Lecture 3

Question 1

Assessment of Model fit

Answer 1

Compare to null model
Compare two models, e.g. :
- one where price is linear
- one where price is part-worth
Goodness of fit:
- Pseudo-R2

Question 2

Likelihood ratio test

Answer 2

• H0 = No differences between models
• Test statistic: Chisq = −2(LL(0) − LL(B))
- Check for significane

Question 3

Goodness of Fit: Pseudo-R2

Answer 3

R2 = 1 - (LL(B)/LL(0))
R2adj = 1 - (LL(B) - nparameters) /LL(0))
› Can be quite small, usually 0.2 to 0.4 can be considered acceptable
› Different interpretation than R2 in linear regression models

Question 4

Relative Attribute Importance

Answer 4

Measure of how much influence each attribute has on people’s choices
- Range of attribute / sum of all attribute ranges

Question 5

Willingness-to-Pay (WTP)

Answer 5

• Requires linear model for price attribute
• Utility of attribute / price coef.
• Calculate for both attributes, calculate range and that is your willingness to pay

Question 6

WTP Limitations

Answer 6

• When respondents are not price sensitive (price vector = 0)
• When respondents react positively to price increases
• When extrapolating to prices that were not in the conjoint design

Question 7

Drawbacks of the Logit Model

Answer 7

Assumes Independence of Irrelevant Alternatives (IIA; “Red Bus / Blue Bus Problem”)
› Aggregate-level, “average” preferences, no preference heterogeneity across consumers

• Latent Class Analysis: Preference Segmentation
• Hierarchical Bayes Analysis: Individual preferences

Question 8

Preference heterogeneity

Answer 8

People have different preferences

Question 9

Finite Mixture (Latent Class): Segment-level

Answer 9

§ Assumption of homogenous segments

§ Respondents j are allocated to segments i with certain probability (pij)

Question 10

Latent Class Analysis (1/2)

Answer 10

› Assumes that the consumers belong to segments
› The mixing distribution f(β) is discrete, i.e., β can take a finite set of distinct values
› Suppose there are M segments that differ in preferences: β1, …, βM
› Consumer n belongs to each segment with a certain probability smn
àSegments are “latent”

Question 11

Latent Class Analysis (2/2)

Answer 11

› “Optimal” number of segments...
• not known prior to the analysis
• not retrieved by the estimation method
› Solution:
• Estimate models for several number of segments
• Find best fit according to
• Log-likelihood-based measures, e.g., information criteria • Classification error
• Interpretability