Consider the Uniformity Trial.jmp sample data table. An agronomic uniformity trial was conducted on an 8x8 grid of plots. In a uniformity trial, a test crop is grown on a field with no experimental treatments applied. The response variable, often yield, is measured. The idea is to characterize variability in the field as background for planning a designed experiment to be conducted on that field. (See Littell et al. 2006, p. 447.)
1.
Select Help > Sample Data Library and open Uniformity Trial.jmp.
2.
Select Analyze > Fit Model.
3.
Select Keep dialog open so that you can return to the launch window in the next example.
4.
Select Yield and click Y.
5.
Select Mixed Model from the Personality list.
6.
Select the Repeated Structure tab.
7.
Choose Spatial from the list next to Structure.
8.
Choose Spherical from the list next to Type.
9.
Select Row and Column and click Repeated.
Figure 7.32 Completed Fit Model Launch Window Showing Repeated Structure Tab
10.
Click Run.
Figure 7.33 Fit Mixed Report - Spatial Spherical
The Fit Mixed report is shown in Figure 7.33. The Actual by Predicted Plot shows that the predicted yield is a single value. This is because only spatial covariance was fit. The Fit Statistics report shows that -2 Log Likelihood is 227.68, and the AICc is 234.08.
Because an isotropic spatial structure was fit, a Variogram plot is shown. Because the trials are laid out in an 8 by 8 grid, there are more pairs of points at small distances than at very large distances. See Figure 7.37 for the layout. The Variogram shows that a spherical spatial structure is an excellent fit for distances up to about 8.4. The distance class for the final distance consists of only the two diagonal pairs of points.
2.
Select Repeated Structure tab.
3.
Select Residual from the Structure list.
4.
Remove Row and Column from the Repeated effects list.
5.
Click Run.
2.
Select the Repeated Structure tab.
3.
Select Row and Column and click Repeated.
4.
Select Spatial with Nugget from the Structure list.
5.
Select Spherical from the Type list.
6.
Click Run.
The Fit Mixed report is shown in Figure 7.34. Notice that the log-likelihoods are essentially equal to those of the spherical with no nugget model, and the AICc is slightly higher (236.36 compared to 234.08). The Repeated Effects Covariance Parameter Estimates report shows that the Nugget covariance parameter has an estimate of zero. There does not appear to be any evidence for a nugget effect.
Figure 7.34 Fit Mixed Report - Spatial Spherical with Nugget
Figure 7.35 Fit Mixed Report - Variogram
9.
Select Repeated Structure tab.
10.
To test anisotropicity, select Spatial Anisotropic from the Structure list.
11.
Select Spherical from the Type list.
12.
Click Run.
The Fit Mixed report is shown in Figure 7.36. The fit statistics indicate not as good a fit as the isotropic (spatial structure) spherical model (AICc 240.54 compared to 234.08). The Repeated Effects Covariance Parameter Estimates report shows that the estimates for the Row (Spatial Spherical Row) and Column (Spatial Spherical Column) covariances are very close. There is no evidence to suggest that spatial correlations within rows and columns of the grid differ.
Figure 7.36 Fit Mixed Report - Spatial Anisotropic Spherical
2.
Select the Repeated Structure tab.
3.
Select Row and Column and click Repeated.
4.
Select Spatial from the Structure list.
5.
Select Power from the Type list.
6.
Click Run.
8.
Select Exponential from the Type list.
9.
Click Run.
11.
Select Gaussian from the Type list.
12.
Click Run.
Figure 7.37 Graph Builder Plot of Proposed Complete and Incomplete Block Designs
2.
Select Repeated Structure tab.
3.
Select Residual from the Structure list.
4.
Remove Row and Column from the effect.
5.
Select the Random Effects tab.
6.
Select Quarter and click Add.
7.
Click Run.
2.
Select the Random Effects tab.
3.
Select Quarter and click Remove.
4.
Select Subquarter and click Add.
5.
Click Run.

Help created on 10/11/2018