Detecting Attributes and Covariates Interaction in Discrete Choice Model
- 1. TitleSubtitleDetecting Attribute by Covariate interaction in discrete choice modelTHINK.CHANGE.DOANZMAC 2010 – Christ Church, New Zealand, 30 November 2010Kyuseop Kwak, Paul Wang, Jordan LouviereUniversity of Technology Sydney
- 2. Motivation of the researchDiscrete Choice Model based on Discrete Choice Experiment (DCE) is used widely in studying people’s choice behaviours in various context (Louviere et al 2000)
- 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
- 7. Example DCE data: Carbon Trading SchemeCarbon trading scheme Discrete Choice Experiment (DCE) dataFive attributes: (1) starting years, (2) redistribution of tax, (3) exemption of transport sector, (4) R&D investment, and (5) special treatment for energy intensive sector
- 8. 35 covariates: demographics, attitudes and opinions3
- 9. Modelling Preference HeterogeneityUnobserved Heterogeneity ModellingContinuous distribution (mixed logit, Train 2002; Hierarchical Bayes, Rossi and Allenby 2003)
- 10. Discrete distribution (latent class, Kamakura and Russell 1989)
- 11. Managerially not very helpfulObserved Heterogeneity ModellingCovariates such as demographics and other consumer characteristics may explain individual heterogeneity and are often managerially relevant
- 12. Concomitant latent class (Kamakura et al. 1994)
- 13. Interaction between attributes and covariates4
- 14. Proposed Approach to Identify Important InteractionsSelect 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 variablesStage 1Run a series of logistic regressions (i.e., unconditional logit) andidentify significant covariates in the resultsSpecify conditional logit choice model with main effects andinteractions (attributes x covariates) identified in previous stepStage 25
- 15. Detecting Attribute by Covariate Interaction – Why it worksSuppose a simple binary choice, i.e., y = 0 or 1, with a single binary attribute, i.e., X = -1 or 1, and a single binary covariate, i.e., Z = -1 or 1
- 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 XInteraction between Z and X6
- 18. Detecting Attribute by Covariate Interaction – Why it works7
- 19. Empirical StudyMonte-Carlo SimulationBased upon banking choice data (Kamakura and Wedel 1994)
- 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
- 22. Effect sizes (parameters) of both main and Interactions were manipulatedProposed approach versus Full Interaction ModelIdentify important interactions suggested by proposed approach
- 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 Levels9
- 27. Monte-Carlo Simulation: Five individual difference variables (covariates)r(G,A) = 0r(G,I) = 0.4r(G,E) = 0r(G,D) = 0Genderr(E,A) = 0r(E,D) = 0.2r(E,I) = 0.7Educationr(I,D) = 0.4r(I,A) = 0.2Incomer(D,A) = 0.3Deposit# AccountGenderEducationIncomeDeposit# Account10
- 28. Monte-Carlo Simulation: Parameter SetupAttributesNote: ‘n.a.’ stands for ‘Not Applicable’, i.e., no parameter assumed in the simulation setup11
- 29. Stage 1 - Unconditional Logit– Detecting interactions based on p-values Minimum BalanceCheck FeeMonthly FeeATM FeeThe performance depends on sample size as well as assumed effect sizeHighly continuous variables are relatively hard to be detectedHigh correlations among covariates made detection harder12
- 30. Stage 2 – Choice Model (Conditional Logit): Fit StatisticsN=300N=600N=900N=1200Fit statistics of proposed model is very close to full interaction modelHOWEVER, ‘BIC’ always picks the proposed model as the best13
- 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 samples14
- 32. Summary of findings and DiscussionsStage 1 - Unconditional logit: Sensitivity to sample size and effect sizeThe larger the sample size is, the better performance in general due to low S.E.
- 33. Actual effect sizes also influence the performance of the proposed approach
- 34. Correlations among covariates also play a role conduct factor analysis first to make variables independentStage 2 - Conditional logit: Fit statistics versus Parameter BiasFit statistics are very close between proposed and full interaction model
- 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
- 37. ConclusionsA novel quick & easy approach
- 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
- 43. Stage 2 - Conditional Logit: Parameter Recovery (bias)Mean Error (ME)Duh!, The larger sample, the closer estimatesBoth produce equally consistent estimates18