Applied Choice Analysis: A Primer

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Figures......Page 15
Tables......Page 20
Preface......Page 25
Part I Basic topics......Page 27
1 In the beginning......Page 29
2.2 Data......Page 34
Ordinal scaled data......Page 35
2.3 A note on mathematical notation......Page 36
2.3.1 Summation......Page 37
2.4 Probability......Page 38
2.4.1 Relative frequencies......Page 39
2.4.3 Probability distribution functions......Page 40
2.4.4 Cumulative distribution functions......Page 42
2.4.5 Multivariate probability density functions......Page 43
2.4.6 The multivariate probability function......Page 44
2.4.8 Conditional probability density functions......Page 47
2.5 Properties of random variables......Page 49
2.5.1 Expected value......Page 51
2.5.1.1 Properties of expected values......Page 52
2.5.2.1 Properties of variance......Page 54
2.5.3 Covariance......Page 56
2.5.3.1 Properties of covariance......Page 57
2.5.4 The variance–covariance matrix......Page 58
2.5.5 Correlation......Page 59
2.5.5.1 Properties of the correlation coefficient......Page 60
2.6.1 The sample mean......Page 62
2.6.3 The sample covariance......Page 64
2.7 Sampling error and sampling distributions......Page 65
2.8 Hypothesis testing......Page 67
2.8.1 Defining the null and alternative hypotheses......Page 68
2.8.2 Selecting the test-statistic......Page 70
2.8.3 Significance of the test and alpha......Page 71
2.8.5 Example hypothesis test: the one sample t-test......Page 77
2.9 Matrix algebra......Page 78
2.9.2 Matrix addition and subtraction......Page 79
2.9.4 Matrix multiplication......Page 80
2.9.5 Determinants of matrices......Page 81
2.9.6 The identity matrix......Page 82
2.9.7 The inverse of a matrix......Page 83
2.9.8 Linear and quadratic forms......Page 84
Appendix 2A Measures of correlation or similarity......Page 85
3.1 Introduction......Page 88
3.2 Individuals have preferences, and they count......Page 89
3.3 Using knowledge of preferences and constraints in choice analysis......Page 97
3.4 Setting up a behavioral choice rule......Page 100
3.5 Deriving a basic choice model......Page 108
3.6 Concluding overview......Page 112
4.1 Introduction......Page 114
4.2 Data consistent with choice......Page 115
Embodiment of constraints......Page 118
Attribute-level invariance......Page 119
Non-chosen alternatives......Page 120
4.3.1 Choice-based sampling......Page 121
Hypothetical scenarios......Page 122
4.5 Further comparisons......Page 123
4.7 Socio-demographic characteristic data......Page 124
5.2 What is an experimental design?......Page 126
5.2.1 Stage 1: problem definition refinement......Page 129
5.2.2.1 Refining the list of alternatives......Page 130
5.2.2.2 Refining the list of attributes and attribute levels......Page 131
5.2.3 Stage 3: experimental design considerations......Page 135
5.2.3.1 Labeled versus unlabeled experiments......Page 138
5.2.3.2 Reducing the number of levels......Page 140
5.2.3.3 Reducing the size of experimental designs......Page 141
5.2.3.4 Dummy and effects coding......Page 145
5.2.3.5 Calculating the degrees of freedom required......Page 148
5.2.3.6 Blocking the design......Page 152
5.2.4 Stage 4: generating experimental designs......Page 153
5.2.4.1 Assigning an attribute as a blocking variable......Page 156
5.2.5 Stage 5: allocating attributes to design columns......Page 157
5.3 A note on unlabeled experimental designs......Page 176
5.4 Optimal designs......Page 178
Appendix 5A Designing nested attributes......Page 180
Appendix 5B Assignment of quantitative attribute-level labels......Page 182
6.2 General survey instrument construction......Page 187
6.3.1 Stage 6: generation of choice sets......Page 192
6.3.2 Stage 7: randomizing choice sets......Page 196
6.3.3 Stage 8: survey construction......Page 198
6.3.3.1 Choice context......Page 199
6.3.3.3 Independence of choice sets......Page 200
6.3.3.4 More than one choice......Page 201
6.3.3.5 The no-choice or delay-choice alternative......Page 202
6.5 Studies involving both RP and SP data......Page 203
6.6 Using RP data in SP experiments: the \"current alternative\"......Page 204
6.7 Sampling for choice data: the theory......Page 210
6.7.1 Simple random samples......Page 211
6.7.2 Stratified random sampling......Page 216
6.7.3 Conclusion to the theory of calculating sample sizes......Page 218
6.8 Sampling for choice data: the reality......Page 219
7.2.1 About NLOGIT......Page 223
7.3.2 Inputting the data......Page 224
7.3.4 The project file......Page 226
7.4 Using NLOGIT......Page 227
7.5.1 Using the Text Editor......Page 228
VERB; other information…$......Page 230
(3) New variables......Page 231
7.6 Useful hints and tips......Page 232
7.7 NLOGIT software......Page 233
Introduction......Page 234
Discrete choice (CLOGIT) and NLOGIT errors......Page 235
8.1 Introduction......Page 244
8.2 The basic data setup......Page 245
8.2.2 Handling data on the non-chosen alternative in RP data......Page 248
8.2.3 Combining sources of data......Page 250
8.2.4 Weighting on an exogenous variable......Page 252
8.2.5 Handling rejection: the \"no option\"......Page 253
8.3.1 Entering data directly into NLOGIT......Page 256
8.3.3 Reading data into NLOGIT......Page 258
8.3.5 Saving data sets......Page 261
8.3.6.1 Changing the maximum default size of the Data Editor......Page 262
8.4 Data entered into a single line......Page 263
8.5 Data cleaning......Page 267
8.5.1 Testing for multicollinearity using NLOGIT......Page 272
Appendix 8A Design effects coding......Page 274
Appendix 8B Converting single-line data commands......Page 276
9.2 Study objectives......Page 280
9.3 The pilot study......Page 282
9.3.1.1 Interviewer briefing......Page 289
9.3.1.3 Analysis of contacts......Page 290
9.4 The main survey......Page 291
9.4.1 The mode-choice experiment......Page 293
fuel cost (per day)......Page 300
return fare......Page 301
9.4.2 RP data......Page 302
9.4.4 The commuter questionnaire......Page 303
9.4.5 The sample......Page 304
9.4.5.1 Screening respondents......Page 308
9.4.5.4 Analysis of total contacts......Page 309
9.4.5.6 Coding and check edit......Page 310
9.5 The case study data......Page 312
9.5.1 Formatting data in NLOGIT......Page 315
9.5.2 Getting to know and cleaning the data......Page 318
Appendix 9A The contextual statement associated with the travel choice experiment......Page 322
Appendix 9B Mode-choice case study data dictionary......Page 324
Appendix 9C Mode-choice case study variable labels......Page 328
10.2 Modeling choice in NLOGIT: the MNL command......Page 334
10.3 Interpreting the MNL model output......Page 342
10.3.1 Maximum likelihood estimation......Page 343
10.3.2 Determining the sample size and weighting criteria used......Page 349
10.3.3 Interpreting the number of iterations to model convergence......Page 350
10.3.4 Determining overall model significance......Page 352
10.3.5 Comparing two models......Page 361
10.3.6 Determining model fit: the pseudo-R......Page 363
10.3.8 Obtaining estimates of the indirect utility functions......Page 365
10.3.8.1 Matrix: LastDsta/LastOutput......Page 369
10.4 Interpreting parameters for effects and dummy coded variables......Page 370
10.5 Handling interactions in choice models......Page 378
10.6 Measures of willingness to pay......Page 383
10.7 Obtaining choice probabilities for the sample......Page 386
10.8 Obtaining the utility estimates for the sample......Page 392
Appendix 10A Handling unlabeled experiments......Page 397
11.1 Introduction......Page 400
11.2.1 Show......Page 401
11.2.2 Descriptives......Page 404
11.2.3 Crosstab......Page 407
11.3 Adding to our understanding of the model parameters......Page 409
11.3.1 ;Effects: elasticities......Page 410
11.3.2 Calculating arc elasticities......Page 418
11.3.3 ;Effects: marginal effects......Page 419
11.4 Simulation......Page 425
11.4.1 Marginal effects for categorical coded variables......Page 433
11.4.2 Reporting marginal effects......Page 437
11.5.1 Endogenous weighting......Page 439
11.5.2 Weighting on an exogenous variable......Page 444
11.6 Calibrating the alternative-specific constants of choice models estimated on SP data......Page 446
11.6.1 Example (1) (the market shares of all alternatives are known a priori)......Page 449
11.6.2 Example (2) (the market shares for some alternatives are unknown)......Page 450
Step 1......Page 452
Step 3......Page 453
Step 4......Page 454
Step 5......Page 456
Step 6......Page 457
Step 8......Page 458
12.1 Introduction......Page 463
12.2 Calibration of a choice model for base and forecast years......Page 464
12.3 Designing a population data base: synthetic observations......Page 465
12.4 The concept of synthetic households......Page 466
12.4.1 Synthetic households\' generation framework......Page 467
12.5 The population profiler......Page 469
12.5.1 The synthetic household specification......Page 470
12.6 The sample profiler......Page 474
12.7 Establishing attribute levels associated with choice alternatives in the base year and in a forecast year......Page 477
12.8 Bringing the components together in the application phase......Page 478
12.9 Developing a decision support system......Page 479
12.9.1 Using the data sample averages in creating the DSS......Page 481
12.9.2 Using the choice data in creating the DSS......Page 487
12.9.3 Improving the look of the DSS......Page 498
12.10 Conclusion......Page 501
Part II Advanced topics......Page 503
13.1 Introduction......Page 505
13.2 Moving away from IID between all alternatives......Page 507
13.3 Setting out the key relationships for establishing a nested logit model......Page 508
13.4 The importance of a behaviorally meaningful linkage mechanism between the branches on a nested structure......Page 512
13.5 The scale parameter......Page 513
13.6 Bounded range for the IV parameter......Page 516
13.7 Searching for the \"best\" tree structure......Page 520
Appendix 13A: Technical details of the Nested Logit Model......Page 521
Level 1 (Elemental alternative)......Page 522
RU1 (normalize mu( j Ιi,l) = 1)......Page 523
RU2 (normalizeτ(l)=1)......Page 525
Level 2 (Branch)......Page 526
RU1 (normalize mu( j Ιi,l) = 1)......Page 527
RU2 (normalizeτ(l) = 1)......Page 530
Level 3 (Limb)......Page 532
RU1 (normalize mu( j Ιi,l) = 1)......Page 533
RU2 (normalize Tau(l) = 1)......Page 535
Level 4 (Trunk)......Page 536
RU1 (normalize mu( j Ιi,l) = 1)......Page 537
RU2 (normalize Tau(I) = 1)......Page 539
The PCS......Page 541
14.1 Introduction......Page 544
14.2 The Hausman-test of the IIA assumption......Page 545
14.3 The nested logit model commands......Page 556
14.3.1 Normalizing and constraining IV parameters......Page 560
14.3.3 Specifying start values for the NL model......Page 564
14.3.4 A quick review of the NL model......Page 565
14.4 Estimating an NL model and interpreting the output......Page 567
14.4.1 Estimating the probabilities of a two-level NL model......Page 575
14.4.2 Comparing RU1 to RU2......Page 582
14.5 Specifying utility functions at higher levels of the NL tree......Page 590
14.6 Handling degenerate branches in NL models......Page 596
14.7 Three-level NL models......Page 600
14.8 Searching for the best NL tree structure: the degenerate nested logit......Page 603
14.9 Combining sources of data: SP-RP......Page 606
14.10 Additional commands......Page 618
Appendix 14A: The Hausman-test of the IIA assumption for models with alternative-specific parameter estimates......Page 621
Level 2......Page 627
Level 3......Page 628
Marginal probabilities......Page 630
15.1 Introduction......Page 631
15.2 Mixed logit choice models......Page 632
15.3 Conditional distribution for sub-populations with common choices......Page 636
15.4.1 Selecting the random parameters......Page 637
Uniform distribution......Page 638
Lognormal distribution......Page 639
15.4.4 Selecting the number of points for the simulations......Page 640
15.4.5 Preference heterogeneity around the mean of a random parameter......Page 642
15.4.6 Accounting for observations drawn from the same individual correlated choice situations......Page 643
15.4.7 Accounting for correlation between parameters......Page 645
15.5 Willingness-to-pay challenges......Page 646
15.6 Conclusions......Page 647
16.2 The mixed logit model basic commands......Page 649
16.3 NLOGIT output: interpreting the mixed logit model......Page 653
16.4 How can we use random parameter estimates?......Page 661
16.4.1 A note on using the lognormal distribution......Page 667
16.5 Imposing constraints on a distribution......Page 671
16.6 Revealing preference heterogeneity around the mean of a random parameter......Page 676
16.6.1 Using the non-stochastic distribution......Page 682
16.6.2 Handling insignificant heterogeneity around the mean parameter estimates......Page 687
16.7 Correlated parameters......Page 693
16.8 Common-choice-specific parameter estimates: conditional parameters......Page 705
16.9 Presenting the distributional outputs graphically using a kernel density estimator......Page 710
16.10 Willingness-to-pay issues and the mixed logit model......Page 712
General statistical terms......Page 721
References......Page 736
Index......Page 740