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2014 | OriginalPaper | Chapter

4. Choice Based Conjoint Studies: Design and Analysis

Author : Vithala R. Rao

Published in: Applied Conjoint Analysis

Publisher: Springer Berlin Heidelberg

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Abstract

One of the major objectives in conjoint analysis has been to predict the choices made by a sample of individuals for a new item which is described in terms of a set of attributes used in a conjoint study. Ratings-based conjoint studies involve the conversion of an individual’s stated utility for an item to predict the probability of choice of an alternative under various conditions (e.g. when other alternatives available). As described in Chap. 3, such a prediction is made using preference data (ratings or rankings) collected on a set of hypothetical choice alternatives. A parallel stream of research pursues the path of choice experiments in which an individual makes a choice among a set of choice alternatives, each of which is typically described by a set of attributes; several choice sets are presented to each individual. These choice data, across all the choice sets and all individuals, are then analyzed using a choice model (usually a multinomial logit model and sometimes multinomial probit model) to obtain a function that relates the attribute levels to probability of choice. This approach has come to be known as choice-based conjoint analysis and has its roots in discrete choice analysis; these methods are also called “stated” choice methods (or stated choice experimental methods) because they represent intended choices of respondents among hypothetical choice possibilities. This chapter describes these methods.

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previous chapter Analysis and Utilization of Conjoint Data (Ratings Based Methods)
next chapter Methods for a Large Number of Attributes
Appendix
Available only for authorised users
Footnotes
1
I thank Professor Olivier Toubia for his careful reading of this chapter and suggestions for improvement.
 
2
Readers may refer to Diener, Chris, Using Choice Modeling to Supercharge Your Business, Ithaca, NY: Paramount Market Publishing, 2008 for a non-technical guide to choice modeling, its benefits, and applications.
 
3
The sample consisted of 89 student subjects. The choice responses were aggregated to yield 103 choice frequencies within choice sets for analysis (each of the 11 alternatives appears 8 times + “other” which appears 15 times). The high correlation (R = 0.95) between the logarithms of the 103 observed relative choice frequencies, fai/ni, and the logarithms of the fitted choice probabilities indicates that the MNL model provides a good account of the data from this task.
 
4
For other examples see Louviere et al. (2001) and Louviere (1991) for an exposition and Louviere (1988) for origin of these methods. See Krieger and Green (1991) for designing Pareto optimal stimuli for choice experiments.
 
5
In the case of linear model, the variance-covariance matrix of s of the estimates is (X′X)−1σ2, where X is the suitably coded design matrix and σ2 is the variance of the error term. The D-efficiency measure is 1/(n|(X′X)−1|1/p) where n is the number of observations and p is the number of parameters.
 
6
It is (X′PX)−1σ2 where P is the matrix of choice probabilities (respondents by choice alternatives) which depends on estimated betas.
 
7
Work in this area spans several years and comes a variety of fields. A bibliography can be found in citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.3364 and a review of methods can be found in Khuri et al. (2006).
 
8
It is (X’PX)−1σ2 where P is a matrix derived from the choice probabilities of choice alternatives, which depends on estimated betas. If all betas are zero (or if the choice probabilities are all equal), the covariance matrix will be similar to that in the ratings data analysis.
 
9
This material is based on the Sawtooth Working Paper, Chrzan, Keith and Bryan Orme, “An Overview and Comparison of Design Strategies for Choice-Based Conjoint Analysis”, 2000. Computer randomized designs and computer optimized designs can be generated with the Sawtooth Software’s CBC product. See also Bunch et al. (1996).
 
10
Please see the CBC documentation for a description of these different kinds of randomized designs (Sawtooth Software 1999).
 
11
These improvements occur also for the ratings-based conjoint designs discussed in Chaps. 2 and 3, particularly when there is asymmetry or unequal number of levels across attributes (or asymmetric plans).
 
12
The design matrix X will be coded using orthogonal coding and X’X matrix will be diagonal for orthogonal designs.
 
13
These standard errors are called Dp-errors because they are errors with reference to the estimate of the parameters for attributes centered around the average of weighted probabilities of choice of the items, as opposed to Do-errors, which refer to the errors when the reference values are the simple means of attribute values.
 
14
Mixed logit models are described later in the chapter.
 
15
We should note that for some contexts incentive-alignment is not easy to accomplish; for example, consider a conjoint study in which hypothetical movies are evaluated.
 
16
If a “no choice alternative” is included in the design, we can treat that option as having zero utility (for normalization purposes).
 
17
See Meyer and Johnson (1995) for a discussion on empirical generalization in modeling consumer choice including the functional specification.
 
18
Variance of the error can be introduced as an additional parameter; in that case, the distribution becomes \( P({\in_k}\leq \in )=\exp (-\exp (-\in /s)),-\infty <\in <\infty \), where s is the scale for the error term. The variance of the error term then is π2s2/6. Implicitly the scale parameter is set equal to 1 in most applications. We will return to this issue alter.
 
19
These data collected by Vishal Narayan, Vithala R. Rao and Carolyne Saunders in 2008 were part of a larger study on how individuals adapt their tradeoffs with new information; our focus here will be on one element of this study.
 
20
I thank Yu Yu of Georgia State University for her help with these analyses. The MDC procedure in the SAS system was used.
 
21
The MDC procedure does not enable estimating a random coefficients logit model. We will show the estimates from the Bayesian method in the next section.
 
22
I thank Chang Hee Park of Binghamton University for his help with this analysis.
 
23
These were computed using the CBC software on August 20, 2009.
 
24
An alternative could be Poisson regression.
 
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Metadata
Title
Choice Based Conjoint Studies: Design and Analysis
Author
Vithala R. Rao
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Book
Applied Conjoint Analysis

Print ISBN: 978-3-540-87752-3

Electronic ISBN: 978-3-540-87753-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-540-87753-0_4