[R-sig-Debian] Function nlme::lme in Ubuntu (but not Win or OS X): "Non-positive definite approximate variance-covariance"

[Dirk Eddelbuettel]

On 7 June 2013 at 11:01, Giuseppe Pagnoni wrote:
| Dear all,
| 
| I am estimating a mixed-model in Ubuntu Raring (13.04¸ amd64), with the
| code:
| 
| fm0 <- lme(rt ~ run + group * stim * cond,
|                  random=list(
|                    subj=pdSymm(~ 1 + run),
|                    subj=pdSymm(~ 0 + stim)),
|                  data=mydat1)
| 
| When I check the approximate variance-covariance matrix, I get:
| 
| > fm0$apVar
| [1] "Non-positive definite approximate variance-covariance"

This comes from the BLAS / LAPACK libraries which you can switch in Debian /
Ubuntu.  Eg I (currently) have both defaults and openblas installed:

edd at max:~$ COLUMNS=72 dpkg -l | grep -i "blas\|lapack"
ii  libblas-dev    1.2.20110419 amd64        Basic Linear Algebra Subroutines 
ii  libblas-test   1.2.20110419 amd64        Basic Linear Algebra Subroutines 
ii  libblas3       1.2.20110419 amd64        Basic Linear Algebra Reference im
ii  libblas3gf     1.2.20110419 all          Transitional package for libblas
ii  liblapack-dev  3.4.2-1~exp3 amd64        Library of linear algebra routine
ii  liblapack-pic  3.4.2-1~exp3 amd64        Library of linear algebra routine
ii  liblapack3     3.4.2-1~exp3 amd64        Library of linear algebra routine
ii  liblapack3gf   3.4.2-1~exp3 all          Transitional package for liblapac
ii  libopenblas-ba 0.2.6-1~exp1 amd64        Optimized BLAS (linear algebra) l
ii  libopenblas-de 0.2.6-1~exp1 amd64        Optimized BLAS (linear algebra) l
edd at max:~$ 

The virtual package libblas is provided by the reference blas, atlas
("tuned") and openblas (multicore); similar for lapack.

edd at max:~$ apt-cache search libblas
libblas-dev - Basic Linear Algebra Subroutines 3, static library
libblas-doc - Basic Linear Algebra Subroutines 3, documentation
libblas3 - Basic Linear Algebra Reference implementations, shared library
libatlas-base-dev - Automatically Tuned Linear Algebra Software, generic static
libatlas3-base - Automatically Tuned Linear Algebra Software, generic shared
libblas-test - Basic Linear Algebra Subroutines 3, testing programs
libblas3gf - Transitional package for libblas
libopenblas-base - Optimized BLAS (linear algebra) library based on GotoBLAS2
libopenblas-dev - Optimized BLAS (linear algebra) library based on GotoBLAS2
edd at max:~$ 

Try installing another package and see if that matters.  

The Windows and OS X versions of R will have used its internally packaged
(not tuned, not multicore) BLAS/LAPACK. This can be changed there too; see
the R Admin+Inst manual.

Dirk
 
| *However*, if I do the same on a Windows or a Mac OS X machine, I get:
| 
| > fm0$apVar
|                reStruct.subj1 reStruct.subj2 reStruct.subj3 reStruct.subj1
| reStruct.subj1   1.952757e-01   3.130089e-01   5.766955e-01  -0.1034862377
| reStruct.subj2   3.130089e-01   5.703211e-01   9.864047e-01  -0.1937902915
| reStruct.subj3   5.766955e-01   9.864047e-01   1.861434e+00  -0.3303689957
| reStruct.subj1  -1.034862e-01  -1.937903e-01  -3.303690e-01   0.0941652375
| reStruct.subj2  -3.464557e-03  -5.933008e-03  -1.102904e-02   0.0163847582
| reStruct.subj3  -6.826057e-01  -1.186231e+00  -2.122872e+00   0.3705613715
| lSigma          -2.058254e-06  -4.764783e-06   1.653583e-05  -0.0000146693
|                reStruct.subj2 reStruct.subj3        lSigma
| reStruct.subj1  -3.464557e-03  -6.826057e-01 -2.058254e-06
| reStruct.subj2  -5.933008e-03  -1.186231e+00 -4.764783e-06
| reStruct.subj3  -1.102904e-02  -2.122872e+00  1.653583e-05
| reStruct.subj1   1.638476e-02   3.705614e-01 -1.466930e-05
| reStruct.subj2   1.931738e-02  -2.020354e-02 -1.925015e-05
| reStruct.subj3  -2.020354e-02   2.825301e+00  2.967063e-05
| lSigma          -1.925015e-05   2.967063e-05  6.299813e-05
| attr(,"Pars")
| reStruct.subj1 reStruct.subj2 reStruct.subj3 reStruct.subj1 reStruct.subj2
|       4.570267       4.299735       1.282732       4.859346       3.206102
| reStruct.subj3         lSigma
|      -2.631377       5.308304
| attr(,"natural")
| [1] TRUE
| 
| 
| I am unable to figure out the reason why I get such a difference in the
| output: all the machines are running the latest version of R (3.0.1) and
| nlme package (3.1-109) as of today (updated from the CRAN master site).
| 
| Many thanks in advance for any suggestions,
| 
| best
| 
| -- 
| Giuseppe Pagnoni
| Dip. Scienze Biomediche, Metaboliche e Neuroscienze
| Sezione Fisiologia e Neuroscienze
| Univ. di Modena e Reggio Emilia
| Via Campi 287
| I-41125 Modena, Italy
| Tel: +39-059-205-5742
| Fax: +39-059-205-5363
| 
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-- 
Dirk Eddelbuettel | edd at debian.org | http://dirk.eddelbuettel.com