VBOOTSTRAP procedure

Performs a parametric bootstrap of the fixed effects in a REML analysis (C.J. Brien).

Options

PRINT = string tokens	Controls printed output (observedteststatistics, pvalues, vdiagnostics, nnotconverged, monitoring, all); default obse, pval
VPRINT = string tokens	Controls the output from the REML analysis of each sample (model, components, effects, means, stratumvariances, monitoring, vcovariance, deviance, Waldtests, missingvalues, covariancemodels); default * i.e. none
PLOT = string	What to plot (histogram); default *
NBOOT = scalar	Number of bootstrap samples to take; default 99
NRETRIES = scalar	Maximum number of extra samples to take when some REML analyses fail to converge; default NBOOT
SEED = scalar	Seed for random number generation; default 0 continues an existing sequence or, if none, selects a seed automatically
METHOD = string token	Indicates whether to use the standard Fisher-scoring algorithm or the new AI algorithm with sparse matrix methods (Fisher, AI); default AI
MAXCYCLE = scalar	Sets a limit on the number of iterations in the REML analyses; default 30
FMETHOD = string token	Controls whether and how to calculate F statistics for fixed terms (automatic, none, algebraic, numerical); default none
WMETHOD = string token	Controls which Wald statistics are saved (add, drop); default add
WORKSPACE = scalar	Number of blocks of internal memory to be set up for use by the REML algorithm

Parameters

SAVE = REML save structures	Specifies the (REML) save structure of the original analysis; default * uses the SAVE structure from the most recent REML analysis
UMEANS = variates	Specifies the expected values for the units under the null hypothesis of no effects from the FIXEDTERMS
UVCOVARIANCE = symmetric matrices	Specifies the variances and covariances of the units under the null hypothesis of no effects from the FIXEDTERMS
FIXEDTERMS = formula	Specifies the fixed terms to test; default * tests all the fixed terms in the original analysis
FSTATISTICS = pointers	Saves a pointer with a variate for each of the FIXEDTERMS, containing the F statistics from the bootstrap samples
PVALUES = pointers	Saves a pointer with a scalar for each of the FIXEDTERMS, containing the test probability obtained from the position of its F statistic within those from the bootstrap samples
NNOTCONVERGED = scalars	Saves the number of bootstrap samples whose REML analysis failed to converge

Description

VBOOTSTRAP performs a parametric bootstrap for fixed effects in a REML analysis. The model to be fitted must be defined using the VCOMPONENTS and VSTRUCTURE directives, in the usual way. The SAVE parameter supplies the save structure from the original analysis; if this is not set, the most recent REML analysis is used.

The bootstrap samples are generated from a multivariate Normal distribution with dimension equal to the number of units in the analysis. The UMEANS parameter supplies the expected values for the distribution, Usually, this contains the fitted values under the null model for the terms being tested. If UMEANS is not set, a variate containing the grand mean of the response is used. The UVCOVARIANCE parameter supplies the variances and covariances of the units. If this is not set, the unit-by-unit variance-covariance matrix from the original analysis is used (see the UVCOVARIANCE option of VKEEP). Note: you can use the VUVCOVARIANCE procedure to form the variance-covariance matrix, if you know the variance components for a REML model that contains no covariance models.

By default all the fixed terms in the original analysis are tested simultaneously. However, you can set the FIXEDTERMS parameter to test a smaller model, and you should then also set UMEANS to specify the expected values under the null model.

The NBOOT option specifies the number of bootstrap samples to take (default 99). The NRETRIES option specifies the maximum number of extra samples to take when some REML analyses fail to converge; the default is to use the same number as specified by NBOOT. The SEED option supplies the seed for the random number generator used to make the permutations; default 0 continues from the previous generation or (if none) initializes the seed automatically. The NNOTCONVERGED parameter can save the number of samples whose analyses did not converge, in a scalar.

Printed output is controlled buy the PRINT option, with settings:

observedteststatistics	to print the values of the observed Wald or F statistics for the fixed terms in the original REML analysis,
pvalues	to print the bootstrap p-values of the observed Wald or F statistics for the fixed terms,
vdiagnostics	to print the diagnostics from the REML analyses performed on the bootstrap samples,
nnotconverged	to print the number of samples whose analyses did not converge,
monitoring	to print the progress of the bootstrapping,
all	to print all the information.

By default, the observed statistics and the p-values are printed.

The VPRINT option controls the output from the REML analyses of the bootstrap samples, with the same settings as the PRINT option of REML. By default, nothing is printed.

The bootstrap p-values are calculated by taking the proportion of F statistics in the bootstrap samples that are larger than the observed F statistic of each fixed term. The WMETHOD option controls whether these statistics are obtained from the table where terms are added sequentially (the default), or from the table where suitable terms are dropped from the full fixed model. Note that, if you use the table where terms are dropped, the only terms that can be tested are those that are not marginal to any other term in the fixed model: for example, the main effect A cannot be tested if the model contains an interaction, such as A.B.

The bootstrap F statistics can be saved, in a pointer with a variate for each of the FIXEDTERMS, using the FSTATISTICS parameter. The p-values can be saved, in a pointer with a scalar for each of the FIXEDTERMS, using the PVALUES parameter. You can obtain a plot of a histogram showing the position of the observed F statistic, compared to those from the bootstrap samples, by setting option PLOT=histogram.

The MAXCYCLE option sets a limit on the number of iterations in the REML analyses (default 30). The METHOD option controls whether REML uses the standard Fisher-scoring algorithm, or the new AI algorithm with sparse matrix methods (the default). The FMETHOD option controls whether and how to calculate F statistics for fixed terms; the default is not to calculate the statistics. (This is relevant if tests for fixed effects are being printed in the REML analyses of the bootstrap samples.) The WORKSPACE option specifies the number of blocks of internal memory to be set up for use by the REML algorithm; the default is to use the same value as in the original REML analysis.

Options: PRINT, VPRINT, PLOT, NBOOT, NRETRIES, SEED, METHOD, MAXCYCLE, FMETHOD, WMETHOD, WORKSPACE.

Parameters: SAVE, UMEANS, UVCOVARIANCE, FIXEDTERMS, FSTATISTICS, PVALUES, NNOTCONVERGED.

See also

Directives: REML, VCOMPONENTS.
Procedures: BOOTSTRAP, VCRITICAL, VFLC, VRPERMTEST. VUVCOVARIANCE.
Commands for: REML analysis of linear mixed models.

Example

CAPTION     'VBOOTSTRAP 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'
" Fit a model with no interaction, and get the fitted values."
VCOMPONENTS [FIXED=variety+nitrogen]\ 
            RANDOM=blocks/wplots/subplots
REML        yield; FITTED=fit
" Fit full model to get variances & covariances of the units."
VCOMPONENTS [FIXED=variety*nitrogen]\ 
            RANDOM=blocks/wplots/subplots
REML        [PRINT=model,comp,Wald] yield; SAVE=fullfixed
VKEEP       [UVCOVARIANCE=V]
" Parameteric bootstrap to test the interaction."
VBOOTSTRAP  [PLOT=histogram; NBOOT=999; SEED=265600] SAVE=fullfixed;\
            UMEANS=fit; UVCOVARIANCE=V; FIXEDTERMS=!f(variety.nitrogen)