2025-05-20 using [comparing practice and final exam cld](https://claude.ai/chat/2a1d7a3f-3da0-4237-b3a3-3032d916186f) # 2025 Final Exam Last-Minute Cheatsheet | Question # | Key Rule/Formula to Remember | Module Connection | Concept Category | | ---------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------- | ------------------------------------------------ | | 1.1 | Sociodemographic variables (income, gender) must be normalized - can only appear in (n-1) utility functions | Module III | 14. Specification and estimation of logit models | | 1.2 | Omitted variable bias occurs when omitted variable correlates with included variables, violating exogeneity assumption where cov(x,e)!=0 - check for confounding factors | Module II | 9. Violations of OLS assumptions | | 1.3 | Exogenous sampling → no weights needed; <br>Endogenous sampling → always apply weights when using in real-world applications | Module IV | 17. Model estimation with sampling strategies | | 1.4 | LR test statistic = 2(LL_unrestricted - LL_restricted) and is ALWAYS non-negative | Module IV | 16. Statistical tests of model specification | | 1.5 | In nested logit, normalize ONE scale parameter (typically μ=1 at top level); others must satisfy μnest > μroot | Module III | 18. Nested logit models | | 1.6 | Bayesian with informative priors → smaller standard errors than MLE (tighter posterior distribution) | Module VI | 22. Bayesian estimation | | | | | | | 2.1 | FOC is necessary but not sufficient for max likelihood - local minima & saddle points also satisfy FOC | Module VI | 22. Likelihood functions & MLE | | 2.2 | For simulation-based estimation: Always use largest possible number of draws for consistent results | Module VI | 21. Simulation based estimations | | 2.3 | Logit mixture with alternative-specific error terms provides more flexibility than simple nested logit | Module III/VI | 20. Mixture models & 19. MEV models | | 2.4 | Different scales in RP/SP capture differences in variance of unobserved factors, NOT choice set differences | Module VI | 24. Combining RP and SP data | | 2.5 | Must have attributes for ALL alternatives (chosen + unchosen) to estimate discrete choice models | Module IV | 17. Data requirements | | | | | | | 3 | Discrete mixtures: P(choice) = π₁P₁ + π₂P₂ where π₁ + π₂ = 1; likelihood = product over all choices | Module VI | 20. Mixture models | | | | | | | 4(a-b) | Duplicating observations: Preserves coefficient estimates, reduces standard errors by factor of √2 | Module II | 6. Least squares regression | | 4(c) | Check for perfect multicollinearity when using transformed variables: ln(x²) = 2ln(x) | Module II | 9. Multicollinearity | | 4(d) | Time series data often violates independence and homoscedasticity assumptions | Module II | 9. Serial correlation & heteroscedasticity | | | | | | | 5(a) | To test gender effects: Add gender variable to utility function OR use market segmentation test | Module IV | 16. Testing group differences | | 5(b) | To test "don't care about cost": Filter data to specific segment, then test H₀: βcost = 0 | Module IV | 16. Testing sensitivities | | 5(c) | To test substitution patterns: Create nest for suspected alternatives, test if μnest ≠ 1 | Module III/IV | 18. Nested logit & correlation structures | | 5(d) | To test income effects: Create income×time interaction OR segment by income and compare | Module IV | 16. Testing interaction effects | **Remember:** - Identification requires normalization (ASCs, sociodemographics, scale parameters) - Always check for endogeneity, multicollinearity, and proper data structure - For hypothesis testing, identify if parameters are restricted, then use t-test or LR test - In nested logit, scale parameters must satisfy μnest > μroot for consistency with utility maximization