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 extremelylike 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 (lowhigh)– 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

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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 variableOR

Predictors = sensory attributes in place of PRODUCT

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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.

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Model 1: LC Regression model -- incorporates Discrete Random intercept and PRODUCT Effects

.( )i m t x m x tl o g i t Y

logit(Yj.k) is the adjacent category logit associated with

rating Y = m (vs. m-1) for product t

xt is the effect of the tth product for class x

1

0T

xtt

and effect coding is used for parameter identification:

where: latent classes x=1,2,… capture the random component

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Model 2: LC Regression with traditional (continuous) Random Intercept

.( )im t im xt

im m i

logit Y

F

Thus,

2

( )

( )

im m

im

E

V

logit(Yj.k) is the adjacent category logit associated with

rating Y = m (vs. m-1) for product t

C-Factor Fi is the factor score for the ith respondent

xt is the effect of the tth product for class x

1

0T

xtt

)1,0(~ NFi

and effect coding is used for parameter identification:

),(~ 2 mim Nor m = 2,3,…,M

where:

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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.