Modeling and Multivariate Methods - SAS

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494 Performing Discriminant Analysis Chapter 20 Discriminating Groups Discriminant Method JMP offers three kinds of Discriminant Analysis. All three calculate distances as the Mahalanobis distance from each point to each group’s multivariate mean. The difference in the methods is only in the covariance matrix used in the computations. Linear Discriminant Analysis uses a common (within-) covariance matrix for all groups. Quadratic Discriminant Analysis uses a separate covariance matrix for each group. Quadratic discriminant suffers in small data sets because it does not have enough data to make nicely invertible and stable covariance matrices. Regularized discriminant ameliorates these problems and still allows for differences among groups. Regularized Discriminant Analysis is a compromise between the linear and quadratic methods, governed by two arguments. When you choose Regularized Discriminant Analysis, a dialog appears allowing specification of these two parameters. The first parameter (Lambda, Shrinkage to Common Covariance) specifies how to mix the individual and group covariance matrices. For this parameter, 1 corresponds to Linear Discriminant Analysis and 0 corresponds to Quadratic Discriminant Analysis. The second parameter (Gamma, Shrinkage to Diagonal) specifies whether to deflate the non-diagonal elements, that is, the covariances across variables. If you choose 1, then the covariance matrix is forced to be diagonal. Therefore, assigning 0,0 to these parameters is identical to requesting quadratic discriminant analysis. Similarly, a 1,0 assignment requests linear discriminant analysis. These cases, along with a Regularized Discriminant Analysis example with l=0.4 and g=0.4 are shown in Figure 20.2. Use Table 20.1 to help decide on the regularization. Table 20.1 Regularized Discriminant Analysis Use lower Lambda (Gamma) when: Covariances are different (Variables are correlated) lots of data small number of variables Use higher Lambda (Gamma) when: Covariances are the same (Variables are uncorrelated) little data many variables
Chapter 20 Performing Discriminant Analysis 495 Discriminating Groups Figure 20.2 Linear, Quadratic, and Regularized Discriminant Analysis Linear Quadratic Regularized, with λ=0.4, γ=0.4 Stepwise Selection If you choose Stepwise Variable Selection, a dialog appears (Figure 20.3) to select variables. You can review which columns have large F ratios or small p-values and control which columns are entered into the discriminant model. In addition, the dialog displays how many columns are currently in and out of the model, and the largest and smallest p-values to be entered or removed.
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Version 10 Modeling and Multivariat
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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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Contents Example Using Standard Lea
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56 Fitting Standard Least Squares M
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100 Fitting Standard Least Squares
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Contents Overview of Stepwise Regre
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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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Contents Introduction to Logistic M
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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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Contents Overview of Neural Network
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280 Creating Neural Networks Chapte
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Contents Launching the Platform. .
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296 Modeling Relationships With Gau
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Contents Overview of the Loglinear
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306 Fitting Dispersion Effects with
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Contents Introduction to Partitioni
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318 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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Page 482 and 483: Contents Principal Components. . .
Page 484 and 485: 484 Analyzing Principal Components
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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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552 Plotting Surfaces Chapter 23 Ke
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Contents Introduction to Profiling
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556 Visualizing, Optimizing, and Si
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630 Comparing Model Performance Cha
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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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