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

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

9. 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. 10 Acknowledgment The authors wish to thank The Kellogg Company for providing the data for this case study.