2D Spline Analysis of Row-Column Design Options

Selects information to be displayed by the analysis, controls certain aspects of the method used and saves some items not available from the usual VKEEP directive.

Display

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

Description	Description of the data and spline basis used in the analysis
Model	Description of the model fitted by the analysis
Predicted means	Predicted means
Estimated effects	Estimates of regression coefficients
Fitted spline surface	Predicted values of the 2D spline surface modelling the spatial trend
Variance components	Estimates of variance parameters
Variance-covariance matrix	Variance-covariance matrix for the variance parameters
Deviance	The residual deviance
Wald tests	Wald Tests for fixed model terms and accompanying F-statistics (if selected)
Missing value estimates	Estimates of values missing from the input
Akaike information coefficient (AIC)	Akaike Information Coefficient to assess the random model
Schwarz information coefficient (SIC)	Schwarz Information Coefficient to assess the random model
Residual checks	Uses the VCHECK procedure to check the residuals for outliers and variance stability
Monitoring	Monitoring information at each iteration

Standard errors

Tables of means and effects are accompanied by estimates of standard errors. You can choose whether Genstat computes standard errors or standard errors of differences (SEDs) for the tables. Approximate least significant differences (LSDs) for the predicted means of the fixed terms specified in the Model terms for effects and means field can be computed by selecting LSDs. These are calculated using the approximate numbers of residual degrees of freedom printed by the analysis in the d.d.f column in the table of tests for fixed tests (produced by selecting the Wald tests display option). The degrees of freedom are relevant for assessing the fixed term as a whole, and may vary over the contrasts amongst the means of the term. So the LSDs should be used with caution. If you are interested in a specific comparison, you should set up a 2-level factor to fit this explicitly in the analysis. The significance level for LSDs can be specified as a percentage (default 5) in the accompanying field.

Model terms for effects and means

This specifies the model terms, as a formula, for which tables of means and/or effects are displayed. For covariates, the associated linear regression parameter can be printed as an effect, but predicted means are not available. Predicted means for other terms are adjusted to the mean of the covariate (but see note below). The formula can include the string ‘Constant’ to include entries for the constant term. Click the Terms to open the Select model terms dialog to select terms from the fixed and random models. If no formula is specified, means or effects are produced for all the fixed model terms and none of the random terms.

Graphics

This specifies which graphics are produced by the analysis.

Contour	This plots fitted 2D spline as a contour plot
Surface	This plots fitted 2D spline as a surface plot
Shade	This plots fitted 2D spline as a shade plot
Spatial	This gives a shade plot of the residuals in field layout
Composite	This gives a default residual plot from the fitted model
Means plots	This gives default plot of the predicted means against the factors in the model

The Plot using colours buttons can be clicked to change the colours used in the contour, surface, and shade plots. The resulting spectrum of colours are shown in the Sample field. The Title field can be used to give a title for these plots. More control over the residual and mean plots can be obtained by using the Further Output dialog.

Estimate missing data values

This specifies whether predictions are formed from the fitted model for missing values of the y-variate; alternatively any units with missing values in the y-variate are excluded from the analysis.

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. Units with missing y values are always excluded from the analysis.

Estimate constant term

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

Covariates centred to zero mean

Specifies whether covariates are centred to zero mean during the analysis. This applies to all covariates in the model. If covariates are centred, tables of predicted means are based on the mean covariate value, otherwise zero for each covariate.

Maximum iterations

This specifies the maximum number of iterations to use to optimize the REML likelihood.

Save

Use this to save results from the analysis in Genstat data structures. After selecting the appropriate boxes, you need to type the names for the identifiers of the data structures into the corresponding In: fields. These results can be saved only when running the analysis. To save other results after running the analysis, use the Save button on the menu.

Predictions for spline surface	Matrix	The predicted values of the spline surface modeling the trend in the row-column design.
Statistics	Pointer	the deviance, AIC, SIC, and degrees of freedom for the fixed and random model
Exit code	Scalar	To the exit code from the REML analysis. If the analysis is successful this will be zero, otherwise it will contain a number (-1,-2, 1…8). See the REML directive for more details on the error codes.

Display in spreadsheet

The saved results, except the pointers to formulae, will also be displayed within a new spreadsheet window.