure 0.0800 0.2000 2.8500
> 1014 Ainverse
> Structure for Trait.sire has 2028 levels defined
> Forming 2038 equations: 10 dense.
> Initial updates will be shrunk by factor 0.100
> Notice: Algebraic ANOVA Denominator DF calculation is not available
> Numerical derivatives will be used.
> Notice: 2 singularities detected in design matrix.
> 1 LogL=-697.455 S2= 1.0000 983 df
> 2 LogL=-687.781 S2= 1.0000 983 df
> 3 LogL=-666.246 S2= 1.0000 983 df
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 4 LogL=-654.848 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 5 LogL=-653.056 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 6 LogL=-653.028 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 7 LogL=-653.016 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 8 LogL=-653.005 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 9 LogL=-652.996 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 10 LogL=-652.988 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 11 LogL=-652.981 S2= 1.0000 983 df : 3 components constrained
> Notice: US matrix updates modified 1 time(s) to keep them positive definite.
> 12 LogL=-652.975 S2= 1.0000 983 df : 3 components constrained
> 13 LogL=-652.969 S2= 1.0000 983 df : 3 components constrained
> 14 LogL=-652.964 S2= 1.0000 983 df : 3 components constrained
> 15 LogL=-652.960 S2= 1.0000 983 df : 3 components constrained
> 41 LogL=-652.921 S2= 1.0000 983 df : 3 components constrained
> Notice: US structures were modified 38 times to make them positive definite.
> If ASReml has fixed the structure [flagged by B], it may not have
> converged to a maximum likelihood solution.
> !EMFLAG 0 Single standard EM update when AI update unacceptable
>
> Source Model terms Gamma Component Comp/SE % C
> Residual UnStructured 1 1 0.827632 0.827632 15.03 0 P
> Residual UnStructured 2 1 0.883629 0.883629 11.06 0 P
> Residual UnStructured 2 2 2.15469 2.15469 13.76 0 P
> Trait.sire UnStructured 1 1 0.603739E-01 0.603739E-01 0.00 0 ?
> Trait.sire UnStructured 2 1 0.393079 0.393079 0.00 0 ?
> Trait.sire UnStructured 2 2 3.22522 3.22522 0.00 0 ?
> Warning: Code B - fixed at a boundary (!GP) F - fixed by user
> ? - liable to change from P to B P - positive definite
> C - Constrained by user (!VCC) U - unbounded
> 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.
> Covariance/Variance/Correlation Matrix UnStructured Residual
> 0.8276 0.6617
> 0.8836 2.155
> Covariance/Variance/Correlation Matrix UnStructured Trait.sire
> 0.6037E-01 0.8908
> 0.3931 3.225
>
> Analysis of Variance NumDF DenDF F_inc Prob
> 12 Trait 2 NA 149.34 NA
> 14 at(Trait,1).age 1 496.8 0.27 0.605
> 15 at(Trait,1).breed 3 735.8 3.16 0.026
> 16 at(Trait,1).group 2 473.3 4.34 0.015
> Notice: The DenDF values are calculated ignoring fixed/boundary/singular
> variance parameters using numerical derivatives.
> 17 Trait.sire 2028 effects fitted ( 740 are zero)
>
>
>

-- 
Best Wishes,
Arthur Gilmour
Jesus went to the synagogue in every town in Galilee to preach and drive out demons.
A leper came, knelt down and said, "If you will, you can make me clean".
Jesus was moved. He reached out and touched him and said 
"I am willing.  Be clean." He was cleansed immediately.
Mobile Number +61 427 227 468
Home phone +61 2 6364 3288  Skype: Arthur.Gilmour
http://www.CargoVale.com.au/ASReml
Travel:
Brazil  Jul27 - Aug 8
UK      Aug 10-14
Mumbai  Aug 16-17