Singularity in Average Information Matrix

Hello everyone,

I have written a program for mapping QTL in a Grand Daughter Design data
structure. When I run the program, it usually tells “Singularity in
Average Information Matrix”. I tested the program with different number
of animals but still the problem exists. In the data file genotypes are
available just from the male animals while phenotype is available from
both sexes. Here comes a control, data and .asr file.

I appreciate any comment on this problem.
Mohsen

Control File:
Mapping QTL Program
animal !P
sire !P
dam !P
phenotype
qtl !SORT 6
pedigree.dat !MAKE
h5.grm
phenfull.dat !MAXIT 20 !report
phenotype ~ mu !r animal qtl
1 1 2
0 0 0
animal 1
animal 0 AINV 0.30 !Gp
qtl 1
qtl 0 GIV1 0.10 !Gp

Data File:
33 13 14 -46.704847 1
35 13 24 3.832740 1
37 21 28 19.300518 2
39 21 26 -3.463549 2
40 33 26 -60.416469 3
48 33 24 -32.993225 3
46 35 26 -13.730570 4
54 35 24 21.396051 4
42 37 26 -9.670238 5
50 37 24 48.271274 5
52 39 24 1.430655 6
44 39 26 -8.357753 6

.asr file:
....

Folder: /w/MR
animal !P
sire !P
dam !P
qtl !SORT 6
Reading pedigree file pedigree.dat : skipping 0 lines
Using an adapted version of Meuwissen & Luo GSE 1992 305-313: Specify
!METHOD 1 for column method.
PEDIGREE [pedigree.dat ] has 55 identities, 170 Non zero elements
Reading h5.grm skipping 0 header lines
Inverse G structure of 6 rows obtained by inverting matrix read from h5.grm

QUALIFIERS: !MAXIT 20 !REPORT
Reading phenfull.dat FREE FORMAT skipping 0 lines
Univariate analysis of phenotype
Using 12 records of 12 read

Model term Size #miss #zero MinNon0 Mean MaxNon0

1 animal !P 55 0 0 33.00 43.33 54.00
2 sire !P 55 0 0 13.00 29.67 39.00
3 dam !P 55 0 0 14.00 24.33 28.00
4 phenotype Variate 0 0 -60.42 -6.759 48.27
5 qtl 6 0 0 1 3.5000 6
6 mu 1
55 Ainverse 0.3000
Structure for animal has 55 levels defined
6 h5 0.1000

Structure for qtl has 6 levels defined
Forming 62 equations: 1 dense.
Initial updates will be shrunk by factor 0.224
1 LogL=-43.4186 S2= 613.31 11 df 1.000 0.3000 0.1000
2 LogL=-41.7362 S2= 178.33 11 df 1.000 2.890 0.5409

3 LogL=-40.8129 S2= 19.986 11 df : 2 components constrained
4 LogL=-40.6964 S2= 1.2961 11 df : 2 components constrained
5 LogL=-40.6888 S2= 0.82104E-01 11 df : 2 components constrained
6 LogL=-40.6883 S2= 0.51932E-02 11 df : 1 components constrained

Notice: 1 singularities appeared in Average Information matrix
This could be a problem of scale or a problem with the model.
It is preferable to revise the model to remove the singularity.
Specify !AISING qualifier to force the job to continue.
Warning: 1 singularities in AI matrix.

Source Model terms Gamma Component Comp/SE % C
Variance 12 11 1.00000 0.519324E-02 0.00 0 S
animal Ainverse 55 138560. 719.575 2.31 999 P
qtl h5Out/h5 6 1084.81 5.63370 0.00 -93 ?
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.

Analysis of Variance NumDF F_inc
6 mu 1 0.28
Estimate Standard Error T-value T-prev
6 mu
1 -8.99381 17.1176 -0.53
5 qtl 6 effects fitted
1 animal 55 effects fitted ( 3 are zero)
Finished: 08 Dec 2006 13:37:03.773 Singularity in Average Information
Matrix

--
Best Regards
Mohsen Jafarikia
PhD Candidate
Centre for the Genetic Improvement of Livestock
Department of Animal and Poultry Science
University of Guelph
Phone: (519) 824-4120 ext.58353