The central notion in all DCM-related models and methods is choice probability and its relationship to utility.
A choice of an item from a set of items has some probability. The actual choice is a realization of this probability. The probability model used for interpretation of the choices is the RUT - Random Utility Theory (Louis Leon Thurstone, 1927). Particular behavioral models that are essence of choice modeling, differ only in the considered conditions and assumptions. In market research (MR), a model is usually anticipated before the actual experiment is run. The same is true for experimental design and estimation method that correspond to the model. There is seldom enough time to test several models, designs and methods, discriminate between them and find the best one. A study is planned to match the assumed model. This requires a thorough knowledge of the problem.
A well designed choice-based exercise complies with the four requirements of a good questionnaire:
Experimental methods of market research (MR) based on DCM rely on choices from sets of items, i.e. simulated actions
conditional to some sets of stimuli being presented. The stimuli may span from the real up to completely
fictional ones. The most common sets are made of products, product profiles, attributes, properties, statements,
Choice is a natural manifestation of human behavior. It is much less culturally or socially dependent than a metric (evaluation-based) statement expressing a preference, attitude or value. Especially when differences between alternatives are small, choice methods are likely to be more sensitive and provide more reliable information than ratings. In addition, internal consistency checks are available that facilitate the identification of respondents who do not have well defined preferences. Experimental conditions can be easily adjusted to mimic the real purchase conditions. The concepts of interest, their attributes, and presence or absence of competing concepts, can be considered jointly, and the preferences analyzed.
Use of choice experiments is an alternative to asking direct questions. In some cases, however, results obtained from a standard way of interviewing can be transformed to a format equivalent to that available from a choice experiment, and analyzed accordingly. The reverse transformation, usually as a part of the data interpretation in form of a simulation of particular events or their equilibrium, is also possible.
The common problem met in interpreting an experiment is that the experimental data do not reflect what they were expected to reflect. Psychology states, in the PEBSE model, the five important treats influencing human behavior:
One can learn a lot about personality and expectations from a research interview, but only very little about the
influence of environment or situation. The behavior in an experiment and conclusions derived from it cannot
reflect the market behavior in its completeness. The results are always subject to the experimental conditions and
the range of collected pieces of information.
A DCM behavioral model should satisfy constraints inherent to the given type of items and the conditions under which the choice is made so that estimated model parameters reflect the observed behavior. The model should allow for the following constraints common in MR:
Choice-based modeling in marketing research draws on the achievements in understanding human behavior and advances in numerical methods. A behavioral model without a feasible way to reliably estimate its parameters would be useless. The following theoretical foundations are essential.
The probabilistic approach provides marketing researcher with a powerful tool for analyzing and predicting consumer choice behavior. Market (revealed) and/or experimental (stated) research data can be combined and analyzed. This does not mean all problems can be solved with a single model, and with the same ease. Many acute problems still show a stubborn resistance.
Choice postulates (Luce, 1958) assign choice
probability to each alternative in a choice set made of uncorrelated items. In the case of such an unstructured
choice set the postulates lead to the well known logit formula also known as BTL - Bradley-Terry-Luce model.
Another consequence of the postulates is the IIA - Independence from Irrelevant Alternatives axiom that deserves a
The outcome of IIA is that the choice probability ratio for any two items in any choice set, independently from
presence or absence of other items in the set, is constant for an individual. The other items are therefore called
irrelevant. Preference shares in a simulation for an individual are usually taken equal to the conditional choice
probabilities given the choice set, and independent from other individuals. This removes part of the IIA
irrelevancy of items between respondents. However, it is still present within simulation for individual
respondents. The false irrelevancy of the items is hidden behind the share averages that do not have constant
ratios due to varying preferences of individuals.
Some products, irrespective of their different brands or other extrinsic properties, are close substitutes. They
are often found among CPG/FMCG products and are understood as commodity rather than products of different
utilities. When present in a real choice set they are taken as a bulk alternative by the decision maker who
selects one of them by random. In a simulation, if only one of such products is present in the set, it gets some
choice probability. If an equivalent product is added to the choice set, the sum of the computed choice
probabilities for the two products is always higher than for a single product in the previous case. In order to
represent reality, it should be about the same. This result is due to the IIA assumption that both products are
irrelevant alternatives. This unfavorable property is often explained as a "red/blue bus" problem.
The logit model gives the IIA property to all alternatives in a set while a nested "mother" logit gives it to alternatives within each hierarchically lowest nest. Of all share simulations, only the first-choice method completely avoids the influence of IIA. However, so that that the results are representative, a sufficiently large sample of individuals is required. To alleviate this, Sawtooth, Inc., developed the RFC - Randomized First Choice simulation method. Another approach might be based on a reasonable size of consideration set of an individual.
If estimation of the behavioral model parameters is based on quantitative evaluations (ratings) of stimuli used
in the experiment, the method is called metric. If we were able to obtain reliable (sufficiently accurate and
precise) and unequivocally interpretable metric data, as it is in some other experimental sciences, no doubt
metric approach would be invincible. As MR deals with a great deal of randomness and uncertainty, a probabilistic
approach must be adopted. Either of the approaches has its caveats.
The term conjoint is believed to be an acronym for "considered jointly". It is assigned to a rich group of
methods allowing extraction of quantitative effects of the stimuli constituents influencing the respondent's
responses in the experiment. The constituents, known as factors in the standard analysis of variance, are called
attributes in MR. The most frequent stimuli are products or services.
All conjoint methods have common features described in Conjoint
Method Overview. The most straightforward and well known application of DCM is CBC
- Choice Based Conjoint.
There is a special case of conjoint design with just a single attribute with levels representing some products,
statements, options, benefits, etc. The goal is to differentiate between the levels and determine their influence
on a decision. A choice-based version known as MXD - Maximum
Difference Scaling method, shortly MaxDiff. An alternative based on the order of choices from a full or
reduced set of items is SCE - Sequential Choice Exercise
that is also suitable as an experimental frame for a DCM-based concept test.
A common task in MR is an overall evaluation of product concepts with fixed properties. The interest is often in
the competitive potential of the concepts. As a standard method, concepts are randomized and presented to
respondents who rate them. The ratings averaged over respondents or their segments make the basis for a metric
evaluation and interpretation.
Prior the rating, the concepts can be sorted and ranked by respondents thus switching from a metric to a
discrete model. Ranks provide an additional discrimination between concepts that are rated equally. The ranks can
be translated into pair-wise choices that can be analyzed with an adequate method. The most often suggested are
Thurstonian, path log-lin and structural equation models (SEM) with latent variables.
A more efficient alternative is a translation into a number of multinomial choices. This approach is used in
the SCE - Sequential Choice Exercise method. Primary
results are random utilities of the profiles allowing a what-if simulation.
In order to utilize the ratings and estimate competitive potential of the concepts in terms of purchase
intentions, calibration is applied.
Several data blocks obtained independently in a survey often relate to some common features. The invaluable gain
from using DCM approach is a possibility to seamless merge the data in a common DCM model. This is seldom
achievable with metric methods.
Merging of several blocks of choice data (rather than parameters estimated prior the merging) with different
measurement "sensitivities" is possible by implicit rescaling (compression or expansion) of parameters for each of
the blocks by the estimation procedure so that the parameters for all the blocks match. The (still unknown)
scaling factors of the choice data blocks are automatically adapted one to another. A disadvantage is potential
distortion of some estimates. As a prevention, both the design of the blocks and estimation procedure require
certain restrictions to be imposed. A merging of SCE -
Sequential Choice Exercise of fixed product profiles designed in a managerial way, possibly used as a filter
in CBS - Choice Based Sampling, and of several class-based CBC
- Choice Based Conjoint blocks of pseudo-randomly modified products, are typical examples.
The problem of matching DCM results with aggregated metric data, e.g. with the market data (revealed preferences), does not have a straightforward solution. The same is true for optional features of a product. However, if one can assume an independence between the core product properties and those of available options, the probability character of choices allows for deriving a model founded on conditional probabilities (a path model).
Estimation of competitive potential of a core product and its selectable options is possible with MBC
- Menu Based Choice. The method relies on choice of a core product in a standard CBC, and, conditionally, a
conjoint method that allows for modeling saturation of needs of the options.
Choice-based methods are very efficient in interpretation and prediction of the events made with high involvement
of the decision maker. Results for low-involvement events are often less reliable but still clearly superior to
metric methods. The reason is simple. In a classic metric-based method, an item is usually rated no more than
once. In a choice-based method, it can be present in many sets and, thus, be evaluated many times under different
conditions and context.
Individual-based estimates are extremely sensitive to the design of choice sets which concerns namely their
orthogonality and balance. The number of freedoms of the estimated system should be always higher than the number
of estimated parameters. The recent developments such as hierarchical
Bayes or other methods that bank on aggregate sample properties and allow estimation of a higher number of
individual parameters than the number of degrees of freedom per individual is, cannot correct the design
deficiency. Especially the bias of estimates may be unpredictable.
A frequent problem encountered in DCM is varying and often unchecked (or even inestimable) precision of the
estimates. The levels of items that have been selected least, e.g. those least attractive in CBC
- Choice Based Conjoint, have the lowest precision for a simple reason - little data is available.
Fortunately, this does not introduce a big problem in a simulation. Such a product will have only a small share.
However, the simulation may be useless when a low part-worth level is combined with a high part-worth level. The
problem lies directly in the conjoint additive kernel. Due to the
error propagation, a sum of part-worths has always lower precision than any of the part-worths alone. When a low
part-worth is "overcome" by a high one the computed item utility may be completely wrong.
An unwanted effect can have an unduly attractive item. When an item has been chosen nearly whenever it was present in the choice task, the information is lost for all items in the given choice set. Inappropriately attractive items or the combinations of levels making them so have always a strongly detrimental effect on the estimates and should be strictly avoided. Design of items for a concept test or a MaxDiff study is fully in hands of the project designer. In a conjoint study, the problems can be efficiently tackled using a design based on product classes.
Deploying robust estimation methods in conjoint studies is also important. Fortunately enough, commercially available programs (e.g. from Sawtooth Software, Inc.) have parametric options that allow to keep tight reins both on the design and computation processes so that satisfactorily reliable estimates can be obtained.