# singularities appeared in AI matrix

From: inekelavrijsen <asremlforum_at_VSNI.CO.UK>
Date: Thu, 10 Sep 2009 11:43:04 +0100

Dear forum-users,

I'm new to the ASReml program and working with a file on osteoarthrosis, scored at different locations accoring a 4 level scale representing increasing diameter of the osteophytes. When doing a simple univariate analysis location A runs fine both left and right, but when running location B the right side gives "singularities appeared in AI matrix" error, while the left side does converge. I can't really make the model any simpler (leaving the SEX effect out doesn't solve the problem). Can anyone explain what is going on?

Any input will be more than welcome,

Ineke

PS I'm planning to do a multivariate analysis to show that the genetic corr. between left and right is ~1, so we are allowed to do a repeated measurements analysis. Beter ideas?
======================================================
Heritability factor of ED in Labrador Retrievers
NHSB !P
SEX !A 2
DOByear !I !SORT
DOBmonth 12
DOBday 31
BREED !A 1
LA !M0
LB !M0
RA !M0
RB !M0
EDlab_forum.csv !SKIP 1 !Fcon !MAXIT 30 !EXTRA 10 !SUM
RB ~ mu SEX !r NHSB
0 0 1
NHSB 1
NHSB 0 AINV 0.01 !GP
======================================================
NHSB !P
SEX !A 2
DOByear !I !SORT
BREED !A 1
LA !M0
LB !M0
RA !M0
RB !M0
PEDIGREE [PedigreeLabradorTweeked.csv.SRT ] has 7283 identities, 23737 Non zero elements
QUALIFIERS: !SKIP 1 !FCON !MAXIT 30 !EXTRA 10 !SUM
Reading EDlab_forum.csv FREE FORMAT skipping 1 lines

Univariate analysis of RB
Using 2760 records of 2760 read

Model term Size #miss #zero MinNon0 Mean MaxNon0
1 NHSB !P 7283 0 0 878.0 5576. 7283.
2 SEX 2 0 0 1 1.2663 2
3 DOByear 14 0 0 1 9.8377 14
4 DOBmonth 12 0 0 1 6.5297 12
5 DOBday 31 0 0 1 16.0043 31
Warning: Fewer levels found in BREED than specified
6 BREED 2 0 0 1 1.0000 1
7 LA 0 0 1.000 1.037 4.000
8 LB 0 0 1.000 1.050 4.000
9 RA 0 0 1.000 1.034 4.000
10 RB Variate 0 0 1.000 1.045 4.000
11 mu 1
7283 Ainverse 0.0100
Structure for NHSB has 7283 levels defined
Forming 7286 equations: 3 dense.
Initial updates will be shrunk by factor 0.183
Notice: Algebraic ANOVA Denominator DF calculation is not available
Numerical derivatives will be used.
Notice: 1 singularities detected in design matrix.
1 LogL= 2061.13 S2= 0.81301E-01 2758 df 1.000 0.1000E-01
2 LogL= 2064.31 S2= 0.80027E-01 2758 df 1.000 0.2428E-01
3 LogL= 2070.91 S2= 0.76832E-01 2758 df 1.000 0.6490E-01
4 LogL= 2079.38 S2= 0.71394E-01 2758 df 1.000 0.1497
5 LogL= 2088.68 S2= 0.62931E-01 2758 df 1.000 0.3264
6 LogL= 2095.24 S2= 0.54610E-01 2758 df 1.000 0.5703
7 LogL= 2100.10 S2= 0.46819E-01 2758 df 1.000 0.8924
8 LogL= 2104.06 S2= 0.39534E-01 2758 df 1.000 1.323
9 LogL= 2107.73 S2= 0.32552E-01 2758 df 1.000 1.931
10 LogL= 2111.79 S2= 0.25571E-01 2758 df 1.000 2.890
11 LogL= 2117.45 S2= 0.18225E-01 2758 df 1.000 4.722
12 LogL= 2128.45 S2= 0.10278E-01 2758 df 1.000 9.721
13 LogL= 2160.66 S2= 0.29056E-02 2758 df : 1 components constrained
14 LogL= 2247.12 S2= 0.19225E-03 2758 df : 1 components constrained
15 LogL= 2339.19 S2= 0.12195E-04 2758 df : 1 components constrained
16 LogL= 2431.65 S2= 0.77144E-06 2758 df 1.000 0.1545E+06
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.

Approximate stratum variance decomposition
Stratum Degrees-Freedom Variance Component Coefficients

Source Model terms Gamma Component Comp/SE % C
Variance 2760 2758 1.00000 0.771441E-06 37.13 0 P
NHSB Ainverse 7283 154470. 0.119165 0.00 0 S
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 DenDF_con F_inc F_con M P_con
11 mu 1 2758.0 2786.35 2786.35 . <.001
2 SEX 1 2758.0 3.90 3.90 A 0.049
Notice: The DenDF values are calculated ignoring fixed/boundary/singular
variance parameters using numerical derivatives.

Estimate Standard Error T-value T-prev
2 SEX
M 0.224031E-01 0.113479E-01 1.97
11 mu
1 1.06002 0.206761E-01 51.27
1 NHSB 7283 effects fitted ( 54 are zero)
SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section 1
4.05
140 possible outliers: see .res file
Finished: 10 Sep 2009 12:13:23.834 Singularity in Average Information Matrix

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