From: <brian.cullis_at_INDUSTRY.NSW.GOV.AU>

Date: Fri, 11 Sep 2009 16:18:16 +1000

Date: Fri, 11 Sep 2009 16:18:16 +1000

Dear Ineke

I shall give you a hasty reply to ensure that you have an answer today and

will try to explain more in a later email

This problem is due to the residual variance updates going negative.

ASReml does not allow this but you will notice that the gamma for additive

variance is getting larger and larger with each successive iteration. The

update for the residual variance would then result in a negative estimate

- which is not allowed.

The reason for this has been explained before in several emails. I would

have to check whether there are threads on the forum for this topic. In

short the use of the pedigree matrix (or so-called animal model) has an

in built polygenic (dominance, epistatic, etc etc)- or residual built into

it and this is confounded in these data with the non-polygenic residual

variation which is non -genetic

You can avoid this empirically by fitting the so-called sire model.

Without more information on the data and application and pedigree I would

not like to make any further recommendations. Solutins to these problems

are difficult to diagnose via emails and forums

I hope this brief email reply helps. Arthur may like to add more detail if

he has time later today

warm regards

Brian Cullis|Research Leader, Biometrics &

Senior Principal Research Scientist |

Industry & Investment NSW | Wagga Wagga Agricultural Institute | Pine

Gully Road | Wagga Wagga NSW 2650 |

PMB | Wagga Wagga NSW 2650

T: 02 6938 1855 | F: 02 6938 1809 | E: brian.cullis_at_industry.nsw.gov,au

W: www.industry.nsw.gov.au |

Visiting Professorial Fellow

School of Mathematics and Applied Statistics

Faculty of Informatics

University of Wollongong

Professor,

Faculty of Agriculture, Food & Natural Resources

The University of Sydney

Adjunct Professor

School of Computing and Mathematics

Charles Sturt University

inekelavrijsen <asremlforum_at_VSNI.CO.UK>

Sent by: ASReml users discussion group <ASREML-L_at_DPI.NSW.GOV.AU>

10/09/2009 08:43 PM

Please respond to

ASREML-L_at_dpi.nsw.gov.au

To

ASREML-L_at_DPI.NSW.GOV.AU

cc

Subject

singularities appeared in AI matrix

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

PedigreeLabradorTweeked.csv.SRT !ALPHA !SKIP 1

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

A-inverse retrieved from ainverse.bin

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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Received on Sat Sep 11 2009 - 16:18:16 EST

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