Random utility models
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The idea of utility related to consumer behavior in the study of economics was formally introduced by von Neumann and Morgenstern in 1947. Since then, it has been used to understand decisions in many contexts from economics to product development. The additive form described here is primarily the result of work done by Fishburn. | The idea of utility related to consumer behavior in the study of economics was formally introduced by von Neumann and Morgenstern in 1947. Since then, it has been used to understand decisions in many contexts from economics to product development. The additive form described here is primarily the result of work done by Fishburn. | ||
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Each measurable term is associated with a specific attribute ''k'' (or group of related attributes). The total utility is then a summation of the alternatives ''j'' and their weights ''β'' with the error term ''&spislon;''. | Each measurable term is associated with a specific attribute ''k'' (or group of related attributes). The total utility is then a summation of the alternatives ''j'' and their weights ''β'' with the error term ''&spislon;''. | ||
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| + | ==Continuous Model== | ||
| + | . This discussion needs to be cleaned up. A linear utility model is shown here. | ||
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| + | attachment:utility.bmp | ||
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| + | Two ways to model utility: | ||
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| + | If the distribution is [[joint normal]] the [[probit]] model is used. | ||
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| + | If the distribution is independent from irrelevant alternatives ([[IIA]]) [[double exponential]] the [[logit]] model is used. | ||
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| + | Utility can be found through the observation of consumer choice. A common methodology involves [:conjoint:conjoint analysis]. In [:conjoint:conjoint analysis], the observable part of the utility can be discrete or continuous. Continuous is the form described above. The discrete form only allows for specific choices within a range. The first term then becomes: | ||
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| + | ==Discrete Model== | ||
| + | attachment:discrete.bmp | ||
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| + | where ''j'' still represents the alternatives, ( attachment:zeta.bmp ) represents the attribute, and ( attachment:omega.bmp ) represents the discrete level of that attribute. These are then used in experimental design. | ||
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| + | Once a form for the utility function is found, the probability of a certain product being chosen can be determined using an estimation technique, such as [[maximum likelihood]]. | ||
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| + | ==External Links== | ||
| + | http://en.wikipedia.org/wiki/Utility | ||
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| + | ==References== | ||
| + | *Fishburn, 1970, ''Utility Theory for Decision Making'', John Wiley and Sons, Inc. | ||
| + | *Keeney & Raiffa, 1976, ''Decisions with Multiple Objectives: Preferences and Value Tradeoffs'', John Wiley and Sons, Inc. | ||
| + | *Papalambros & Wilde, 2000, ''Principles of Optimal Design, Modeling and Computation'', Cambridge University Press. | ||
| + | *von Neumann & Morgenstern, 1947, ''Theory of Games and Economic Behavior'', Princeton University Press. | ||
Revision as of 00:35, 13 December 2006
The idea of utility related to consumer behavior in the study of economics was formally introduced by von Neumann and Morgenstern in 1947. Since then, it has been used to understand decisions in many contexts from economics to product development. The additive form described here is primarily the result of work done by Fishburn.
Utility is the measure of a person's preference for a certain product. Utility is not measured directly, but rather indirectly by observing a person's behavior. A utility function is one in which alternatives with higher utility value are preferred.
In random utility model (RUM) it is generally assumed that the attributes determining the utility of an alternative are only partly observed, and utility is modeled with two terms:
The first is a measurable term based upon observable choices βx where x is the attribute itself and attachment:beta.bmp represents a weighted preference for that attribute. The second term is some associated error that is not measurable attachment:epsilon.bmp .
Each measurable term is associated with a specific attribute k (or group of related attributes). The total utility is then a summation of the alternatives j and their weights β with the error term &spislon;.
Contents |
Continuous Model
. This discussion needs to be cleaned up. A linear utility model is shown here.
attachment:utility.bmp
Two ways to model utility:
If the distribution is joint normal the probit model is used.
If the distribution is independent from irrelevant alternatives (IIA) double exponential the logit model is used.
Utility can be found through the observation of consumer choice. A common methodology involves [:conjoint:conjoint analysis]. In [:conjoint:conjoint analysis], the observable part of the utility can be discrete or continuous. Continuous is the form described above. The discrete form only allows for specific choices within a range. The first term then becomes:
Discrete Model
attachment:discrete.bmp
where j still represents the alternatives, ( attachment:zeta.bmp ) represents the attribute, and ( attachment:omega.bmp ) represents the discrete level of that attribute. These are then used in experimental design.
Once a form for the utility function is found, the probability of a certain product being chosen can be determined using an estimation technique, such as maximum likelihood.
External Links
http://en.wikipedia.org/wiki/Utility
References
- Fishburn, 1970, Utility Theory for Decision Making, John Wiley and Sons, Inc.
- Keeney & Raiffa, 1976, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, John Wiley and Sons, Inc.
- Papalambros & Wilde, 2000, Principles of Optimal Design, Modeling and Computation, Cambridge University Press.
- von Neumann & Morgenstern, 1947, Theory of Games and Economic Behavior, Princeton University Press.
