# Re: Parameters at the boundary

From: <fmujibi_at_UALBERTA.CA>
Date: Thu, 28 May 2009 14:42:21 -0600

Much appreciated

```--
Denis Fidalis Mujibi
1430 College Plaza
8215 112 St, Edmonton
fmujibi_at_ualberta.ca
Quoting "Arthur Gilmour" <arthur.gilmour_at_CARGOVALE.COM.AU>:
> 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
>> 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
>
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>
```
Received on Fri May 28 2009 - 14:42:21 EST

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