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| + | #REDIRECT [[discrete choice analysis]] |
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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.
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| - | 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.
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| - | 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:
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| - | The first is a measurable term based upon observable choices ''β<sub>x</sub>'' 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 .
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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 ''&epislon;''.
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| - | ==Continuous Models==
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| - | <math> \quad u_j= \sum_k \beta_k x_{jk}+\epsilon_j </math>
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| - | Based on the assumptions of observed attribute ''x<sub>jk</sub>''and unobserved attribite ''&epislon;<sub>j</sub>'', different models are derived, such as [[logit model]], [[probit model]], [[mixed logit|mixed logit model]], etc.
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| - | Utility can be found through the observation of consumer choice. A common methodology involves [[conjoint analysis]]. In 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 Models==
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| - | <math> \quad u_j= \sum_{\zeta} \sum_{\omega} \beta_{\zeta \omega} \delta_{j \zeta \omega} </math>
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| - | where ''j'' still represents the alternatives, ''ζ'' represents the attribute, and ''ω'' 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==
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| - | http://en.wikipedia.org/wiki/Utility
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| - | ==References==
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| - | *Fishburn, 1970, ''Utility Theory for Decision Making'', John Wiley and Sons, Inc.
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| - | *Keeney & Raiffa, 1976, ''Decisions with Multiple Objectives: Preferences and Value Tradeoffs'', John Wiley and Sons, Inc.
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| - | *Papalambros & Wilde, 2000, ''Principles of Optimal Design, Modeling and Computation'', Cambridge University Press.
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| - | *von Neumann & Morgenstern, 1947, ''Theory of Games and Economic Behavior'', Princeton University Press.
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| - | [[Category:discrete choice models]]
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