We talk nearly every day with a conjoint method user who has run into
a problem of some kind. The problem responsible for the most frequent customer support calls is using too many
prohibitions. The system won't be able to produce a good design, and may fail altogether.
Prohibitions, if at all possible, should be avoided. Too many prohibitions, in the best case, can lead to
imprecise utility estimation and, in the worst case, unresolvable (confounded) effects and the complete
inability to calculate stable utilities. Allegedly, there have been entire data sets with hundreds of
respondents going to waste ...
[ Freely by
Sawtooth Software, Inc. ]
A frequent requirement in testing products is concerned with prohibitions between levels of two or more
attributes. Common is conditional pricing due to presence or absence of some levels such as brand, product
alternative, package, size, etc. However, unwisely set prohibitions can be detrimental, and sometimes even fatal,
for the design efficiency. As seeing is believing, a simple example is provided below.
Any experimental plan can be partitioned into smaller design building blocks. Say one of the blocks is a L4
||Level of A1
||Level of A2
||Level of A3
The block has this covariance matrix:
design plan L4
Values in the diagonal elements are variance propagation coefficients. They tell us about the extent by which a
random error in the data will be projected into the parameter estimates. Values of non-diagonal elements are the
same measure for mutual dependence of errors between the attributes. The design is orthogonal when all
non-diagonal elements are zero, and fully balanced when all diagonal elements are equal.
Now we decide that, for some good reason, we cannot combine all levels and must introduce a prohibition leading
to the change of level of attribute A3 from 1 to 2 in profile 4. The covariance matrix changes as follows:
design plan L4 with a prohibition
Not only the variance of the affected attribute A3 has increased fourfold, but those of the other attributes have
doubled. Even worse, a strong dependence between attributes has been introduced which means that errors will not
compensate. If there are interactions between attributes, the introduced bias will accumulate over respondents.
Since small interactions between attributes are common, a design with prohibitions will lead to the bias that may
prevail over the main effects of estimated parameters.
There are many suggestions in the literature how to deal with prohibitions and test their influences. We have
adopted the standard method of randomized blocked design made up of "product classes" in combination with ASD
Specific Design. A class is defined as a complete Cartesian set of profiles from allowed intervals, i.e. a
set with no prohibitions among attributes allowed. In a plain language, a class is the complete set of profiles
for products with attribute levels from some intervals common to all products in the set. Only representative
subsets of orthogonal profiles obtained for each of the product classes are used in the experiment. The method is
statistically clean, easy to manage, understandable for client to specify and, as of practical importance, can be
converted to the prohibition strategy implemented in commercially available design programs. The class approach
guarantees all part-worths are estimable with a minimal bias.
A class for the purpose of a conjoint study design is usually composed from the profiles whose certain attributes
are limited to fixed intervals. It is desirable that the defined classes can be ordered in some way, typically by
assumed quality, size of packaging, way of usage, etc. Nominal classes are usually much harder to be handled with,
and, therefore, are often grouped in ordinal hyper-classes. The number of hierarchical levels is, at least in
In a typical stated preference experiment, a choice set consists of several alternatives among which the respondent
is asked to discriminate. The alternatives should (1) provide sufficient variations of attribute values in the
managerially permissible intervals and (2) guarantee estimability of the model parameters without a danger of having
introduced correlations caused by attribute level prohibitions.
A representative of a class is a product with the attribute levels varied in an allowable range. If some
combinations of attribute levels are still detected as not feasible the set of product profiles must be
partitioned into 2 (or more) classes with attribute level intervals chosen so that all possible combinations of
attribute levels in a class are allowed. A nested class structure is common.
The most simple example of a class is a product offered at a fixed number of different price levels in a pricing
test. The price levels are mapped onto a price axis with discrete price values. The perceptional differences
between neighboring values of prices should be about constant (e.g. in fixed %) so that the prior log-likelihood
differences are equal. This approach minimizes the number of prices shown to respondents and facilitates
estimation of an independent price part-worth for each shown price.
A conjoint exercise should be composed of the product classes relevant for a given respondent, i.e. of the
alternatives supposed to be from the respondent's evoked/consideration
set. This can be accomplished by use of CBS - Choice
Based Sampling that allows to assign a range of classes to a respondent.
Class structure of tested products often comes from the goal of the study quite naturally. E.g., cars can be
classified as commercial and personal motor vehicles, these as small, lower middle, upper middle, luxury ones,
off-roads, etc., and perhaps further divided into sub-classes by make, equipment features, etc. Consumption goods
can be divided into categories, these into low-level up to luxury classes, then according to the packaging, etc.
The class structure and order of the class levels always depends on the conditions and objectives of the
study in a way that does not contradict the rules of DOE
- Design Of Experiments.
- A class structure must be strictly hierarchical. No exceptions are allowed.
- The whole range of tested products (rather than attribute ranges) is partitioned into product classes such
that all combinations of attribute levels belonging to the class are allowed inside the class. If this is
not possible by classifying products in a single hierarchy level, a class should be divided into lower-level
- The ranges of attribute levels in the lowest level class must be narrow enough not to allow generation of
extremely attractive or totally unacceptable product profiles. All profiles in a class should be
- At the same time, the ranges of attribute levels in the class must be broad enough to allow estimation of
- Partitioning of the products into classes does not mean partitioning of the attribute ranges. No exclusivity
of the attribute ranges in classes is required, i.e., ranges of the respective attribute levels may (and usually
- Classes should reflect different types of anticipated behavior and perceptions of respondents.
- Classes may or may not have common attributes. The latter case requires using ASD
- Alternative Specific Design method.
- Each attribute in a class is defined on a given range of values. The range may contain one level (e.g. of a
brand attribute) or more levels (e.g. of a price attribute).
- If the range is made up of a single level, the class is a specific alternative.
- In turn, a specific alternative can have only one attribute on a single level. If there were two or more
attributes on a single level, their utilities would not be estimable. Either a composite attribute or
sub-classes should be created.
- The same number of levels of a common attribute (typically price) should be used in each class. The number
should be very reasonable so as not to exceed an acceptable total number of levels in the study.
- The range of level values or items in a class should be broad enough to asses the effect of attribute
levels in the class but narrow enough not to exceed managerially acceptable values.
- A conjoint study based on product classes can be understood as a merger of several sub-conjoint studies where
there are no prohibitions between attribute levels in any of the sub-conjoint exercises.
The approach of composing a conjoint exercise from product classes has appeared as very useful:
To a limited extent, product classes can be given predefined weights to simulate market distribution and
availability of the products the classes represent.
- Products often fall into classes quite naturally.
- Ranges of attributes levels can be easily defined and modified.
- The profiles shown to respondents are credible.
- As attribute ranges in a class are usually quite narrow interactions between attribute levels can be neglected
and omitted from the estimation.
- A blocked design has usually a substantially lower number of parameters than an equivalent model with
interactions. In our experience, about the same fit of the models is obtained. The model description is more
compact and the precision of a simulation unimpaired.
- Part-worths from a blocked design are usually more stable (have lower variance) than those from a non-blocked
- Class attribute is usually hidden from respondents. Its level part-worths may or may not be estimated. The
latter case is typical for the classes serving only as an aid in the design.
- If estimated, interpretation of the part-worths related to the classes is usually more straightforward than of
those based on interactions. E.g., it is much easier to understand and interpret a single value of
price-based elasticity of substitution or conventional share-based price elasticity for a brand than, say,
values for several price levels and the same number of values for interaction between the brand and the price
- The spans of the implicit conjoint blocks, i.e. the classes that make them up, usually overlap. This
contributes to the overall stability and reliability of the estimates.
- Last but not least advantage is the client can easily see where and why the design might be deficient and can
promptly make the proper provisions.
In the product classes approach, the overall design may be slightly out of balance in respect to some attribute
levels, most often to the outer levels of a value-based attribute such as price. This effect is often recognized
as positive because the least frequently shown outer levels are usually the least managerially important.
Nevertheless, if the off-balance should be a problem, the design weight (presentation frequency) of the affected
levels may be boosted.
- A design made up of classes should not be confused with an alternative specific design analyzed as a nested
"mother logit" model.
- A typical use of the class approach is for various types of packages made by bundling products or services.
Each package may be of its own class and have ranges of its properties set independently from properties of
- Representatives of all classes in a conjoint exercise are usually shown to respondent equally often, i.e.
with ratio 1 : 1 : 1 : ... . This is in agreement with the null hypothesis
that all classes are (a priori) equally attractive to the subject. If relevant the frequency can be set
to a ratio of small natural numbers, e.g. 3 : 2 : 1 : ..., e.g. if the class is
a brand with many more varieties than other brands offer.
- The cardinal motivation to introduce the product classes based construction of a CBC study was to avoid
adaptive methods of interviewing such as ACA
- Adaptive Conjoint Analysis. The usual goal in marketing engineering is to asses potential of the
concepts embodying the intentions of the vendor as compared to the current products, and the reason for
differences. In adaptive approach, respondents tend to exclude undesirable levels in addition to those
completely unacceptable. This is in a direct contrast to the fact that real customers tolerate minor
disadvantages when the important properties are satisfying. An adaptive strategy tends to emphasize the
idealized wishes of the customers. The possibility to exclude certain levels of attributes before the actual
presentation and evaluation of concepts often leads to exclusion of certain groups of common products from the
evaluations, and, consequently, does not provide relevant data to answer the posed problem.
- The recently introduced ACBC
- Adaptive Choice-Based Conjoint (Sawtooth, Inc., 2009) is an adaptive method of a new generation.
Unfortunately, the author has no direct experience with it.