Modeling and Multivariate Methods - SAS

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672 Statistical Details Appendix A The Usual Assumptions Figure A.4 Comparison of Effects Tests for Nominal and Ordinal Fits The least squares means are also different. The nominal LSMs are not all estimable, but the ordinal LSMs are. You can verify the values by looking at the cell means. Note that the A*B LSMs are the same for the two. Figure A.5 shows least squares means for an nominal and ordinal fits. Figure A.5 Least Squares Means for Nominal and Ordinal Fits The Usual Assumptions Before you put your faith in statistics, reassure yourself that you know both the value and the limitations of the techniques you use. Statistical methods are just tools—they cannot guard you from incorrect science (invalid statistical assumptions) or bad data.
Appendix A Statistical Details 673 The Usual Assumptions Assumed Model Most statistics are based on the assumption that the model is correct. To the extent that your model may not be correct, you must attenuate your credibility in the statistical reports that result from the model. Relative Significance Many statistical tests do not evaluate the model in an absolute sense. Significant test statistics might only be saying that the model fits better than some reduced model, such as the mean. The model can appear to fit the data but might not describe the underlying physical model well at all. Multiple Inferences Often the value of the statistical results is not that you believe in them directly, but rather that they provide a key to some discovery. To confirm the discovery, you may need to conduct further studies. Otherwise, you might just be sifting through the data. For instance, if you conduct enough analyses you can find 5% significant effects in five percent of your studies by chance alone, even if the factors have no predictive value. Similarly, to the extent that you use your data to shape your model (instead of testing the correct model for the data), you are corrupting the significance levels in your report. The random error then influences your model selection and leads you to believe that your model is better than it really is. Validity Assessment Some of the various techniques and patterns to look for in assessing the validity of the model are as follows: • Model validity can be checked against a saturated version of the factors with Lack of Fit tests. The Fit Model platform presents these tests automatically if you have replicated x data in a nonsaturated model. • You can check the distribution assumptions for a continuous response by looking at plots of residuals and studentized residuals from the Fit Model platform. Or, use the Save commands in the platform popup menu to save the residuals in data table columns. Then use the Analyze > Distribution on these columns to look at a histogram with its normal curve and the normal quantile plot. The residuals are not quite independent, but you can informally identify severely non-normal distributions. • The best all-around diagnostic tool for continuous responses is the leverage plot because it shows the influence of each point on each hypothesis test. If you suspect that there is a mistaken value in your data, this plot helps determine if a statistical test is heavily influenced by a single point. • It is a good idea to scan your data for outlying values and examine them to see if they are valid observations. You can spot univariate outliers in the Distribution platform reports and plots. Bivariate outliers appear in Fit Y by X scatterplots and in the Multivariate scatterplot matrix. You can see trivariate outliers in a three-dimensional plot produced by the Graph > Scatterplot 3D. Higher dimensional outliers can be found with Principal Components or Scatterplot 3D, and with Mahalanobis and jack-knifed distances computed and plotted in the Multivariate platform.
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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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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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158 Fitting Multiple Response Model
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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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306 Fitting Dispersion Effects with
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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 Launch the Multivariate Pl
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Contents Introduction to Clustering
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472 Clustering Data Chapter 18 K-Me
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476 Clustering Data Chapter 18 Norm
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478 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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556 Visualizing, Optimizing, and Si
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Page 652 and 653: Contents The Response Models . . .
Page 654 and 655: 654 Statistical Details Appendix A
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Page 696 and 697: 696 Index Customizing 267 Nonlinear
Page 698 and 699: 698 Index reliability analysis 453-
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Modeling and Multivariate Methods - SAS

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