Modeling and Multivariate Methods - SAS

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670 Statistical Details Appendix A The Factor Models Ordinal Least Squares Means As stated previously, least squares means are the predicted values corresponding to some combination of levels, after setting all the other factors to some neutral value. JMP defines the neutral value for an effect with uninvolved ordinal factors as the effect at the first level, meaning the control or baseline level. This definition of least squares means for ordinal factors maintains the idea that the hypothesis tests for contained effects are equivalent to tests that the least squares means are equal. Singularities and Missing Cells in Ordinal Effects With the ordinal coding, you are saying that the first level of the ordinal effect is the baseline. It is thus possible to get good tests on the main effects even when there are missing cells in the interactions—even if you have no data for the interaction. Example with Missing Cell The example is the same as above, with two observations per cell except that the A3B2 cell has no data. You can now compare the results when the factors are coded nominally with results when they are coded ordinally. The model as a whole fits the same as seen in tables shown in Figure A.1. Table A.15 Observations Y A B 12 1 1 14 1 1 15 1 2 16 1 2 17 2 1 17 2 1 18 2 2 19 2 2 20 3 1 24 3 1
Appendix A Statistical Details 671 The Factor Models Figure A.1 Comparison of Summary Information for Nominal and Ordinal Fits The parameter estimates are very different because of the different coding. Note that the missing cell affects estimability for some nominal parameters but for none of the ordinal parameters. Figure A.2 Comparison of Parameter Estimates for Nominal and Ordinal Fits The singularity details show the linear dependencies (and also identify the missing cell by examining the values). Figure A.3 Comparison of Singularity Details for Nominal and Ordinal Fits The effect tests lose degrees of freedom for nominal. In the case of B, there is no test. For ordinal, there is no loss because there is no missing cell for the base first level.
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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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Contents Example Using Standard Lea
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56 Fitting Standard Least Squares M
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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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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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508 Fitting Partial Least Squares M
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Contents Introduction to Item Respo
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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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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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Page 640 and 641: 640 References Becker, R.A. and Cle
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Page 652 and 653: Contents The Response Models . . .
Page 654 and 655: 654 Statistical Details Appendix A
Page 690 and 691: 690 Index Birth Death Subset.jmp 46
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Page 696 and 697: 696 Index Customizing 267 Nonlinear
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Page 700 and 701: 700 Index Stable 363 Stable Inverti
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Modeling and Multivariate Methods - SAS

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