4.9 Covariance components
Next, the parameter file needs to specify values for all (co)variance components in the
model of analysis. For variance component estimation, these are the starting values
used. For simple BLUP analyses and simulation runs, these are the values assumed to
be the population values.
The input matrices for full rank analyses must be positive definite, i.e. cannot have
eigenvalues less than the operational zero. For reduced rank (PC) analyses, some
‘zero’ but no negative eigenvalues are acceptable, provided the rank (i.e. the number
of non-zero eigenvalues) is equal to (or greater than) the number of principal
components to be fitted.
4.9.1 Residual covariances
126.96.36.199 ‘Standard’ multivariate analyses
The residual covariance matrix is specified by
- A line beginning with the code RESIDUAL (can be abbreviated to RES)
or ERROR (can be abbreviated to ERR). This is followed by the dimension
of the covariance matrix, (integer number, space separated). If an
analysis type PC has been specified, a second number specifying the rank
of the estimated covariance matrix, needs to be given (even if this is equal
Optionally, this can be followed (space separated) by a qualifier:
DIAG specifies that the residual covariance matrix is diagonal
NOSTART (can be abbreviated to NOS) specifies that no starting values are
given; this is only valid in conjunction with the run option --pool !
- Without qualifier: The elements of the upper triangle of the
residual covariance matrix, given row-wise (i.e. , , , , ,
, , ).
These can be given several elements per line (space separated, taking care not
to exceed the total line length of 78 characters), or one per line, or a mixture –
WOMBAT will attempt to read until it has acquired all elements
With qualifier: If DIAG is specified only the diagonal elements (, …, )
are read, and if NOSTART is given, no values are read.
188.8.131.52 Random regression analyses
Again, the residual covariance matrix is specified by
- A line beginning with the code RESIDUAL (can be abbreviated to RES) or ERROR
(can be abbreviated to ERR). This should be followed by the dimension
() of each residual covariance matrix (integer number), usually
equal to the number of traits, and a code indicating what kind of error
covariance function is to be fitted. The following codes are recognised
HOM This code specifies homogeneous error covariances for all values of
the control variable.
HET This code specifies heterogeneous error covariances, with the
covariance function a step function of the control variable. It should
be followed (space separated) by an integer number giving the
number of steps.
- If the model involves multiple control variables, the name of the variable to be
used to determine the temporary environmental covariance structure needs to
be given at the end of the line.
- One or more lines with the residual covariance matrices, consisting of the
elements of the upper triangle given row-wise, and, if applicable,
- For HOM only a single covariance matrix needs to be given.
- For HET the number of covariance matrices specified must be equal to
the number of steps (in the step function, i.e. intervals). Each should
begin on a new line and be preceded by two integer values (space
separated) which give the upper and lower limits (inclusive) of the
interval of the control variable, for which this matrix is applicable.
N.B.: ‘Step intervals’ must cover the complete range of
values for the control variable encountered in the data.
EXAMPLE: For a univariate RR analysis with values of the
control variable ranging from 1 to 5, say we want to fit
separate residual variances for 1 & 2, 3 & 4 and 5:
VAR residual 1 HET 3 1 2 1.234 3 4 3.456 5 5 5.678
4.9.2 Covariances for random effects
Similarly, for each covariance matrix due to random effects to be estimated, a
‘header’ line and the elements of the covariance matrix need to be specified.
- A line beginning with the code VARIANCE (can be abbreviated to VAR),
followed by the name of the random effect and the dimension of the
covariance matrix, (integer number, space separated). If an analysis
type PC has been specified, a second number specifying the rank of the
estimated covariance matrix, needs to be given (even if this is equal to
The name can simply the random effects name as specified for the model
of analysis. Alternatively, it can be of the form “vn1+vn2” where vn1 and
vn2 are names of random effects specified in the MODEL block. This denotes
that the two random effects are assumed to be correlated and that their
joint covariance matrix is to be estimated.
Again, a qualifier DIAG or NOSTART, as described above for the residual
covariance matrix (see 184.108.40.206) is recognized.
- The elements of the upper triangle of the covariance matrix,
given row-wise (i.e. , , , , , , , ).
Again, these can be given several elements per line (space separated, taking
care not to exceed the total line length of 78 characters), or one per line,
or a mixture – WOMBAT will attempt to read until it has acquired all
As above, if DIAG is specified, only the variances are read and with
NOSTART no values are acquired.