Modeling and Multivariate Methods - SAS

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298 Modeling Relationships With Gaussian Processes Chapter 11 The Gaussian Process Report Functional interaction effects, computed in a similar way, are also listed in the Model Report table. Summing the value for main effect and all interaction terms gives the Total Sensitivity, the amount of influence a factor and all its two-way interactions have on the response variable. Mu, Theta, and Sigma The Gaussian correlation structure uses the product exponential correlation function with a power of 2 as the estimated model. This comes with the assumptions that Y is Normally distributed with mean μ and covariance matrix σ 2 R. The R matrix is composed of elements r ij –θ k ( x ik – x jk ) 2 = exp k In the Model report, μ is the Normal distribution mean, σ 2 is the Normal Distribution parameter, and the Theta column corresponds to the values of θ k in the definition of R. These parameters are all fitted via maximum likelihood. Note: If you see Nugget parameters set to avoid singular variance matrix, JMP has added a ridge parameter to the variance matrix so that it is invertible. The Cubic correlation structure also assumes that Y is Normally distributed with mean μ and covariance matrix σ 2 R. The R matrix is composed of elements r ij = ∏ ρ( d ; θ k ) k d = x ik –x jk where ρ( d; θ) = 1 – 6( dθ) 2 + 6( d θ) 3 , d 1 ≤ ----- 2θ 21 ( – d θ) 3 1 , ----- < d 2θ 0, 1 -- < d θ 1 ≤ -- θ For more information see Santer (2003). The theta parameter used in the cubic correlation is the reciprocal of the parameter used in the literature. The reason is so that when a parameter (theta) has no effect on the model, then it has a value of zero, instead of infinity.
Chapter 11 Modeling Relationships With Gaussian Processes 299 Platform Options Marginal Model Plots The Marginal Model plots are shown in Figure 11.4. Figure 11.4 Marginal Model Plots These plots show the average value of each factor across all other factors. In this two-dimensional example, we examine slices of X1 from –1 to 1, and plot the average value at each point. Platform Options The Gaussian Process platform has the following options: Profiler brings up the standard Profiler. Contour Profiler brings up the Contour Profiler. Surface Profiler brings up the Surface Profiler. Details on Profiling are found in the “Visualizing, Optimizing, and Simulating Response Surfaces” chapter on page 553. Save Prediction Formula Save Variance Formula creates a new column in the table containing the prediction formula. creates a new column in the table containing the variance formula. Save Jackknife Predicted Values stores the jackknife predicted values to the data table. These are the x-axis values for the Actual by Predicted Plot. Script contains options that are available to all platforms. See Using JMP. In Figure 11.5, we use the saved prediction formula to compare the prediction to the actual data points.
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Version 10 Modeling and Multivariat
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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6 Emphasis Options for Standard Lea
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8 Models with Crossed, Interaction,
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10 8 Analyzing Screening Designs Us
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12 Examining the Residuals . . . .
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14 Response Frequencies . . . . . .
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16 19 Analyzing Principal Component
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18 Interpreting the Profiles . . .
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20 Discriminant Analysis . . . . .
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Contents Book Conventions. . . . .
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24 Learn about JMP Chapter 1 Book C
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26 Learn about JMP Chapter 1 Book C
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28 Learn about JMP Chapter 1 Additi
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30 Learn about JMP Chapter 1 Additi
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Contents Launch the Fit Model Platf
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34 Introduction to the Fit Model Pl
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56 Fitting Standard Least Squares M
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136 Fitting Stepwise Regression Mod
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Contents Example of a Multiple Resp
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158 Fitting Multiple Response Model
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Contents Overview of Generalized Li
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180 Fitting Generalized Linear Mode
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200 Performing Logistic Regression
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Contents Overview of the Screening
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232 Analyzing Screening Designs Cha
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Contents Introduction to the Nonlin
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244 Performing Nonlinear Regression
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246 Performing Nonlinear Regression
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348 Recursively Partitioning Data C
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350 Recursively Partitioning Data C
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Contents Launch the Platform . . .
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354 Performing Time Series Analysis
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Contents The Categorical Platform .
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386 Performing Categorical Response
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Contents Introduction to Choice Mod
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404 Performing Choice Modeling Chap
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Contents Launch the Multivariate Pl
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444 Correlations and Multivariate T
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Contents Introduction to Clustering
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462 Clustering Data Chapter 18 The
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464 Clustering Data Chapter 18 Hier
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470 Clustering Data Chapter 18 K-Me
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472 Clustering Data Chapter 18 K-Me
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474 Clustering Data Chapter 18 Norm
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476 Clustering Data Chapter 18 Norm
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478 Clustering Data Chapter 18 Self
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480 Clustering Data Chapter 18 Self
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Contents Principal Components. . .
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484 Analyzing Principal Components
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Contents Introduction . . . . . . .
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494 Performing Discriminant Analysi
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Contents Overview of the Partial Le
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Contents Introduction to Item Respo
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526 Scoring Tests Using Item Respon
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Contents Surface Plots . . . . . .
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538 Plotting Surfaces Chapter 23 La
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544 Plotting Surfaces Chapter 23 Th
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546 Plotting Surfaces Chapter 23 Th
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548 Plotting Surfaces Chapter 23 Pl
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550 Plotting Surfaces Chapter 23 Pl
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Contents Introduction to Profiling
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556 Visualizing, Optimizing, and Si
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640 References Becker, R.A. and Cle
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642 References Draper, N. and Smith
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644 References Hooper, J. H. and Am
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646 References Matsumoto, M. and Ni
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648 References Rawlings, J.O. (1988
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650 References Umetrics (1995), Mul
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Contents The Response Models . . .
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654 Statistical Details Appendix A
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690 Index Birth Death Subset.jmp 46
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692 Index Ellipses Transparency 451
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694 Index test for curvature 46 Kru
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696 Index Customizing 267 Nonlinear
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698 Index reliability analysis 453-
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700 Index Stable 363 Stable Inverti
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702 Index
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Modeling and Multivariate Methods - SAS

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