Modeling and Multivariate Methods - SAS

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Contents Introduction to Choice Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .403 Choice Statistical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .403 Product Design Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .403 Data for the Choice Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Example: Pizza Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405 Launch the Choice Platform and Select Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Choice Model Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Subject Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .410 Utility Grid Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 Platform Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .414 Example: Valuing Trade-offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .414 One-Table Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 Example: One-Table Pizza Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .423 Special Data Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Default choice set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Subject Data with Response Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .428 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .428 Transforming Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Transforming Data to Two Analysis Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Transforming Data to One Analysis Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .436 Logistic Regression for Matched Case-Control Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .438
Chapter 16 Performing Choice Modeling 403 Introduction to Choice Modeling Introduction to Choice Modeling Choice modeling, pioneered by McFadden (1974), is a powerful analytic method used to estimate the probability of individuals making a particular choice from presented alternatives. Choice modeling is also called conjoint modeling, discrete choice analysis, and conditional logistic regression. The Choice Modeling platform uses a form of conditional logistic regression. Unlike simple logistic regression, choice modeling uses a linear model to model choices based on response attributes and not solely upon subject characteristics. For example, in logistic regression, the response might be whether you buy brand A or brand B as a function of ten factors or characteristics that describe you such as your age, gender, income, education, etc. However, in choice modeling, you might be choosing between two cars that are a compound of ten attributes such as price, passenger load, number of cup holders, color, GPS device, gas mileage, anti-theft system, removable-seats, number of safety features, and insurance cost. Choice Statistical Model Parameter estimates from the choice model identify consumer utility, or marginal utilities in the case of a linear utility function. Utility is the level of satisfaction consumers receive from products with specific attributes and is determined from the parameter estimates in the model. The choice statistical model is expressed as follows. Let X[k] represent a subject attribute design row, with intercept Let Z[j] represent a choice attribute design row, without intercept Then, the probability of a given choice for the k'th subject to the j'th choice of m choices is P i [ jk] where exp( β' ( Xk [ ] ⊗ Zj [])) = --------------------------------------------------------------- m exp( β' ( Xk [ ] ⊗ Zl [])) l = 1 ⊗ is the Kronecker row-wise product the numerator calculates for the j'th alternative actually chosen, and the denominator sums over the m choices presented to the subject for that trial. Product Design Engineering When engineers design a product, they routinely make hundreds or thousands of small design decisions. Most of these decisions are not tested by prospective customers. Consequently, these products are not optimally designed. However, if customer testing is not too costly and test subjects (prospective customers) are readily available, it is worthwhile to test more of these decisions via consumer choice experiments.
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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6 Emphasis Options for Standard Lea
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20 Discriminant Analysis . . . . .
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Contents Book Conventions. . . . .
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Contents Launch the Fit Model Platf
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232 Analyzing Screening Designs Cha
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538 Plotting Surfaces Chapter 23 La
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Modeling and Multivariate Methods - SAS

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