Basic Analysis and Graphing - SAS

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Contents Overview of Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Nominal Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Ordinal Logistic Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Example of Nominal Logistic Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Launch the Logistic Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 The Logistic Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219 Logistic Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Whole Model Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223 Logistic Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224 ROC Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Save Probability Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226 Inverse Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226 Additional Examples of Logistic Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226 Example of Ordinal Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226 Additional Example of a Logistic Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228 Example of ROC Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .230 Example of Inverse Prediction Using the Crosshair Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Example of Inverse Prediction Using the Inverse Prediction Option . . . . . . . . . . . . . . . . . . . . . . . . .232 Statistical Details for the Logistic Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Statistical Details for the Whole Model Test Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Chapter 7 Performing Simple Logistic Regression 217 Overview of Logistic Regression Overview of Logistic Regression Logistic regression has a long tradition with widely varying applications such as modeling dose-response data and purchase-choice data. Unfortunately, many introductory statistics courses do not cover this fairly simple method. Many texts in categorical statistics cover it (Agresti 1998), in addition to texts on logistic regression (Hosmer and Lemeshow 1989). Some analysts use the method with a different distribution function, the normal. In that case, it is called probit analysis. Some analysts use discriminant analysis instead of logistic regression because they prefer to think of the continuous variables as Ys and the categories as Xs and work backwards. However, discriminant analysis assumes that the continuous data are normally distributed random responses, rather than fixed regressors. Simple logistic regression is a more graphical and simplified version of the general facility for categorical responses in the Fit Model platform. For examples of more complex logistic regression models, see the Modeling and Multivariate Methods book. Nominal Logistic Regression Nominal logistic regression estimates the probability of choosing one of the response levels as a smooth function of the x factor. The fitted probabilities must be between 0 and 1, and must sum to 1 across the response levels for a given factor value. In a logistic probability plot, the y-axis represents probability. For k response levels, k -1 smooth curves partition the total probability (which equals 1) among the response levels. The fitting principle for a logistic regression minimizes the sum of the negative natural logarithms of the probabilities fitted to the response events that occur (that is, maximum likelihood). Ordinal Logistic Regression When Y is ordinal, a modified version of logistic regression is used for fitting. The cumulative probability of being at or below each response level is modeled by a curve. The curves are the same for each level except that they are shifted to the right or left. The ordinal logistic model fits a different intercept, but the same slope, for each of r - 1 cumulative logistic comparisons, where r is the number of response levels. Each parameter estimate can be examined and tested individually, although this is seldom of much interest. The ordinal model is preferred to the nominal model when it is appropriate because it has fewer parameters to estimate. In fact, it is practical to fit ordinal responses with hundreds of response levels. Example of Nominal Logistic Regression This example uses the Penicillin.jmp sample data table. The data in this example comes from an experiment where 5 groups, each containing 12 rabbits, were injected with streptococcus bacteria. Once the rabbits were confirmed to have the bacteria in their system, they were given different doses of penicillin. You want to find out whether the natural log (In(dose)) of dosage amounts has any effect on whether the rabbits are cured.
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6 Options for Categorical Variables
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8 Nonparametric Bivariate Density R
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12 Statistical Details for the Logi
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14 Use Categorical Variables . . .
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18 Launch the Scatterplot Matrix Pl
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Contents Book Conventions. . . . .
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22 Learn about JMP Chapter 1 Book C
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24 Learn about JMP Chapter 1 Book C
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26 Learn about JMP Chapter 1 Additi
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90 Introduction to the Fit Y by X P
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Contents Example of the Chart Platf
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314 Creating Summary Charts Chapter
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340 Creating Overlay Plots Chapter
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374 Creating Contour Plots Chapter
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384 Creating Bubble Plots Chapter 1
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406 Creating Maps Chapter 16 Exampl
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450 Creating Parallel Plots Chapter
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460 Creating Cell Plots Chapter 18
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468 Creating Tree Maps Chapter 19 E
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470 Creating Tree Maps Chapter 19 E
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496 Creating Ternary Plots Chapter
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504 References Becker, R.A. and Cle
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506 References Dunnett, C.W. (1955)
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508 References Hosmer, D.W. and Lem
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510 References McLachlan, G.J. and
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Basic Analysis and Graphing - SAS

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