It\'s presented at ANZMAC 2010. This shows a simple way of analyzing large number of covariates (e.g., demographics) in discrete choice data.

1. Title Subtitle Detecting Attribute by Covariate interaction in discrete choice model THINK.CHANGE.DO ANZMAC 2010 – Christ Church, New Zealand, 30 November 2010 Kyuseop Kwak, Paul Wang, Jordan Louviere University of Technology Sydney

3. Identifying preference heterogeneity, e.g. segmentation, may require observable consumer characteristics or covariates

4. Online panel often provides more than 100 individual characteristics or covariates,

5. Of which many are categorical or nominally scaled, requiring more dummy coded variables  consumption of degrees of freedom

6. Thus, a systematic approach to screening important interactions of attribute by covariate is demanded2

8. 35 covariates: demographics, attitudes and opinions3

10. Discrete distribution (latent class, Kamakura and Russell 1989)

12. Concomitant latent class (Kamakura et al. 1994)

13. Interaction between attributes and covariates4

14. Proposed Approach to Identify Important Interactions Select cases where the option is chosen (y = 1) or simply weigh the stacked choice data using the dummy coded choice variable (y=1 or 0) Let each attribute be a dependent variable and other covariates such as demographics be independent variables Stage 1 Run a series of logistic regressions (i.e., unconditional logit) and identify significant covariates in the results Specify conditional logit choice model with main effects and interactions (attributes x covariates) identified in previous step Stage 2 5

16. Contingency table where each cell represents number of respondents who make choice, is a simple way of analysing the interaction effects

17. Assume there are 100 respondents and their preferences are equally distributedNO Interaction between Z and X Interaction between Z and X 6

18. Detecting Attribute by Covariate Interaction – Why it works 7

20. Assumed four attributes with three levels each (3^4) and five covariates

21. Varied sample sizes (100, 300, 600, 900 and 1200 individuals) and 9 choice sets per each individual

23. Calibrate three groups of models: (1) main effects only, (2) main + proposed interactions, and (3) full interactions

24. Compare model fit statistics across various sample sizes

25. Compare parameter recoveries (bias or error) with true parameter values8

26. Monte-Carlo Simulation: Attributes and Levels 9

27. Monte-Carlo Simulation: Five individual difference variables (covariates) r(G,A) = 0 r(G,I) = 0.4 r(G,E) = 0 r(G,D) = 0 Gender r(E,A) = 0 r(E,D) = 0.2 r(E,I) = 0.7 Education r(I,D) = 0.4 r(I,A) = 0.2 Income r(D,A) = 0.3 Deposit # Account Gender Education Income Deposit # Account 10

28. Monte-Carlo Simulation: Parameter Setup Attributes Note: ‘n.a.’ stands for ‘Not Applicable’, i.e., no parameter assumed in the simulation setup 11

29. Stage 1 - Unconditional Logit– Detecting interactions based on p-values Minimum Balance Check Fee Monthly Fee ATM Fee The performance depends on sample size as well as assumed effect size Highly continuous variables are relatively hard to be detected High correlations among covariates made detection harder 12

30. Stage 2 – Choice Model (Conditional Logit): Fit Statistics N=300 N=600 N=900 N=1200 Fit statistics of proposed model is very close to full interaction model HOWEVER, ‘BIC’ always picks the proposed model as the best 13

31. Stage 2 – Choice Model (Conditional Logit): Parameter Recovery (bias) Mean Absolute Error (MAE) Mean Absolute Percentage Error (MAPE) The models based on the proposed approach produce smaller biases across the samples 14

33. Actual effect sizes also influence the performance of the proposed approach

35. HOWEVER, Bayesian Information Criteria (BIC) supports the proposed model due to its parsimony

36. In addition, the proposed model produces consistent estimates and lower biases regardless of sample size15

38. New insights into modelling individual heterogeneity

39. More replication studies are needed using both simulated data and actual SP or RP data

40. More power analyses are required to fully understand the impact of sample size and effect size on the performance of the proposed approach

41. Explore different techniques such as CART, MARS, etc16

42. Thank you! Any Questions? 17

43. Stage 2 - Conditional Logit: Parameter Recovery (bias) Mean Error (ME) Duh!, The larger sample, the closer estimates Both produce equally consistent estimates 18