https://books.google.com/books?isbn=1317783220
Norman H. Anderson - 2014 - Psychology
The littleused but attractive partworth parameter isalsoconsidered. First, however, itis
necessary to address thefact, already mentioned, thatnovalidity
criterionis ...
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1.
(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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1.
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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 ...
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1.
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.
textlab.io/doc/.../on-theoretical-and-empirical-aspects-of-marginal-distrib...
1.
Feb 12, 2016 - Let Â∗ 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 k∈J 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 (CA) approach we finally reconstruct the complete Markov Chain transition probabilities.
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