Modeling and Multivariate Methods - SAS

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180 Fitting Generalized Linear Models Chapter 6 The Generalized Linear Model Personality The Generalized Linear Model Personality Generalized linear models are fit as a personality of the Fit Model Dialog. After selecting Analyze > Fit Model, select Generalized Linear Model from the drop-down menu before or after assigning the effects to the model. Figure 6.1 Generalized Linear Model Launch Dialog When you specify that you are fitting a generalized linear model, the Fit Model dialog changes to allow you to select a Distribution and a Link Function. In addition, an Offset button, an option for overdispersion tests and intervals, and an option for Firth Bias-adjusted Estimates appears. Examples of Generalized Linear Models You construct a generalized linear model by deciding on response and explanatory variables for your data and choosing an appropriate link function and response probability distribution. Explanatory variables can be any combination of continuous variables, classification variables, and interactions.
Chapter 6 Fitting Generalized Linear Models 181 Examples of Generalized Linear Models Table 6.1 Examples of Generalized Linear Models Model Response Variable Distribution Canonical Link Function Traditional Linear Model continuous Normal identity, g(μ) = μ Logistic Regression a count or a binary random variable Binomial logit, g( μ) = log ----------- μ 1 – μ Poisson Regression in Log Linear Model a count Poisson log, g(μ) = log(μ) Exponential Regression positive continuous Exponential -- 1 μ JMP fits a generalized linear model to the data by maximum likelihood estimation of the parameter vector. There is, in general, no closed form solution for the maximum likelihood estimates of the parameters. JMP estimates the parameters of the model numerically through an iterative fitting process. The dispersion parameter φ is also estimated by dividing the Pearson goodness-of-fit statistic by its degrees of freedom. Covariances, standard errors, and confidence limits are computed for the estimated parameters based on the asymptotic normality of maximum likelihood estimators. A number of link functions and probability distributions are available in JMP. The built-in link functions are identity: g(μ) = μ logit: g( μ) = log ----------- μ 1 – μ probit: g(μ) = Φ -1 (μ), where Φ is the standard normal cumulative distribution function log: g(μ) = log(μ) 1 reciprocal: g(μ) = -- μ power: g( μ) μ λ = if ( λ ≠ 0) log( μ) if λ = 0 complementary log-log: g(m) = log(–log(1 – μ)) When you select the Power link function, a number box appears enabling you to enter the desired power. The available distributions and associated variance functions are normal: V(μ) = 1 binomial (proportion): V(μ) = μ(1 – μ)
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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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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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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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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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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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