Http Www.jmp.com Software Trial Reply Download.shtml Snum Qrtsxbjjjh&os Mac
Spatial Instance: Uniformity Trial
Consider the Uniformity Trial.jmp sample information 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 every bit groundwork for planning a designed experiment to be conducted on that field. (Meet Littell et al. 2006 , p. 447.)
Your objective is to use the data from these data to blueprint a yield trial with 16 treatments. Specifically, y'all desire to make up one's mind whether to deport future experiments on the field:
• a consummate cake design with 4 blocks (denoted Quarter in the data)
• an incomplete cake pattern with 16 blocks (denoted Subquarter in the data)
• a completely randomized design with spatially correlated errors
With this objective, spatial information can be treated as repeated measures with two or more than dimensions as repeated effects. So, y'all can compare and choose an appropriate model using the values in the Fit Statistics written report. You lot start by determining if there is significant spatial variability, then you determine whether there is a nugget effect.
In one case you accept established whether there is a nugget consequence, you determine the all-time plumbing equipment spatial covariance construction. Finally, you fit the blocking models and compare these to the best spatial construction. In this example, both AICc and BIC are used to select a best model. Spatial Correlation Structure provides more information about nugget effects and other spatial terminology.
Tip: This section walks you through many aspects of plumbing fixtures spatial data (from plumbing equipment the model to deciding on the all-time covariance structure). Leave the Fit Model launch window open equally you work through each example.
Fit a Spatial Structure Model
To decide whether at that place is pregnant spatial variability, you can fit a model that accounts for spatial variability. Then you lot tin can compare the likelihood for this spatial model to the likelihood for a model that does not account for spatial variability. You lot can do this because the independent errors model is nested within the spatial model family: The independent errors model is a spatial model with spatial correlation, ρ, equal to 0. This means that you tin perform a formal likelihood ratio test of the two models.
First, fit the model that accounts for spatial structure.
1. Select Help > Sample Information Library and open Uniformity Trial.jmp.
ii. Select Analyze > Fit Model.
3. Select Continue dialog open up and then that you can return to the launch window in the next example.
iv. Select Yield and click Y.
5. Select Mixed Model from the Personality list.
six. Select the Repeated Construction tab.
7. Cull Spatial from the listing next to Structure.
8. Choose Spherical from the list next to Type.
9. Select Row and Column and click Repeated.
Effigy 8.32 Completed Fit Model Launch Window Showing Repeated Structure Tab
10. Click Run.
Figure 8.33 Fit Mixed Study - Spatial Spherical
In the Fit Mixed written report, the Bodily past Predicted Plot shows that the predicted yield is a unmarried value. This is because only spatial covariance was fit. The Fit Statistics study shows that -ii Log Likelihood is 227.68, and the AICc is 234.08.
Considering an isotropic spatial structure was fit, a Variogram plot is shown. Considering the trials are laid out in an 8 by viii grid, there are more pairs of points at small-scale distances than at very large distances. See Figure 8.37 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 simply the two diagonal pairs of points.
The Repeated Effects Covariance Parameter Estimates study gives estimates of the range (Spatial Spherical = 2.71) and the sill (Balance = 3.26). Run into Variogram.
Fit the Independent Errors Model
Next, fit the independent errors model.
one. Return to the Fit Model Launch Window.
2. Select Repeated Structure tab.
3. Select Rest from the Construction listing.
4. Remove Row and Column from the Repeated effects listing.
Otherwise, a warning appears: "Repeated columns and subject field columns are ignored when the Rest covariance structure is selected."
5. Click Run.
The fit statistics for the independent errors model are: -2 Log Likelihood = 254.22, and AICc = 258.41. Each of these exceeds the corresponding value for the spatial correlation model, where -2 Log Likelihood is 227.68 and the AICc is 234.08. Because smaller values of these statistics signal a ameliorate fit, the spatial model might provide a better fit.
Deport a Likelihood Ratio Test (Optional)
A formal likelihood ratio examination shows whether the spatial correlation model explains significant variation. 1 model must be nested in another model to create valid likelihood ratio tests.
Typically, spatial models are compared using AICc or BIC rather than through formal likelihood ratio testing. Evaluating the AICc or BIC is faster, and many spatial models are not nested.
You can conduct a likelihood ratio test in this example, because the independent errors model is nested within the spatial model family. The independent errors model is a spatial model with spatial correlation, ρ, equal to 0. This means that you lot tin can perform a formal likelihood ratio test of the two models.
In this example, the likelihood ratio examination statistic is 254.22-227.68=26.54. Comparing this to a Chi-foursquare distribution on one degree of freedom, the null hypothesis of no spatial correlation is rejected with a p-value < 0.0001. Yous can conclude that these data contain pregnant spatial variability.
Select the Type of Spatial Covariance
Side by side, you determine which spatial covariance structure best fits the data:
• with or without a nugget event (variation over relatively modest distances)
• isotropic (spatial correlation is equal in all directions) or anisotropic (spatial correlation differs in the two directions)
• type of structure, spherical, Gaussian, exponential, or power.
ane. Return to the Fit Model launch window.
2. Select the Repeated Construction tab.
iii. Select Row and Column and click Repeated.
iv. Select Spatial with Nugget from the Construction list.
5. Select Spherical from the Blazon list.
6. Click Run.
The Fit Mixed report is shown in Figure eight.34. Find 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 announced to be whatever bear witness for a nugget effect.
Figure viii.34 Fit Mixed Study - Spatial Spherical with Nugget
7. Click the Variogram ruddy triangle and select Spatial > Spherical.
Figure 8.35 Fit Mixed Study - Variogram
The ii variograms are virtually identical. This also suggests that in that location is no bear witness of a asset effect.
viii. Return to the Fit Model launch window.
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 Effigy 8.36. The fit statistics indicate non as expert a fit equally 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 show to suggest that spatial correlations within rows and columns of the grid differ.
Figure 8.36 Fit Mixed Report - Spatial Anisotropic Spherical
Determine the Type of the Spatial Construction
An isotropic spatial structure with no nugget is advisable. To determine the type of the spatial structure, you lot can compare the available types.
1. Return to the Fit Model launch window.
ii. Select the Repeated Structure tab.
iii. Select Row and Cavalcade and click Repeated.
four. Select Spatial from the Structure listing.
5. Select Ability from the Type listing.
6. Click Run.
Notation the AICc and BIC values for the model fit.
vii. Render to the Fit Model launch window.
8. Select Exponential from the Type list.
9. Click Run.
Note the AICc and BIC values for the model fit.
10. Return to the Fit Model launch window.
eleven. Select Gaussian from the Type list.
12. Click Run.
Note the AICc and BIC values for the model fit.
The observed AICc values for these types and the other fits that you lot performed are summarized in Tabular array 8.2.
| Construction | Type | AICc | BIC |
|---|---|---|---|
| Spatial | Spherical | 234.08 | 240.sixteen |
| Rest | 258.41 | 262.53 | |
| Spatial with Nugget | Spherical | 236.36 | 244.31 |
| Spatial Anisotropic | Spherical | 240.54 | 248.50 |
| Spatial | Power | 240.24 | 246.32 |
| Spatial | Exponential | 240.24 | 246.32 |
| Spatial | Gaussian | 238.37 | 244.44 |
The best plumbing equipment model (using the smallest AICc value) is the Spatial structure model with Spherical covariance structure. Now you will compare this model to the complete and incomplete block models to complete the objectives of the uniformity trial.
Compare the Model to Block Designs
1. Render to the Uniformity Trial information table.
2. In the Tables console, run the Graph Builder script.
Figure 8.37 Graph Builder Plot of Proposed Complete and Incomplete Block Designs
This plot shows the proposed complete and incomplete block designs for the field. The colour indicates the quarter fields that would serve as consummate blocks. The numbered points represent the sub-quarter fields that would serve as incomplete blocks.
To fit the complete block model, follow these steps:
1. Return to the Fit Model launch window.
2. Select Repeated Structure tab.
3. Select Residue from the Structure listing.
four. Remove Row and Column from the issue.
Otherwise, a popular-up window appears, stating, "Repeated columns and bailiwick columns are ignored when the Balance covariance construction is selected."
5. Select the Random Furnishings tab.
6. Select Quarter and click Add.
vii. Click Run.
To fit the incomplete block model, follow these steps:
1. Return to the Fit Model launch window.
2. Select the Random Effects tab.
3. Select Quarter and click Remove.
4. Select Subquarter and click Add.
five. Click Run.
The following list shows both AICc and BIC values for the competing models. The spherical covariance structure results in the all-time model fit. This indicates that, for future studies using this field, a completely randomized design with spatially correlated errors is preferred.
• Spherical model (see Determine the Type of the Spatial Structure)
– AICc: 234.08
– BICc: 240.xvi
• Complete block (RCBD) model
– AICc: 259.90
– BICc: 265.97
• Incomplete block model
– AICc: 248.77
– BICc: 254.85
Http Www.jmp.com Software Trial Reply Download.shtml Snum Qrtsxbjjjh&os Mac
Posted by: vickitrone1987.blogspot.com
0 Komentar
Post a Comment