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LCA - Latent Class Analysis

 

 

 

Segmenting for success in both consumer and B2B markets means going beyond traditional segmenting variables, such as demographics or company type, and focusing on needs, attitudes and lifestyle.

[Erika Bruhn, Sawtooth Technologies Consulting]

 

Problem

As consumer diversity is increasing firms have sought to differentiate their products relative to both customers and competitors. Segmenting customers with similar needs and responses into groups provides a way of disaggregating markets into targets that can be served more profitably through advertising, positioning, placement and other generally oriented ways.

The most common segmentation bases are demographics (socioeconomic characteristics, usage habits), psycho-graphics (personality, attitudes, opinions, life style) and benefits sought, often obtained from MR. It is known that the statements obtained from isolated questions presented to respondents one by one often reflect self-perceptions of the individuals rather than the attitudes influencing actual behavior. Differences in evaluations of product features are smoothed out as nearly every aspect becomes important when evaluated separately. Therefore a segmentation based on direct questioning is often rather diffuse, and location of the really important aspects is misty.

When a future behavior is concerned, people have tendency to give answers they think they should give, often for the simple reason to be polite. Bias in stated preferences to more expensive and higher quality products compared to the reality is common . 


Solution

An experimental type of interviewing carried out in the competitive context has proved to provide more reliable stated preferences and a sharper picture of the differences between various cognitive and perceptual aspects. This is supported by the observation that items chosen in a simulated experiment or simply from a selection of possible characteristics are often in disagreement with the hypothetical choices inferred from the statements about personal preferences derived from isolated questions asked in the same interview. 

A typical experiment in a MR interview is realized as a number of choices from selections. When the selections are made of representative products or their profiles composed of attributes, the method is a variant of a CBC - Choice Based Conjoint or SCE - Sequential Choice Exercise method. When the selections are constructed as batteries of pre-declared statements from which the respondent selects the one or a small number of the most appropriate ones conditional to the asked question, the choices will be from a multinomial distribution and can be analyzed with the tools of log-lin analysis.

There is a general belief that simulated experiments will give a better view of endogenous factors entering future markets than predictions bases on historic data. This is attributed to the fact that any market data are backward looking while data from a research experiment are forward looking. Behavior of targets is changing with changing experience, needs and expectations. With these ideas on mind we have added LCA ? Latent Class Analysis of choice experiments to our portfolio of market research methods.

 

A flash review of LCA

As the simplest possible case, all the available data from a market research study can be separated into two basic sets. The first set X is made of the descriptive variables, called exogenous, that do not directly express the possible behavior of the individuals. The classical segmentation variables such as demographics belong to this set. The variables in the second set Y, called endogenous, are directly expressing the actual or expected behavior, or are indirectly bound to it in some way. This set is typically composed of subjective statements, choices from statement batteries, events (choices) on the real or simulated market, etc. While the number of variables in both groups can be quite high, only a limited number of marketing strategies, each for some behavioral segment of consumers, can be developed. The segments obtained with LCA are called latent classes that make the set L. There are two basic tasks to be done:

  1. Identification of reasonable behavioral latent classes L of individuals based on the behavioral variables Y.
  2. Finding a way, based on the known set of exogenous (descriptive) variables X, to assign the most probable latent class to an individual (e.g. if direct marketing is of concern).
The two tasks can be formally described using the symbol ? for causal ordering by the following scheme:

X ? L ? Y

In the actual estimation, the causal orderings, e.g. L ? Y, are replaced by the respective conditional probability densities, e.i. (Y|L). Not a fully exact but useful notion of the estimation process is a regression of the "dependent" variables from the set Y on the set L of latent variables and, at the same time, regression of the latent variables from the set L on the "independent" variables from the set X so that the total density (L|X)×(Y|L) is maximized.

The simplest type of analysis is solving for just the causal ordering L ? Y for an unknown set L of multinomial class variables. The solution is analogous to the dimension reduction of a set of linear continuous variables. The important difference is the levels of variables in the set L represent discrete, mutually exclusive latent classes of individuals.

It is quite common to consider only one multinomial variable in the set L. Then the causal ordering X ? L can be solved as a multinomial regression of L on the variables from the set X . This procedure is known as segment profiling.

When both causal orderings in X ? L ? Y are solved in one estimation step, the variables in the set X are called concomitant variables. This approach is known as log-linear path modeling for categorical variables, and is analogous to structural equation modeling of linear continuous variables (LISREL). In our experience this technique is worth of trying but fails when the set X is structurally dominant and the set Y diffuse which leads to trivial classes induced mostly by the set X. In such a case the independent segment profiling is the preferred procedure.

Conjoint analysis is one of the most efficient sources of behavioral data, namely in the forward-looking context. The set U of the profile utilities in the choice sets implicates the set C of choices. When the set Y in the latent class model L ? Y is replaced by the causal ordering U ? C , the model

L ? U ? C

is obtained. It is implemented in the commercial software CBC Latent Class Module of Sawtooth, Inc. As the software does not have capability to include concomitant variables only the successive segment profiling by multinomial regression can be used.

 

LCA properties

LCA is based on maximization of the total probability of the observations over the subjects belonging to a distinct class. This distinguishes LCA from other clustering methods.
  • LCA is especially useful for discrete (dichotomous, multinomial and choice) data. 
  • Both discrete and metric data can enter an LCA analysis.
  • With continuous data, LCA is principally independent from scaling of the analyzed variables. The clustering criterion is less arbitrary than that of any metric distance based clustering method. 
  • LCA is markedly insensitive to unimportant variables that are ignored by principle. The most influential features that make differences between the classes are revealed.
  • If the data are behavioral, LCA provides insight into behavioral classes (segments) and their sizes.
  • Interpretation of latent classes is usually simple. It is based on influences of the stimuli as projected onto the observations that were brought about by them. 
  • LCA is not a hierarchical method. Any two solutions for a different number classes are independent. However, when the number of classes is increased by one, LCA has often a tendency to generate a new class by partitioning one of the previous classes into two (see examples below). The obtained structure of clustering is thus close to a hierarchical one. This property is found only rarely with metric distance based clustering techniques. In contrast, hierarchical segmentation methods lead to hierarchical dendrograms that have too many branches and are difficult to read.
  • Constraints can be imposed on the model parameters to obtain more parsimony so important for an interpretation. Application of constraints in metric segmentation models is difficult if at all possible.
  • The distinct advantage of LCA is that all effects from all variables are projected on the same scale and can be compared.

The knowledge of membership of an individual to a behavior-based segment can be an asset in efficient addressing him or her as a potential decision maker (buyer, contributor, voter, etc.). If the future behavior is embodied in historic data for individuals the latent classes can be derived from such data. At the same time, exogenous variables can be used as concomitant variables and make the identification more precise. In this way the behavioral class membership can be predicted from readily available data, e.g. from a client database. The typical use is in the direct marketing. In case of a general marketing problem it is supposed the segment profiling of the forward-looking data from a MR study should be utilized.

Unfortunately, there is no universal method for finding the most appropriate set of latent classes and a way of assignment of an individual to the appropriate class. The problem is strongly "analyst dependent".

As aside

Example: Acquirement benefit set

The data of this example are those used in the MXD - Maximum Difference Scaling example. Discrimination between segments of potential users is quite stable. The segment of "Discount seekers" in two-segment solution (36 %) has lost only 6 % in five-segment solution. The composed segments of "Download seekers and photo hobbyists" and "SW Users and security seekers" split very cleanly. The found percentages might be useful for a refinement of the optimal portfolio example based on the identical source data.

Example of LCA-based segmentation of MXD data

As aside

Example: CBC of tariff benefits

The data for this example come from a commercial CBC study of a particular type of mobile telecommunication tariff benefits.

The segments in this example have mostly arisen from price sensitivities to the service rates and avidness for free benefits. As a surprising fact we had to accept an unexpectedly high number of SMS users who were distinctly more benefit sensitive than other users. Again, the segments are very stable in respect to the number of segments in the solution. We leave out the detailed explanation of the segment labels for apparent reasons.

Example of LCA-based segmentation

An additional tabular and/or graphic presentation of attribute projections onto the identified consumer classes (a cross-tabulation, not shown here) is a standard for a successful interpretation of the analysis.

 

Segment profiling

Next to a (hopefully successful) segmentation the question arises who the targets are and how to find them. For a targeted marketing effort it is desirable to have means for prediction of the segment an individual belongs to. As the segments are disjunctive a suitable tool may be based on multinomial regression of the segments on some available data on the individuals. The data may typically reflect attitudes, perceptions, usage, previous actions, demographics etc. This technique is known as segment profiling.

It is very hard to predict prior the study if the analysis will give usable results. The success or failure depends on the relevancy of the data in the available database. In our experience, the results lie between the two extremes.
  • The result is so clear that it is trivial.
    Preferences of local beers by local customers, food surrogates by low incomers, bank product options by long-term customers of the bank, brands by users of the brand, etc. may serve as examples.
  • There is no significant relationship between the segments and the database variables.
    Such a result should be taken positively provided the underlying data from both sides (concomitant and behavioral variables) are informative and reliable. There may be two basic reasons.
    • The targets are spread in the population evenly. An effort to address different targets in a different way would be a loss of resources.
    • The concomitant variables are not those that are effective. They should be replaced by some other ones.

In practice, the results lie in between the extremes. The analysis can tell which variables are useful, which are not and might be omitted, and which additional variables, if available in the study, should be added to the standard collection.

Example: Leaflet stationery

A financial institution decided to introduce new leaflet formats for informing regular clients about new products. With SCE - Sequential Choice Exercise as the interviewing procedure and LCA by LEM from LEM software as the analytical method, we ascertained the most promising leaflet formats for three identifiable classes of clients making about 60% of the total. The identification could be made on 4 readily available variables. The average likelihood of the generalized statement based on "would read it", "would be interested in", etc., was two to three times higher compared to sending leaflets in a format selected randomly.


Latent classes of items

While LCA is most often used to classify targets it can be also used to classify items such as brands, companies, locations, etc. Usage and attitude studies often rely on discrete single (radio button) or multiple (check-box) response based questionsorganized into batteries. The answers are direct candidates for a DCM-based analysis. Data from Likert scale questions can be used "as is", i.e. as linear level values, or, preferably, transformed to a discrete choice format using the rank-explosion rule.The inherent non-linearity of the scale is thus avoided.

Vector based perceptual mapping systems such as Sawtooth Software CPM (Composite Product Mapping) use projection of perceptions on vector components. Usually two components are used so that the complex relationships can be distilled into a single two-dimensional picture (a perceptual map) that conveys the insights. In contrast, LCA produces several classes that have indeterminate orientation in the space. LCA searches for the differences between groups of the items rather than between individual items. As a rule of thumb, a product belongs mostly to a single class, and only rarely to more than two neighboring classes. The classes can be taken for vectors, and the items visualized in a single picture by averaging their probabilities of membership in the classes.

Example: Potato chips (crisps)

Five classes of potato chips (crisps) were identified as optimal. The size of bubbles is only half of the actual overlay size of the classification (the full size of the bubbles would make the picture unclear). Position of a brand can reach at most the circle encompassing the ends of the coordinates (not shown) that represent the "clean" classes and can be understood as class archetypes. In this particular case, no brand of chips is commonly perceived as being for young or wise, or having an image of unmatched quality. The perceptions are uniquely personal and user dependent, but on average, most of the brands are perceived as "simply chips at a leisure time".

LCA map of chips

The classification has been done using 7 perception batteries. Projection of the perceptions into the classes can give a picture of the perception associations related to the classes. Projections of one of the batteries onto the five extracted classes is in the picture below.

LCA Chips Dimensions

It is clearly seen that the terms "innovative" or "matchless" do not add to discrimination between the product classes.

As aside

 

Rev. 2013-11-07