Bending

# Bending

```Dear Arthur,

I'm trying to fit a multivariate model (3-variate) but I get some
problems (the problem appears when I add the third variable). The fact
is that in some iterations ASREML modifies the variance components with
Bending and finally the LogL gets into a cycle. I tried the model with
and without scaling the variables. I want you to know that the third
variable is a function of the other two variables.

Is there any way to solve this problem ?
I tried scaling the variables, reducing the stepsize, changing initial
values, increasing the number of iterations, etc.

Regards,
Hermann

PS: Here is a part of the asr file:

ASREML [16 Feb 2000]
09 Jul 2000 17:41:58.890 128.00 Mbyte  MSWIN
C:\ASREML-Win\PC-CR\Transf\h1d1v1
***************************************************
* ASREML 2000  Residuals now written to .yht file *
********************************************* ARG *
skipping  1  lines
PEDIGREE [C:\asreml-win\pc-cr\transf\pedigree.txt ] has     4364
identities,    8684 Non zero elements
QUALIFIERS: !skip 1 !maxit 20
skipping  1  lines
Multivariate analysis of h1             dap1           vol1
Using     1876 records [of    1876 read from    1876 lines of
C:\asreml-win\pc-cr\]
1876  identity
3  US=UnStr    4.33    4.31    7.14    0.12    0.18    0.01
5628 records assumed sorted    3 within 1876
3  US=UnStr    0.80    1.16    2.62    0.03    0.06    0.00
4364  Ainverse
Structure of Tr.arbol     has   13092 levels defined
3  US=UnStr    0.86    0.51    0.69    0.02    0.02    0.00
396  identity
Structure of Tr.numblo.fa has    1188 levels defined
Forming  14490  equations:  210  dense
Initial updates will be shrunk by factor    0.000
NOTICE:    48 (more) singularities,
LogL= 731.810     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5055     0.6946
0.1678E-01
0.1684E-01 0.4562E-03
LogL= 731.810     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5055     0.6946
0.1678E-01
0.1684E-01 0.4561E-03
LogL= 731.811     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5055     0.6946
0.1678E-01
0.1684E-01 0.4561E-03
LogL= 731.824     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5055     0.6946
0.1678E-01
0.1684E-01 0.4561E-03
LogL= 731.942     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5062     0.6946
0.1680E-01
0.1686E-01 0.4561E-03
LogL= 732.220     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5088E-02 0.7989      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8600     0.5082     0.6944
0.1687E-01
0.1693E-01 0.4558E-03
WARNING: Variance parameters were modified by BENDing
to make the matrix Positive Definite
LogL= 731.634     S2=  1.0000       5466 df1   1.000      4.333
4.310
7.135     0.1201     0.1836     0.5088E-02 0.7989      1.160
2.623
0.3157E-01 0.6459E-01 0.1623E-02 0.8601     0.5047     0.6946
0.1674E-01
0.1679E-01 0.4551E-03
WARNING: Variance parameters were modified by BENDing
to make the matrix Positive Definite
LogL= 731.661     S2=  1.0000       5466 df1   1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8602     0.5047     0.6948
0.1676E-01
0.1682E-01 0.4563E-03
LogL= 731.809     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5055     0.6947
0.1678E-01
0.1684E-01 0.4562E-03
LogL= 731.930     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5062     0.6946
0.1680E-01
0.1686E-01 0.4561E-03
LogL= 732.214     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7989      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8600     0.5081     0.6944
0.1687E-01
0.1692E-01 0.4558E-03
WARNING: Variance parameters were modified by BENDing
to make the matrix Positive Definite
LogL= 731.634     S2=  1.0000       5466 df1   1.000      4.333
4.310
7.135     0.1201     0.1836     0.5088E-02 0.7989      1.160
2.623
0.3157E-01 0.6459E-01 0.1623E-02 0.8601     0.5047     0.6946
0.1674E-01
0.1679E-01 0.4551E-03
WARNING: Variance parameters were modified by BENDing
to make the matrix Positive Definite
LogL= 731.661     S2=  1.0000       5466 df1   1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8602     0.5047     0.6948
0.1676E-01
0.1682E-01 0.4563E-03
LogL= 731.809     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5055     0.6947
0.1678E-01
0.1684E-01 0.4562E-03
LogL= 731.930     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8601     0.5062     0.6946
0.1680E-01
0.1686E-01 0.4561E-03
LogL= 732.214     S2=  1.0000       5466 df    1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7989      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8600     0.5082     0.6944
0.1687E-01
0.1692E-01 0.4558E-03
WARNING: Variance parameters were modified by BENDing
to make the matrix Positive Definite
LogL= 731.634     S2=  1.0000       5466 df1   1.000      4.333
4.310
7.135     0.1201     0.1836     0.5088E-02 0.7989      1.160
2.623
0.3157E-01 0.6459E-01 0.1623E-02 0.8601     0.5047     0.6946
0.1674E-01
0.1679E-01 0.4551E-03
WARNING: Variance parameters were modified by BENDing
to make the matrix Positive Definite
LogL= 731.661     S2=  1.0000       5466 df1   1.000      4.333
4.311
7.136     0.1201     0.1836     0.5087E-02 0.7988      1.159
2.623
0.3156E-01 0.6459E-01 0.1623E-02 0.8602     0.5047     0.6948
0.1676E-01
0.1682E-01 0.4563E-03
WARNING:   6 variance structures were modified to make them positive
definate
ASREML may have fixed the  structure [flagged by B]
and may not have converged to  a maximum likelihood solution.

Suggestion: rerun with  -C option

Source                Model  terms     Gamma     Component    Comp/SE
% C
Residual            US=UnStr     1   4.33289       4.33289      10.91
0 P
Residual            US=UnStr     1   4.31084       4.31084      10.82
0 P
Residual            US=UnStr     2   7.13577       7.13577      12.56
0 P
Residual            US=UnStr     1  0.120085      0.120085      10.93
0 P
Residual            US=UnStr     2  0.183623      0.183623      13.03
0 P
Residual            US=UnStr     3  0.508747E-02  0.508747E-02  13.57
0 P
Tr.arbol            US=UnStr     1  0.798888      0.798888       1.86
0 P
Tr.arbol            US=UnStr     1   1.15950       1.15950       2.77
0 P
Tr.arbol            US=UnStr     2   2.62286       2.62286       4.35
0 P
Tr.arbol            US=UnStr     1  0.315615E-01  0.315615E-01   2.73
0 P
Tr.arbol            US=UnStr     2  0.645900E-01  0.645900E-01   4.41
0 P
Tr.arbol            US=UnStr     3  0.162326E-02  0.162326E-02   4.25
0 P
Tr.numblo.fami      US=UnStr     1  0.860010      0.860010       3.83
0 P
Tr.numblo.fami      US=UnStr     1  0.508151      0.508151       2.22
0 P
Tr.numblo.fami      US=UnStr     2  0.694436      0.694436       2.22
0 P
Tr.numblo.fami      US=UnStr     1  0.168665E-01  0.168665E-01   2.69
0 P
Tr.numblo.fami      US=UnStr     2  0.169248E-01  0.169248E-01   2.11
0 P
Tr.numblo.fami      US=UnStr     3  0.455803E-03  0.455803E-03   2.11
0 P
Covariance/Variance/Correlation Matrix US=UnStructu
4.333     0.7753     0.8088
4.311      7.136     0.9637
0.1201     0.1836     0.5087E-02
Covariance/Variance/Correlation Matrix US=UnStructu
0.7989     0.8010     0.8764
1.160      2.623     0.9899
0.3156E-01 0.6459E-01 0.1623E-02
Covariance/Variance/Correlation Matrix US=UnStructu
0.8600     0.6575     0.8519
0.5082     0.6944     0.9513
0.1687E-01 0.1692E-01 0.4558E-03

SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section   1
0.45   0.46   0.85
14  possible outliers: see .res file
Finished: 09 Jul 2000 17:45:06.690    WARNING: LogL not converged

--
Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml
```

• Follow-Ups: