Thursday, April 7, 2016

conjoint The difficulties grows when the aim is providing scenarios analysis involving future states perhaps never performed before. In this situation we need information gathered from experts and we cannot resort to past data



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Norman H. Anderson - 2014 - ‎Psychology

The littleused but attractive partworth parameter isalsoconsidered. First, however, itis necessary to address thefact, already mentioned, thatnovalidity criterionis ...


people.sutd.edu.sg/~natarajan.../MDM_paper_secondRevision_MS.pdf

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(see for example Train (44), Allenby and Rossi (1)) assumes that the partworth parameter vector βi is sampled from a distribution β0 + ˜ϵi a. In this way, the utility ...


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by X Wang - ‎Related articles

Jul 22, 2014 - only a single partworth parameter vector is estimated and this estimate uses – in the case of. Table 1 – 100 times more data than is available at ...


www.idosi.org/mejsr/mejsr9(3)11/22.pdf

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partworth (parameter) estimates of the attributes is proportional to (X'XY'. The efficiency of a design is based on the information matrix. An efficient design will.


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Feb 12, 2016 - Let  be the maximum log-likelihood estimator and Â0 be the truepartworth parameter vector. From the theory of maximum likelihood .


Traditional  preference modeling methods such as conjoint analysis (Carroll & Green,  1995), (Green & Srinivasan, 1978), (Green & Srinivasan, 1990)have been  used for many preference modeling applications (Wittink & Cattin, 1989)  typically with data gathered under controlled conditions such as through  questionnaires. However, much of the available information today about  choices of people, such as scanner or clickstream data, is not gathered in  such a controlled way and therefore is more noisy (Cooley, Srivastava, &  Mobasher, 1997),  (Kohavi, 2001). It is therefore important to develop new  preference modeling methods that are (a) highly accurate, (b) robust to  noise,  and  (c)  computationally  efficient  in  order  to  handle  the  large  amounts of choice data available.  

Several statistical approaches to information retrieval, and other ranking  problems like preference modeling, assume that there is explicit metric  information available (Cui & Curry, 2003), or other side information like  transitive rankings (Herbrich, Graepel, & Obermayer, 1999), or frequency of  clicks  (Joachims,  2002).   In  choice  based  data,  we  only  know  which  combination is the highest ranking, among the available options. 


The objective of choice based conjoint analysis, for a market researcher,  is to determine the most preferred combination of attributes, typically for  new  product  development  (Toubia,  Simester,  Hauser,  &  Dahan,  2003)(Toubia,  Hauser,  &  Simester,  2004).  In  this  chapter  we  present  regularized learning methods that can learn such user preferences from  choice  based  data.  We  compare  our  SVM  based  methods  with  logistic  regression (Ben‐Akiva & Lerman, 1985) (Louviere, Hensher, & Swait, 2000),  Hierarchical Bayes (HB) (DeSarbo & Ansari, 1997)(Allenby, Arora, & Ginter,  1998)(Arora,  Allenby,  &  Ginter,  1998),  and  the  polyhedral  estimation  methods  of  (Toubia,  Hauser,  &  Simester,  2004)  using  simulations  as  in  (Arora  &  Huber,  2001);  (Toubia,  Hauser,  &  Simester,  2004).  We  show  experimentally that the SVM based methods are more robust to noise than  both logistic regression and the polyhedral methods, to either significantly  outperform  or  never  be  worse  than  both  logistic  regression  and  the  polyhedral methods, and to estimate nonlinear utility models faster and  better than all methods including HB. 




In practice, an adequate modeling of consumer heterogeneity is important for accurate choice prediction. To account for taste variation among the customers, the Mixed Logit (MixL) model (see for example Train (44), Allenby and Rossi (1)) assumes that the partworth parameter vector βi is sampled from a distribution β0 +˜i a . In this way, the utility function U˜ ij = (β0 +˜i a ) 0xij + ˜ij captures consumer taste variation across the attributes. By integrating over the density, the choice probabilities under mixed logit model is derived as Pij = R Pij (i a )g(i a )di a , where Pij (i a ) is the choice probability for given i a , and g(·) denote the probability density of ˜i a . For instance, when the error terms ˜ij are i.i.d Gumbel, the MNL formula applies and Pij (i a ) = e (β0+i a) 0xij X kJ e (β0+i a) 0xik . Authors’ names blinded for peer review Article submitted to Management Science; manuscript no. MS-MS-12-00426.R2 3 At the same time, g(i a ) is typically assumed to be a continuous unimodal distribution such as the multivariate normal distribution. The choice probabilities and parameters for the MixL model are then estimated using simulation techniques




Middle-East Journal of Scientific Research 9 (3): 431-436, 201 1 ISSN 1990-9233 © IDO SI Publications, 2011 Estimation of Markov Chains Transition Probabilities Using Conjoint Analysis (Expert Preference) N. Akhondi, G. Yari, E. Pasha and R. F amoosh Department of Statistics, Science and Research Branch, Islamic Azad University, Teharan, Iran Abstract: This paper proposes methodology to estimate transition probabilities on the base of judgments by experts that may be useful in situations of data absence. The Fractional Factorial Design (FFD) is used to cope with the curse of dimensionality. By means of Conjoint Analysis (CA) approach we finally reconstruct the complete Markov Chain transition probabilities. The experiment results show it is promising for us to use (CA) in estimating of the entropy rate of Markov Chains with a finite state space. Key words:Markov Chain - Transition probabilities - Design in Conjoint Analysis Conjoint Analysis - Design of experiments - Efficient INT RODUC TION The present paper proposes a framework based on expert opinion elicitation, developed to estimate the transition probability matrix of an irreducible, discrete time, homogeneous Markov Chain with a finite state space. In this article we address the question of estimating the transition probability matrix of Markov Chain in situations of data absence. In general, the full probability distribution for a given stochastic problem is unknown. When data are available, the most objective estimation of them is the maximurnlikelihood estimation of the transition probabilities (P11). The difficulties grows when the aim is providing scenarios analysis involving future states perhaps never performed before. In this situation we need information gathered from experts and we cannot resort to past data [1]. Our methodology has the new idea of estimating transition probabilities using conjoint (FFD) methods that is useful in this conditions. Conjoint analysis has as its roots the need to solve important academic and industry problems [2]. It is a popular marketing research technique. In order to respond to consumers” needs, makers have to research consumers” preferences of products, services and their selection criteria of products. The conjoint analysis measures the degree of importance which is given to particular aspects of a product or service [3]. The real genius is making appropriate tradeoffs so that real consumers in real market research settings are answering questions from which useful information can be inferred. In the thirty years since the original conjoint analysis articles, researchers in marketing and other disciplines, have explored these tradeoffs [2]. In conjoint experiments, each respondent receives a set of profiles to rate (or rank). Designing these experiments involves determining how many and which profiles each respondent has to rate (or rank) and how many respondents are needed [4]. Experimental design is a fundamental component of (CA). The complexity of experimental design arises from the exponential growth inthe number of attributes, i.e. the curse of dimensionality. Use of a full factorial design (all profiles) will place an excessive burden on respondent for providing evaluations. Therefore, utilize (FFD), i.e. orthogonal design, or a subset of all profiles [5]. The basic partworths that best explain the overall preference judgments made by respondents [2]. (CA) is a technique based on a main effects analysis-of-variance researchers fractional balanced conjoint problem is to estimate the model that decomposes the judgment data into components, based on qualitative attribute of the products or services [6]. Most commonly used methods to acquire partworths are the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), Hierarchical Bayes (HB) methods, Multivariate Analysis of Variance (MANOVA) and Ordinary Least Squares (OL S) Regression [7]. Corresponding Author: N. Akhondi, Department of Statistics, Science and Research Branch, Islamic Azad University, Teharan, Iran. E-mial: akhondinasrin@gmail.com.


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cope with the curse of dimensionality. By means of Conjoint Analysis (CAapproach we finally reconstruct the complete Markov Chain transition probabilities.
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