+--------------------------------------------------------------------+
 |                                                                    |
 |                        VARIANCE-COVARIANCE                         |
 |                                                                    |
 +--------------------------------------------------------------------+

 MEANING: Variance-covariance matrix
 CONTEXT: NONMEM output

 DISCUSSION:
 NONMEM output refers to "VARIANCE-COVARIANCE" (or "COVARIANCE") matri-
 ces in three contexts:

 OMEGA and SIGMA
      OMEGA is the variance-covariance matrix for the first level  ran-
      dom effects ETA.  SIGMA is the variance-covariance matrix for the
      second-level random effects EPSILON.

      Error  messages  referring  to  "VARIANCE-COVARIANCE  COMPONENTS"
      arise  from  difficulties  with  the  initial  estimates of OMEGA
      and/or SIGMA, either those supplied by the user, or when no esti-
      mates are supplied, with those obtained in NONMEM's Initial Esti-
      mates Step.  Initial estimates of both OMEGA and  SIGMA  must  be
      positive definite.

      With NONMEM 7.3 and higher, if the initial estimate of a block is |
      not positive definite because of rounding errors, a value will be |
      added  to  the  diagonal elements to make it positive definite. A |
      message in the NONMEM report file will  indicate  that  this  was |
      done.  E.g.,                                                      |
      DIAGONAL SHIFT OF  1.1000E-03 WAS IMPOSED TO ENSURE POSITIVE DEF- |
      INITENESS

 VAR-COV
      Error messages referring to "VAR-COV" (in particular,  "ESTIMATED
      TO  BE SINGULAR" or "ESTIMATED TO BE 0") arise when the variance-
      covariance matrix for an individual's data is non-positive  defi-
      nite.  For example, with the error model
      Y=F+F*EPS(1)
      predicted  values for some observations (i.e. values of F) may be
      zero or close to 0.  Then variances for these observations (which
      are  proportional  to F**2) are also zero, and this gives rise to
      such an error message.

 COVARIANCE MATRIX OF ESTIMATE
      This variance-covariance matrix refers  to  an  estimate  of  the
      variability  and covariability of the parameter estimates.  It is
      computed in the Covariance Step, from the R and S  matrices.   An
      error message from the Covariance Step, stating that one of these
      two matrices is non-positive definite, indicates that  the  mini-
      mization  procedure  did  not  find  a  true  or  unique  minimum
      (See covariance).

REFERENCES: Guide I Section C.3.5.2
REFERENCES: Guide IV Section III.B.10, III.B.11
REFERENCES: Guide V Section 5.4, 13.4.3


  
Go to main index.
  

    Created by nmhelp2html v. 1.0 written by Niclas Jonsson (Modified by AJB 5/2006,11/2007,10/2012)