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Background

This case study compares LC Regression models with discrete and continuous random intercepts for estimating and comparing consumer liking ratings for different products. The results reveal segment differences in consumer preferences.

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  1. Background A new class of continuous factor (C-Factor) models have been proposed as a parsimonious alternative to HB for conjoint and choice modeling.

  2. Example • Products: 15 crackers • Consumers: n=157 (category users) • evaluated all products over three days • 9-point liking scale (dislike extremelylike extremely) • completely randomized block design balanced for the effects of day, serving position, and carry-over • Sensory attribute evaluations: trained sensory panel (n=8) • 18 flavor attributes, 20 texture attributes, 14 appearance rated on 15-point intensity scales (lowhigh) • reduced (via PCA) to four appearance, four flavor, and four texture factors

  3. Objectives • Consider the following simulation, with n = 157 cases. To estimate and compare alternative models • LC Regression model -- the latent classes provide a discrete random intercept and discrete random product effects • LC Regression model with a traditional continuous random intercept – a CFactor is used for the random intercept

  4. LC Regression Model • LC Regression (Latent GOLD 4.0) • liking rating for each product treated as ordinal • no scale adjustment for an individual’s average rating over all products (no adjustment for response level effects) • 2 segments identified using a LC regression model

  5. LC Regression Models Restructure the data for LC regression: • Dependent variable = overall liking of product 1,2,…,15 • T = 15 records (replications) per case • Predictor = nominal PRODUCT variable OR Predictors = sensory attributes in place of PRODUCT

  6. LC Regression Data Layout The data file is now restructured so that the dependent variable RATING can be predicted as a function of 1) PRODUCT or 2) the taste attributes.

  7. Model 1: LC Regression model -- incorporates Discrete Random intercept and PRODUCTEffects latent classes x=1,2,… capture the random component where: logit(Yj.k)is the adjacent category logit associated with rating Y= m (vs. m-1) for product t xtis the effect of thetth product for class x and effect coding is used for parameter identification:

  8. Model 2: LC Regression with traditional (continuous) Random Intercept Thus, where: logit(Yj.k)is the adjacent category logit associated with rating Y= m (vs. m-1) for product t C-FactorFiis the factor score for the ith respondent xtis the effect of thetth product for class x or m = 2,3,…,M and effect coding is used for parameter identification:

  9. Summary of Results • Model 2 provided clear evidence of segment differences in consumers’ liking ratings • While some products appealed to everybody, some products appealed much more to one segment than the other. • Similar to “centering,” LC Regression with a random intercept allowed for a cleaner separation of the overall level effect than standard LC regression.

  10. Acknowledgment The authors wish to thank The Kellogg Company for providing the data for this case study.

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