Automatic Spatial Analysis of Row-Column Design Options

Selects information to be printed by the analysis and controls certain aspects of the method used.

Display from selection of random model

This specifies which items of output are to be produced by the analysis.

Best model	A description of the best model found.
Candidate models	A summary of each candidate model tried.

Display output from the best model

This specifies which items of output are to be produced by the analysis using the best fitting model.

Model	Description of the model fitted by the analysis.
Variance components	Estimates of variance parameters.
Wald tests	Wald tests for fixed model terms.
Means	Predicted means.
Effects	Estimates of effects for the fixed effects.
Standard errors	Estimates of standard errors for means or effects.
Residual checks	Uses the VCHECK procedure to check the residuals for outliers and variance stability

Standard errors

Tables of means and effects can be accompanied by estimates of standard errors if selected above. You can choose whether Genstat computes standard errors or standard errors of differences (SEDs) for the tables giving all values or just a summary of these.

Differences	Display the minimum, mean and maximum standard errors of differences between means or effects.
Estimates	Display the minimum, mean and maximum standard errors of estimates for means or effects.
All differences	Display all the standard errors of differences between pairs of means or effects.
All estimates	Display all the standard errors of estimates for means or effects.

Criterion to assess models

This specifies the criterion to use to select the best random model.

Akaike information coefficient	take the model with the smallest value of the Akaike information coefficient.
Bayesian/Schwarz information coefficient	take the model with the smallest value of the Bayesian or equivalently the Schwarz information coefficient.

Strategy for selecting model

This specifies the strategy for selecting the random model.

All random terms	fits the full random model. This is appropriate if the random factors played a key role in the design and its randomization. For example, some factors may have been applied to complete rows or complete columns of a row-and-column-design (as in a strip-block design).
All feasible random terms	Tries to fit the full random model. If this is not possible, it tries models removing first one random term, then two and so on, until successful.
Only additional random terms	Simply uses the random model (if any) defined by the Additional random terms field on the dialog. This is useful when you know the random model and want to investigate the effect of adding spatial covariance models.
Only feasible additional random terms	Tries to fit the random model defined by the Additional random terms field on the dialog. If this is not possible, it tries models removing first one random term, then two and so on, until successful.
Best possible random model	Tries all feasible random models and takes the best one. With row-and-column designs this may take a while, and so may be best left for the occasions when you are unsure what to do, or want to check the result from an automatic search.
Fast strategy to find best model	follows an automatic strategy that aims to find the best random model for a row-and-column design without having to fit all of them. So, for example, it does not try models that include a column main effect as well as a spatial covariance model along rows.

Try spatial model for rows and columns

This specifies whether spatial correlation models are tried with the row and column effects. For a regular grid, the analysis 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.

Try linear trend across rows and columns

This specifies whether to investigate if linear row and column trends (i.e. covariates) are needed in the fixed model. If this is selected, row and column coordinates must be provided.

Constrain variance components to be positive

This specifies whether the variance components are constrained to be positive.

Estimate missing data values

This specifies whether predictions are formed from the fitted model for missing values of the y-variate.

Include units with missing factor values

This specifies whether data units with missing values in any of the factors in the fixed or random models are included in the analysis.

Estimate constant term

Specifies whether a constant term is included in the fixed model.

Maximum number of iterations

Specifies the maximum number of iterations that can be used by the REML analysis to converge to a solution.