Modeling and Multivariate Methods - SAS

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186 Fitting Generalized Linear Models Chapter 6 Examples Second, goodness-of-fit statistics are presented. Analogous to lack-of-fit tests, they test for adequacy of the model. Low p-values for the ChiSquare goodness-of-fit statistics indicate that you may need to add higher-order terms to the model, add more covariates, change the distribution, or (in Poisson and binomial cases especially) consider adding an overdispersion parameter. AICc is also included and is the corrected Akaike’s Information Criterion, where AICc = -2loglikelihood + 2k( k+ 1 )) 2k + ------------------------- n – k – 1 and k is the number of estimated parameters in the model and n is the number of observations in the data set. This value may be compared with other models to determine the best-fitting model for the data. The model having the smallest value, as discussed in Akaike (1974), is usually the preferred model. The Effect Tests table shows joint tests that all the parameters for an individual effect are zero. If an effect has only one parameter, as with simple regressors, then the tests are no different from the tests in the Parameter Estimates table. The Parameter Estimates table shows the estimates of the parameters in the model and a test for the hypothesis that each parameter is zero. Simple continuous regressors have only one parameter. Models with complex classification effects have a parameter for each anticipated degree of freedom. Confidence limits are also displayed. Poisson Regression with Offset The sample data table Ship Damage.JMP is adapted from one found in McCullugh and Nelder (1983). It contains information on a certain type of damage caused by waves to the forward section of the hull. Hull construction engineers are interested in the risk of damage associated with three variables: ship Type, the year the ship was constructed (Yr Made) and the block of years the ship saw service (Yr Used). In this analysis we use the variable Service, the log of the aggregate months of service, as an offset variable. An offset variable is one that is treated like a regression covariate whose parameter is fixed to be 1.0. These are most often used to scale the modeling of the mean in Poisson regression situations with log link. In this example, we use log(months of service) since one would expect that the number of repairs be proportional to the number of months in service. To see how this works, assume the linear component of the GLM is called eta. Then with a log link function, the model of the mean with the offset included is: exp[Log(months of service) + eta] = [(months of service) * exp(eta)]. To run this example, assign • Generalized Linear Model as the Personality • Poisson as the Distribution, which automatically selects the Log link function • N to Y • Service to Offset • Type, Yr Made, Yr Used as effects in the model • Overdispersion Tests and Intervals with a check mark
Chapter 6 Fitting Generalized Linear Models 187 Examples The Fit Model dialog should appear like the one shown in Figure 6.4. Figure 6.4 Ship Damage Fit Model Dialog When you click Run, you see the report shown in Figure 6.5. Notice that all three effects (Type, Yr Made, Yr Used) are significant.
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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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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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236 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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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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