Analyses an incomplete-block design by REML, allowing automatic selection of random and spatial correlation models (R.W. Payne).
Options
PRINT = string tokens |
Controls what summary output is produced about the models (deviance, aic, bic, sic, dffixed, dfrandom, change, exit, best, description); default best, desc |
|---|---|
PBEST = string tokens |
Controls the output from the REML analysis with the best model (model, components, effects, means, stratumvariances, monitoring, vcovariance, deviance, Waldtests, missingvalues, covariancemodels, aic, sic, bic); default * i.e. none |
PTRY = string tokens |
Controls the output to present from the REML analysis used to try each model (model, components, effects, means, stratumvariances, monitoring, vcovariance, deviance, Waldtests, missingvalues, covariancemodels, aic, sic, bic); default * i.e. none |
FIXED = formula |
Fixed model terms; default * i.e. none |
RANDOM = formula |
Additional random model terms; default * i.e. none |
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 |
REPLICATES = factor |
Replicate factor |
BLOCKS = factor |
Block factor; no default (must be specified) |
ROWS = factor |
Row factor for spatial analysis |
COLUMNS = factor |
Column factor for spatial analysis |
ROWCOORDINATES = variate or factor |
Row coordinates for fitting trends and spatial models if the design is irregular; if unset, these are defined from the levels of the ROWS factor |
COLCOORDINATES = variate or factor |
Column coordinates for fitting trends and spatial models if the design is irregular; if unset, these are defined from the levels of the COLUMNS factor |
PLOTFACTOR = factor |
Factor numbering the plots in the design; if unset, a local factor is defined automatically |
PTERMS = formula |
Terms (fixed or random) for which effects or means are to be printed; default * implies all the fixed terms |
PSE = string token |
Standard errors to be printed with tables of effects and means (differences, estimates, alldifferences, allestimates, none); default diff |
MVINCLUDE = string tokens |
Whether to include units with missing values in the explanatory factors and variates and/or the y-variates (explanatory, yvariate); default * i.e. omit units with missing values in either explanatory factors or variates or y-variates |
VCONSTRAINTS = string token |
Whether to constrain variance components to be positive (none, positive); default none |
RSTRATEGY = string token |
Strategy for selecting the random model (all, allfeasible, optimal, automatic, full); default allf |
METHOD = string token |
Criterion to choose the best random model (aic, sic, bic); default sic |
TRYSPATIAL = string token |
Whether to try spatial models (always, ifregular); default * i.e. no spatial models |
TRYTRENDS = string token |
Whether to see whether row and column trends are needed in the fixed model (yes, no); default no |
SPATIALFACTOR = factor |
Factor to use to define the term for a two-dimensional power-distance model; if unset, a local factor is defined automatically |
Parameters
Y = variates |
Response variates |
|---|---|
BESTMODEL = pointers |
Saves a model-definition structure for the best model for each y-variate |
EXIT = scalars |
Exit status of the best model for each y-variate |
SAVE = REML save structures |
Save structure from the analysis of the best model for each y-variate |
Description
VABLOCKDESIGN analyses data from an incomplete-block design by REML. An incomplete-block design is one where the blocks each have too few units to contain one of each of the treatments. In the context of a REML analysis, the treatment factors are usually the fixed factors. So this is to say that the blocks are unable each to contain a unit with every combination of levels of the fixed factors.
Some designs are resolvable. The blocks can then be grouped together into subsets in which each treatment is replicated once. These groupings of blocks thus form replicates, which may be useful while the experiment is taking place. For example, if several operators are needed to make observations in a field trial, it is usual to get each one to observe the plots of a complete replicate. Then any operator differences will be included in the between-replicate variation, and will not add to the variability of the treatment estimates. Of course it can be useful to include a replicate factor even if the “replicates” are not exact, e.g. if some of the treatments do not occur at every level of the replicate factor.
The RSTRATEGY option selects the strategy to use to determine the random model, with the following settings.
all |
fits the full random model (replicates and blocks within replicates if a replicate factor has been specified, or just blocks if there are no replicates). |
|---|---|
allfeasible |
tries to fit the full random model. If this is not possible, it tries models removing one, and then two random terms, until successful. |
optimal |
tries all feasible random models. |
full |
synonym of all. |
automatic |
synonym of optimal. |
The full random model should reflect the way in which the treatments were randomized onto the experiment, so it is generally best to use this. The default of RSTRATEGY=allfeasible, will do this if possible, or use a simpler random model if REML is unable to fit the full model. Note: VABLOCKDESIGN regards a model as successful, if the REML directive returns an exit status of zero (i.e. successful fitting) and there are no bound or aliased variance parameters.
The BLOCKS option must specify the block factor, and the replicate factor (if any) is specified by the REPLICATES option. If you want to fit spatial covariance models, you must specify row and column factors, using by the ROWS and COLUMNS options respectively. If the replicates are adjacent to each other in the field and you want to fit spatial covariance models across the whole field, rather than within each replicate, you should define the levels of the row and column factors to run across the experiment. Otherwise they should be defined within replicates (i.e. using the same numbers within each replicate). The spatial models will then be fitted within replicates.
You can use the ROWCOORDINATES and COLCOORDINATES options to specify variates or factors giving the actual positions of the plots in the field. These are needed if you want to fit row or column trends (i.e. covariates) in the fixed model, or to fit a power-distance covariance model when the plots are on an irregular grid. If the levels of the ROWS and COLUMNS factors are defined across the whole experiment rather than within replicates, their values are used as defaults if ROWCOORDINATES and COLCOORDINATES are not set. Their values are also used as defaults if ROWCOORDINATES or COLCOORDINATES are set to variates or factors with no values; the variates or factors are then defined to contain those values.
The PLOTFACTOR option allows you to specify a factor to index the plots, which is used to define the null random model (i.e. the one with no block or replicate effects), or to include a random term for measurement error when fitting covariance models. If this is not set, a local factor called plots is set up automatically.
The FIXED option specifies the fixed terms to be fitted in the analysis. The default fixed model consists of just the constant term, which then becomes the grand mean. The constant term can be omitted by setting option CONSTANT=omit, provided a fixed model has been specified. The FACTORIAL option sets a limit on the number of factors and variates allowed in each fixed term (default 3); any term containing more than that number is deleted from the model. The RANDOM option allows you to you specify any extra random terms to include (in addition to replicates and blocks-within-replicates). The VCONSTRAINTS option allows you to constrain the variance components to be positive; by default they are not constrained.
The TRYSPATIAL option indicates whether to try fitting spatial models, with settings:
always |
always tries to fit them, |
|---|---|
ifregular |
fit them only if the plots are on a regular grid. |
With the default, TRYSPATIAL=*, no spatial models are fitted. For a regular grid, VAROWCOLUMNDESIGN tries models with order 1 auto-regressive structures on the rows and/or the columns of the design, provided there are more than four rows or columns, respectively. For an irregular grid, if there are more than four rows and more four columns, it tries an anisotropic power-distance model using city-block distance. Otherwise, if there is only one dimension with more than four coordinates, it tries an isotropic power-distance model.
The SPATIALFACTOR option allows you to specify a factor to use to define the term required for a two-dimensional power-distance model. If this is not set, a local factor called RowColumn2d is used.
You can set option TRYTRENDS=yes to see whether row and column trends (i.e. covariates) are needed in the fixed model. By default this is not done.
The MVINCLUDE option controls whether units with missing values in the explanatory factors and variates and/or the y-variate are included in the analysis, as in the REML directive.
The METHOD option specifies how to assess the random (and spatial) models
aic |
uses their Akaike information coefficients, |
|---|---|
sic or bic |
uses their Schwarz (Bayesian) information coefficients (default). |
The PRINT option specifies the summary output to be produced about the models. The settings are mainly the same as those of the VRACCUMULATE procedure (which is used to store and then print details of the analyses). There is an extra setting, description, to provide a description of the model and strategy. There is also a setting, best, to print the description of the best model. By default, PRINT=best,description.
The PBEST option specifies the output to be produced from the REML analysis with the best model. Similarly, the PTRY option indicates what output should be produced for each candidate random model when it is tried. Their settings are mainly the same as those of the PRINT option of the REML directive. There are also extra settings aic and sic (with a synonym bic) to print the Akaike and Schwarz (Bayesian) information coefficients, respectively. The default for both these options is to produce no output.
The PTERMS option operates as in REML, to specify the terms whose means and effects are printed by PBEST and PTRY; the default is all the fixed terms. Likewise, the PSE option controls the type of standard error that is displayed with the means and effects; the default is to give a summary of the standard errors of differences.
The Y parameter specifies the response variate. A model-definition structure for the best model can be saved, in a pointer, by the BESTMODEL parameter; the VMODEL procedure can use this to define the model (using the VCOMPONENTS and VSTRUCTURE directives) so that you can reanalyse it yourself using the REML directive. Alternatively, you can save the REML save structure from the analysis with the best model using the SAVE parameter. The EXIT parameter allows you to save a code from REML, giving the “exit status” of the fit (zero if successful).
Options: PRINT, PBEST, PTRY, FIXED, RANDOM, CONSTANT, FACTORIAL, REPLICATES, BLOCKS, ROWS, COLUMNS, ROWCOORDINATES, COLCOORDINATES, PLOTFACTOR, PTERMS, PSE, MVINCLUDE, VCONSTRAINTS, RSTRATEGY, METHOD, TRYSPATIAL, TRYTRENDS, SPATIALFACTOR.
Parameters: Y, BESTMODEL, EXIT, SAVE.
Method
Model definition structures are defined for the various candidate models. (Run the example to see those that are considered for a resolvable block design.) The VARANDOM procedure is used to fit them, with the VRACCUMULATE procedure storing the necessary details for the best one to be selected.
See also
Directives: REML, VCOMPONENTS, VSTRUCTURE.
Procedures: VAOPTIONS, VARANDOM, VARECOVER, VAROWCOLUMNDESIGN, VASERIES, VALINEBYTESTER, VFMODEL, VFSTRUCTURE.
Commands for: REML analysis of linear mixed models.
Example
CAPTION 'VABLOCKDESIGN example',\
!t('Resolvable incomplete-block design',\
'(5x5 simple lattice from Cochran & Cox 1957, page 406).');\
STYLE=meta,plain
FACTOR [NVALUES=50; LEVELS=2] Replicates
& [LEVELS=5] Blocks,Plots,A,B
& [LEVELS=25; VALUES=\
(1...25),(1,6...21),(2,7...22),(3,8...23),(4,9...24),(5,10...25)] Variety
GENERATE Replicates,Blocks,Plots
& [TREATMENT=Variety; REPLICATES=Replicates; BLOCKS=Blocks] A,B
READ Yield
6 7 5 8 6 16 12 12 13 8 17 7 7 9 14 18 16 13 13 14 14 15 11 14 14
24 13 24 11 8 21 11 14 11 23 16 4 12 12 12 17 10 30 9 23 15 15 22 16 19:
VABLOCKDESIGN [PRINT=best,description,deviance,aic,bic,dfrandom; PTRY=*;\
FIXED=Variety; REPLICATES=Replicates; BLOCKS=Blocks;\
RSTRATEGY=optimal] Y=Yield; BESTMODEL=bestmodel; SAVE=savebest
VDISPLAY [PRINT=model,components,wald] savebest