VUVCOVARIANCE procedure

Forms the unit-by-unit variance-covariance matrix for specified variance components in a REML model (R.W. Payne).

Options

FIXED = formula	Fixed model terms; default *
CONSTANT = string token	How to treat the constant term (estimate, omit); default esti
FACTORIAL = scalar	Limit on the number of factors or covariates in each fixed term; default 3
SEED = scalar	Seed for the random numbers used to generate a dummy y-variate; default 12345

Parameters

RANDOM = formula structures	Random model terms
COMPONENTS = variates	Values for the variance components and residual variance
UVCOVARIANCE = symmetric matrices	Saves the unit-by-unit variance-covariance matrices

Description

Procedure VBOOTSTRAP assesses the significance of for fixed terms in a REML analysis, by using a parametric bootstrap. The bootstrap samples are generated from a multivariate Normal distribution with dimension equal to the number of units in the analysis, and this requires a unit-by-unit variance-covariance matrix.

If you want to take the variance-covariance matrix from a previous analysis, this can be done by using the UVCOVARIANCE option of VKEEP. VUVCOVARIANCE provides a solution for the situation where there is no suitable previous analysis, but you can make reasonable assumptions about the likely sizes of the variance components. Note, however, that it cannot handle covariance models.

The RANDOM parameter specifies a formula structure, defining the random model. This may also contain the residual term, but that is not essential. If it is not present, the residual is added as the final model term. The COMPONENTS parameter specifies the variance components for the random terms, including the residual variance (at the end, if VUVCOVARIANCE needs to add this to the RANDOM formula). The UVCOVARIANCE parameter saves the unit-by-unit variance-covariance matrix.

The FIXED, CONSTANT and FACTORIAL options define the fixed model in the usual way. (See VCOMPONENTS.) The SEED option provides a seed for random numbers (default 12345). These are used to generate a dummy y-variate, that is used in a REML analysis inside the procedure to calculate UVCOVARIANCE.

Options: FIXED, CONSTANT, FACTORIAL, SEED.

Parameters: RANDOM, COMPONENTS, UVCOVARIANCE.

Method

UVCOVARIANCE obtains the unit-by-unit variance-covariance matrix by using the COMPONENTS as initial values for the random terms in VCOMPONENTS, and performing a REML analysis with the number of iterations set to zero. The y-variate for the analysis contains Normally distributed random numbers, generated with the specified SEED.

See also

Directive: REML, VCOMPONENTS.

Procedure: VBOOTSTRAP.

Commands for: REML analysis of linear mixed models.

Example

CAPTION       'VUVCOVARIANCE example',!t('Split plot design, see the',\
              'Guide to Genstat, Part 2, Section 4.2.1.'); STYLE=meta,plain
SPLOAD        [PRINT=*] '%gendir%/data/Oats.gsh'
" Form unit-by-unit variance-covariance matrix, assuming variance
  components of 200 for blocks and 100 for whole-plots within blocks,
  and a residual variance of 150."
VUVCOVARIANCE [FIXED=variety*nitrogen] !f(blocks/wplots/subplots);\
              COMPONENTS=!(200,100,150); UVCOVARIANCE=uvcov
PRINT         [RLWIDTH=5] uvcov; FIELD=9