This is another block entry. The block begins with a line containing the code MODEL (can be abbreviated to MOD), and finishes with a line beginning with END. The block then should contain one line for each effect to be fitted and one line for each trait in the analysis.

Each of the ‘effect’ lines comprises the following

- (a)
- a three-letter code for the type of effect,
- (b)
- the effect name, where the effect name is a combination of the variable
name for a column in the data file and, if appropriate, some additional
information.

No abbreviations for variable names are permitted, i.e. there must be an exact match with the names specified in the DATA block. - (c)
- If the effect is to be fitted for a subset of traits only, the running numbers of these traits must be given (space separated).

Fixed effects can be cross-classified or nested fixed effects or covariables. The
following codes are recognised :
**
FIX **This specifies a fixed effect in the model of analysis.

NB The name for a fixed effect should not contain a “(”, otherwise it is assumed that this effect is a covariable.

A simple, one-way interaction of two variables can be specified as vn1*vn2, with vn1 and vn2 valid variables names. [Not yet implemented !]

HINT: ‘Not implemented’ here means merely that WOMBAT will not code the interaction for you – you can, of course, still fit a model with an interaction effect, but you a) have to insert an additional column in the data file with the code for the appropriate subclass, b) fit this as if it were a crossclassified fixed effect, and c) specify any additional dependencies arising explicitly (using ZEROUT, see below).

Valid codes for basis functions are
**
POL **for ordinary polynomials.

This is the default and can be omitted, i.e “vn()” is equivalent to
“vn(,POL)”. For instance, denotes a quadratic regression. Note
that WOMBAT deviates both records and covariables from their
respective means prior to analysis.

N.B.: This yields a regression equation of the form

rather than an equation of form

This should be born in mind when interpreting any solutions for regression coefficients for POL covariables from WOMBAT - while there is a straightforward relationship between coefficients and , they are not interchangeable.

For example, denotes a cubic polynomial, i.e. comprises a linear,
quadratic and cubic regression coefficient, but no intercept (This differs
from the implementation for random regressions where denotes a
cubic polynomial).
**
BSP **for B-spline functions

For analyses fitting spline functions, the degree of the spline is selected
by specifying “L”, “Q” or “C” for linear, quadratic and cubic,
respectively, immediately (no space) after the code BSP. Note that
the default spline function is an equi-distant B-spline (i.e. the
range of values of the covariable is divided into intervals of equal
size), with the number of knots and intervals determined from the
number of regression coefficients and the degree of the spline
( where is the number of knots and is the degree,
for “L”, for “Q” and for “C”) [27, section
2.2]. Other spline functions are readily fitted as user-defined basis
functions.
**
USR **for user defined functions

Fitting of an intercept (in addition to deviation from means) can be enforced by preceding with a minus sign – this is not recommended unless there are no other fixed effects in the model.

A covariable to be fitted as nested within a fixed effect is specified as “vn1*vn2(,BAF)”, with vn1 the name of the fixed effect. If vn1 is not fitted as a fixed effect, it must be specified an an ‘extra’ effect (see below).

WOMBAT is fussy when it encounters a covariable which has a value of zero:
Covariables which can take such value are only permitted if a SPECIAL option
is given which confirms that these are valid codes and not ‘missing’ values; see
4.11.7.

Random effects include the ‘control variables’, i.e. random covariables for random
regression analyses. The following codes are recognised:
**
RAN **This code specifies a random effect. It should be followed (space separated) by
the name of the random effect. After the name, a three-letter code describing
the covariance structure of the effect can be given.

Valid codes for covariance structures are :
**
NRM **which denotes that the random effect is distributed proportionally to
the numerator relationship matrix.

If this code is given, a pedigree file must be supplied.
**
SEX **which denotes that the random effect is distributed proportionally to
the numerator relationship matrix for X-linked genetic effects. This
inverse of this matrix is set up directly from the pedigree information,
as described by Fernando and Grossman [11].

If this code is given, it is assumed that an autosomal genetic effects
(option NRM with corresponding pedigree file) is also fitted and has
already been specified. In addition, the pedigree file is expected to
have an additional column specifying the number of X-chromosomes
for each individual.
**
IDE **which denotes that different levels of the random effect are
uncorrelated. This is the default and can be omitted.
**
GIN **which denotes that the random effect is distributed proportionally to
an ‘arbitrary’ (relationship or correlation) matrix.

The user must supply the inverse of this matrix in the form outlined
in 6.
**
PEQ **which denotes a permanent environmental effect of the animal
for data involving ‘repeated’ records, which is not to be fitted
explicitly. Instead, an equivalent model is used, which accounts for the
respective covariances as part of the residual covariance matrix. This is
useful for the joint analysis of traits with single and repeated
records.

N.B.: Do not use this option for other effects - WOMBAT has no mechanism for checking that this option is appropriate.

For ’standard’ uni- and multivariate analyses, the random effect name is simply
the variable name as given for data file.

For random regression analyses, the variable name is augmented by information about the number of random regression coefficients for this effect and the basis functions used. It becomes “vn(,BAF)”, analogous to the specification for covariables above. As above, specifies the number of regression coefficients to be fitted. In contrast to fixed covariables, however, an intercept is always fitted. This implies that gives the order, not the degree of fit. For instance, in conjunction with a polynomial basis function specifies a quadratic polynomial with the 3 coefficients corresponding to the intercept, a linear and a quadratic term. WOMBAT allows for different control variables to be used to fit random regressions for different effect. If the model has more than one RRC statement (see below), the specification of random effects needs to be extended to tell WOMBAT which control variable to use for which effect, i.e. “vn(,BAF,rrcn)” with rrcn the name of the control variable.

Valid codes for BAF are:
**
POL **for ordinary polynomials.

This is the default and can be omitted, i.e “vn()” is equivalent to
“vn(,POL)”.
**
LEG **for Legendre polynomials.
**
BSP **for B-spline functions
**
USR **for user defined functions
**
IDE **for an identity matrix, i.e. the th basis function has a single
coefficient of “1” for the th coefficient with all other elements
zero. This requires the number of RR coefficients to be equal to the
number of levels of the control variable.

It is useful when fitting a multi-trait model as a RR model, e.g. to
allow for heterogeneous residual variances.
**
ONE **to assign a value of unity (“1”) to all coefficients.

This option has been introduced to facilitate a standard multivariate
analysis with repeated records by fitting a random regression
model to model an arbitrary pattern of temporary environmental
covariances correctly.

**
RRC **This code specifies a ‘control variable’ in a random regression analysis. It should
be followed (space separated) by the name of the variable, as given in the
DATA statement.

Optionally, immediately after the name (no spaces), the range of values of the
variable to be considered can be specified as , with the lower and
the upper limit.

N.B.: WOMBAT expects the value of the control variable to be non-negative (i.e. or greater) and not to be a fraction (the control variable is read as a real variable but converted to the nearest integer, e.g. values of 3,.0, 3.1 and 3.4 would be treated as 3) – scale your values appropriately if necessary!

N.B.: For multivariate analyses, WOMBAT collects the range of values for the control variable (i.e. minimum and maximum) across all traits. This may be undesirable if different traits have distinct ranges and Legendre polynomials are used as basis function - if so, use the USR option and set up your own file which maps the range for each trait exactly as you want it!

For animal model analyses, WOMBAT assumes that the code for the first genetic
effect fitted also identifies the subject on which measurements are taken. For some
analyses (in particular those not fitting any additive genetic effects!) and sire models
this is not appropriate, and such identifier needs to be supplied as an extra column in
the data file.
**
SUBJ **This code needs to be followed by the name of the variable which identifies
the individual.

For some models, coding is required for effects which are not explicitly fitted in the
model of analysis, for instance, when fitting nested effects. These need to be specified
as ‘extra’ effects.
**
EXT **This code, followed by the respective variable name, denotes an effect which
is not fitted in the model but which is required to define other effects.

One line should be given for each trait. It should contain the following information :

- (a)
- The code TRAIT (can be abbreviated to TR).
- (b)
- The name of the trait, as specified in the DATA block.
- (c)
- The running number of the trait.
- In most cases, this is simply the number from 1 to , where is the total number of traits in a multivariate analysis.
- In addition, WOMBAT provides the opportunity to replace the trait number
in the data file with a different number. This is useful, for instance, to carry
out an analysis involving a subset of traits without the need to edit the data
file. The syntax for this is : “k”->m. This specifies that value in the
data file should be replaced with value for the analysis. If this
is encountered, any records with trait numbers not selected in this
fashion are ignored, i.e. this provides a mechanism for automatic subset
selection.
HINT: All traits in the analysis should be specified in this manner, even if for some trait(s).

- (d)
- Optional : A numeric value (integer) representing a ‘missing’ value - any
records with the trait equal to this value are ignored in the analysis (default is
).
^{1}