VRESIDUAL directive

Defines the residual term for a REML analysis, or the residual term for an experiment within a meta-analysis (combined analysis of several experiments).


Options

EXPERIMENT = scalar
Level of the EXPERIMENTS factor for which the residual is being defined

TERM = formula
Model term to be used as the residual

FORMATION = string
Whether the structure is formed by direct product construction or by definition of the whole matrix (direct, whole); default dire

VARIANCE = scalar
Allows an initial estimate to be provided for the residual variance of the experiment

CONSTRAINT = string
Allows the residual variance to be fixed at its initial value (fix, positive) default posi

COORDINATES = matrix or variates
Coordinates of the data points to be used in calculating distance-based models


Parameters

MODEL = strings
Type of covariance model associated with the residual term, or with individual factors in the term if FORMATION=direct (identity, fixed, AR, MA, ARMA, power, banded, correlation, antedependence, unstructured, diagonal, uniform, FA, FAequal) default iden

ORDER = scalar
Order of model

HETEROGENEITY = string
Heterogeneity for correlation matrices (none, outside); default none

METRIC = string
How to calculate distances when MODEL=power (cityblock, squared, euclidean); default city

FACTOR = factors
Factors over which to form direct products

MATRIX = identifiers
To define matrix values for the term or the factors when MODEL=fixed

INVERSE = identifiers
To define values for matrix inverses (instead of the fixed matrices themselves) when MODEL=fixed

INITIAL = identifiers
Initial parameter values for each correlation matrix

CONSTRAINTS = texts
Texts containing strings none, fix or positive to define constraints for the parameters in each model

EQUALITYCONSTRAINTS = variates
Non-zero values in the variate indicate groups of parameters whose values are to be constrained to be equal


Description

VRESIDUAL is used to define the residual term for a REML analysis or to define separate residual terms for different experiments within a multi-experiment (or meta-) analysis. The TERM option is used to specify the formula for the residual term. This term need not have been specified previously by the VCOMPONENTS statement.

   For a single experiment, VRESIDUAL can be used to impose a covariance structure on the residual term. This could also be done by specifying the covariance structure using VSTRUCTURE, but VRESIDUAL has the advantage that the algorithm then checks that the correct residual term is used.

   In a multi-site experiment, VRESIDUAL can be used to specify a different residual model for each separate experiment. The EXPERIMENT option is used to define the experiment(s) for which the model is to be used.

   The VARIANCE option is used to give an initial value for the residual variance in the current experiment(s). You can set option CONSTRAINT=fix to fix the residual variance at the initial value rather than estimating it (as a positive value).

   The definition of the residual terms then follows as for the definition of correlated error terms through VSTRUCTURE.

   For a multi-experiment analysis, the factors and variates for the separate experiments should be concatenated into structures which run over all the experiments. For example, consider an experiment set up at two sites to compare a set of 24 varieties in four replicates. In one site the experiment was laid out as a grid of eight rows by 12 columns, in the other a grid of 16 rows by six columns was used. In these circumstances, a single set of factors (of length 192) can be used to specify the design, using factors to describe variety, rows and columns, plus a factor expt defining the allocation of units to experiments.

VCOMPONENTS [FIXED=Variety; EXPERIMENTS=Expt]

VRESIDUAL [EXPERIMENT=1; TERM=Row.Col] MODEL=AR,AR; \

  ORDER=1,1; FACTOR=Row,Col

VRESIDUAL [EXPERIMENT=2; TERM=Row.Col] MODEL=AR,AR; \

  ORDER=1,1; FACTOR=Row,Col

Where some factors differ between experiments, these should be defined on the units relevant to the appropriate experiment(s) and missing elsewhere. When an EXPERIMENTS factor has been defined, the default action of the MVINCLUDE option of REML is changed to include units with missing y-values and missing factor levels.

 

Options: EXPERIMENT, TERM, FORMATION, VARIANCE, CONSTRAINT, COORDINATES

Parameters: MODEL, ORDER, HETEROGENEITY, METRIC, FACTOR, MATRIX, INVERSE, INITIAL, CONSTRAINTS, EQUALITYCONSTRAINTS.