Parameters at the boundary

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)

-- 
Denis Fidalis Mujibi
1430 College Plaza
8215 112 St, Edmonton
T6G 2C5, AB, Canada.
fmujibi_at_ualberta.ca