Appendix D: How the Simulator Uses Latent Class Data

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Sawtooth Software provides Latent Class analysis routines as part of our CBC System for Choice-Based Conjoint.  With Latent Class, rather than computing a set of part-worths (utilities) for each respondent, the algorithm finds groups of respondents with similar preferences and estimates average part-worths within these segments.


As when using cluster analysis, the Latent Class analyst specifies how many groups to use in the segmentation.  In contrast to cluster analysis, respondents are not assigned to different segments in a discrete (all-or-nothing) manner under Latent Class analysis, but have probabilities of membership in each segment that sum to unity.  The sum of the probabilities of membership across respondents for each group defines the total weight (class size) of that segment.


One can conduct overall market simulations with Latent Class results by computing shares of preference within each segment and taking the weighted average of these shares across segments.  This is the approach used in Sawtooth Software's Latent Class Simulator in version 1 of the software (LSIM.EXE) which was used in the 1990s.  


Another way to use Latent Class data is to convert the segment-based results into pseudo individual-level estimates.  While these estimates are not as accurate at characterizing respondent preferences as Hierarchical Bayes analysis (especially if using low-dimensionality solutions, such as eight classes or fewer), they are an appropriate extension of the Latent Class model.


The Market Simulator converts the group-based Latent Class part-worths into individual-level part-worths in the following way: For each respondent, a weighted combination of the group part-worth vectors is computed, where the weights are each respondent's probabilities of membership in each group.


Converting the Latent Class utilities to individual-level part-worths provides added flexibility for market simulations.  It lets the analyst apply segmentation variables as filters, banner points or weights without requiring that a new Latent Class solution be computed each time.


However, creating individual-level utilities from a segment-based solution slightly alters the results when comparing the output of Sawtooth Software's Latent Class module to the same data used within the Market Simulator.  While the overall shares of preference for the market are nearly identical, the within-class results reported in the Market Simulator output are slightly less differentiated between segments (pulled toward the overall market mean).  That is because for the purpose of banner points and filters, the Market Simulator assigns respondents fully into the latent class for which they have the greatest probability of membership.  For example, consider a respondent whose preferences are characterized as 80% like group 1 and 20% like group 2.  His contribution to the mean values reported in the group 1 column (banner point) includes some group 2 tendencies.


The differences between the within-class means reported by Latent Class and the Market Simulator are not usually very great since respondents' probabilities of membership in classes usually tend toward zero or one.  The smoothing that occurs when reporting the by-segment results in the Market Simulator will probably not substantially change your interpretation of the results.


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