Applied choice analysis:
Gespeichert in:
Hauptverfasser: | , , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2015
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Ausgabe: | 2. ed. |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Includes bibliographical references and index |
Beschreibung: | XXX, 1188 S. Ill., graph. Darst. |
ISBN: | 9781107465923 9781107092648 |
Internformat
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245 | 1 | 0 | |a Applied choice analysis |c David A. Hensher ; John M. Rose ; William H. Greene |
250 | |a 2. ed. | ||
264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2015 | |
300 | |a XXX, 1188 S. |b Ill., graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
500 | |a Includes bibliographical references and index | ||
650 | 4 | |a Decision making / Mathematical models | |
650 | 4 | |a Probabilities / Mathematical models | |
650 | 4 | |a Choice | |
650 | 4 | |a Mathematisches Modell | |
650 | 0 | 7 | |a Statistische Entscheidungstheorie |0 (DE-588)4077850-2 |2 gnd |9 rswk-swf |
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700 | 1 | |a Rose, John M. |e Verfasser |0 (DE-588)130335355 |4 aut | |
700 | 1 | |a Greene, William |d 1951- |e Verfasser |0 (DE-588)124700551 |4 aut | |
776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-316-13623-2 |
856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027674278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
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adam_text | Contents
List ojfgures page xvii
Listoftables xxii
Preface xxix
Part I Getting started i
1 In the beginning З
1.1 Choosing as a common event 3
1.2 A brief history of choice modeling 6
1.3 The journey ahead 11
2 Choosing 16
2.1 Introduction 16
2.2 Individuals have preferences and they count 17
2.3 Using knowledge of preferences and constraints in choice analysis 27
3 Choice and utility 30
3.1 Introduction 30
3.2 Some background before getting started 32
3.3 Introduction to utility 45
3.4 The observed component of utility 48
3.4.1 Generic versus alternative-specific parameter estimates 49
3.4.2 Alternative-specific constants 51
3.4.3 Status quo and no choice alternatives 53
3.4.4 Characteristics of respondents and contextual effects in
discrete choice models 54
3.4.5 Attribute transformations and non-linear attributes 57
3.4.6 Non-linear parameter utility specifications 71
3.4.7 Taste heterogeneity 75
76
76
78
80
80
81
83
86
87
93
98
98
100
101
102
104
105
106
108
109
110
112
114
116
117
117
117
126
133
136
138
145
147
148
150
Contents
Concluding comments
Appendix ЗА: Simulated data
Appendix 3B: Nlogit syntax
Families of discrete choice models
Introduction
Modeling utility
The unobserved component of utility
Random utility models
4.4.1 Probit models based on the multivariate normal
distribution
4.4.2 Logit models based on the multivariate Extreme value
distribution
4.4.3 Probit versus logit
Extensions of the basic logit model
4.5.1 Heteroskedasticity
4.5.2 A multiplicative errors model
The nested logit model
4.6.1 Correlation and the nested logit model
4.6.2 The covariance heterogeneity logit model
Mixed (random parameters) logit model
4.7.1 Cross-sectional and panel mixed multinomial logit models
4.7.2 Error components model
Generalized mixed logit
4.8.1 Models estimated in willingness to pay space
The latent class model
Concluding remarks
Estimating discrete choice models
Introduction
Maximum likelihood estimation
Simulated maximum likelihood
Drawing from densities
5.4.1 Pseudo-random Monte Carlo simulation
5.4.2 Halton sequences
5.4.3 Random Halton sequences
5.4.4 Shuffled Halton sequences
5.4.5 Modified Latin Hypercube sampling
5.4.6 Sobol sequences
vfi Contents
5.4.7 Antithetic sequences 153
5.4.8 PMC and QMC rates of convergence 155
5.5 Correlation and drawing from densities 157
5.6 Calculating choice probabilities for models without a closed
analytical form 166
5.6.1 Probit choice probabilities 166
5.7 Estimation algorithms 176
5.7.1 Gradient, Hessian and Information matrices 176
5.7.2 Direction, step-length and model convergence 180
5.7.3 Newton-Raphson algorithm 183
5.7.4 BHHH algorithm 184
5.7.5 DFP and BFGS Algorithms 186
5.8 Concluding comment 186
Appendix 5A: Cholesky factorization example 187
6 Experimental design and choice experiments 189
6.1 Introduction 189
6.2 What is an experimental design? 191
6.2.1 Stage 1: problem definition refinement 194
6.2.2 Stage 2: stimuli refinement 195
6.2.3 Stage 3: experimental design considerations 201
6.2.4 Stage 4: generating experimental designs 223
6.2.5 Stage 5: allocating attributes to design columns 228
6.2.6 Generating efficient designs 247
6.3 Some more details on choice experiments 255
6.3.1 Constrained designs 255
6.3.2 Pivot designs 256
6.3.3 Designs with covariates 258
6.4 Best-worst designs 259
6.5 More on sample size and stated choice designs 264
6.5.1 D-efficient, orthogonal, and S-efficient designs 266
6.5.2 Effect of number of choice tasks, attribute levels, and attribute
level range 270
6.5.3 Effect of wrong priors on the efficiency of the design 275
6.6 Ngene syntax for a number of designs 276
6.6.1 Design 1: standard choice set up 276
6.6.2 Design 2: pivot design set up 279
6.6.3 Design 3: D-efficient choice design 281
6.7 Conclusions 287
290
290
291
294
297
301
301
304
305
306
308
309
312
313
318
320
320
320
321
327
330
333
334
335
336
340
346
351
360
360
360
362
363
Contents
Appendix 6A: Best-worst experiment
Appendix 6B: Best-worst designs and Ngene syntax
6B.1 Best-worst case 1
6B.2 Best-worst case 2
6B.3 Best-worst case 3
Appendix 6C: An historical overview
6C.1 Louviere and Hensher (1983), Louviere and Woodworth
(1983), and others
6C.2 Fowkes, Toner, Wardman et al. (Institute of Transport, Leeds,
1988-2000)
6C.3 Bunch, Louviere and Anderson (1996)
6C.4 Huber and Zwerina (1996)
6C.5 Sandor and Wedel (2001, 2002, 2005)
6C.6 Street and Burgess (2001 to current)
6C.7 Kanninen (2002, 2005)
6C.8 Bliemer, Rose, and Scarpa (2005 to current)
6C.9 Kessels, Goos, Vandebroek, and Yu (2006 to current)
Statistical inference
Introduction
Hypothesis tests
7.2.1 Tests of nested models
7.2.2 Tests of non-nested models
7.2.3 Specification tests
Variance estimation
7.3.1 Conventional estimation
7.3.2 Robust estimation
7.3.3 Bootstrapping of standard errors and confidence intervals
Variances of functions and willingness to pay
7.4.1 Delta method
7.4.2 Krinsky-Robb method
Other matters that analysts often inquire about
Demonstrating that the average of the conditional distributions
aggregate to the unconditional distribution
8.1.1 Observationally equivalent respondents with different
unobserved influences
8.1.2 Observationally different respondents with different
unobserved influences
Random regret instead of random utility maximization
Contents
ix
8.3 Endogeneity 370
8.4 Useful behavioral outputs 371
8.4.1 Elasticities of choice 371
8.4.2 Partial or marginal effects 374
8.4.3 Willingness to pay 378
Part II Software and data 385
9 Nlogit for applied choice analysis 387
9.1 Introduction 387
9.2 About the software 387
9.2.1 About Nlogit 387
9.2.2 Installing Nlogit 388
9.3 Starting Nlogit and exiting after a session 388
9.3.1 Starting the program 388
9.3.2 Reading the data 388
9.3.3 Input the data 390
9.3.4 The project file 390
9.3.5 Leaving your session 391
9.4 Using Nlogit 391
9.5 How to Get Nlogit to do what you want 392
9.5.1 Using the Text Editor 392
9.5.2 Command format 393
9.5.3 Commands 395
9.5.4 Using the project file box 396
9.6 Useful hints and tips 397
9.6.1 Limitations in Nlogit 398
9.7 Nlogit software 398
10 Data set up for Nlogit 400
10.1 Reading in and setting up data 400
10.1.1 The basic data set up 401
10.1.2 Entering multiple data sets: stacking and melding 405
10.1.3 Handling data on the non-chosen alternative in RP data 405
10.2 Combining sources of data 408
10.3 Weighting on an exogenous variable 410
10.4 Handling rejection: the no option 411
10.5 Entering data into Nlogit 414
Xi ^ Contents
10.6 Importing data from a file 415
10.6.1 Importing a small data set from the Text Editor 418
10.7 Entering data in the Data Editor 421
10.8 Saving and reloading the data set 422
10.9 Writing a data file to export 424
10.10 Choice data entered on a single line 424
10.11 Data cleaning 427
Appendix 10A: Converting single line data commands 431
Appendix 10B: Diagnostic and error messages 432
Part III The suite of choice models 435
11 Getting started modeling: the workhorse - multinomial logit 437
11.1 Introduction 43 7
11.2 Modeling choice in Nlogit: the MNL command 437
11.3 Interpreting the MNL model output 444
11.3.1 Determining the sample size and weighting criteria used 445
11.3.2 Interpreting the number of iterations to model convergence 445
11.3.3 Determining overall model significance 446
11.3.4 Comparing two models 453
11.3.5 Determining model fit: the pseudo-R2 455
11.3.6 Type of response and bad data 456
11.3.7 Obtaining estimates of the indirect utility functions 457
11.4 Handling interactions in choice models 461
11.5 Measures of willingness to pay 463
11.6 Obtaining utility and choice probabilities for the sample 465
Appendix 11 A: The labeled choice data set used in the chapter 466
12 Handling unlabeled discrete choice data 472
12.1 Introduction 472
12.2 Introducing unlabeled data 472
12.3 The basics of modeling unlabeled choice data 473
12.4 Moving beyond design attributes when using unlabeled choice data 478
Appendix 12A: Unlabeled discrete choice data Nlogit syntax and
output 483
13 Getting more from your model 492
13.1 Introduction 492
xi Contents
13.2 Adding to our understanding of the data 494
13.2.1 Descriptive output (Dstats) 494
13.2.2 ;Show 496
13.2.3 ;Descriptives 499
13.2.4 ;Crosstab 501
13.3 Adding to our understanding of the model parameters 502
13.3.1 Starting values 503
13.3.2 ;effect: elasticities 504
13.3.3 Elasticities: direct and cross - extended format 507
13.3.4 Calculating arc elasticities 512
13.3.5 Partial or marginal effects 513
13.3.6 Partial or marginal effects for binary choice 515
13.4 Simulation and “what if’ scenarios 518
13.4.1 The binary choice application 522
13.4.2 Arc elasticities obtained using ;simulation 524
13.5 Weighting 527
13.5.1 Endogenous weighting 527
13.5.2 Weighting on an exogenous variable 535
13.6 Willingness to pay 543
13.6.1 Calculating change in consumer surplus associated with an
attribute change 546
13.7 Empirical distributions: removing one observation at a time 547
13.8 Application of random regret model versus random utility model 547
13.8.1 Nlogit syntax for random regret model 553
13.9 The Maximize command 554
13.10 Calibrating a model 555
14 Nested logit estimation 560
14.1 Introduction 560
14.2 The nested logit model commands 561
14.2.1 Normalizing and constraining IV parameters 565
14.2.2 Specifying IV start values for the NL model 567
14.3 Estimating a NL model and interpreting the output 567
14.3.1 Estimating the probabilities of a two-level NL model 575
14.4 Specifying utility functions at higher levels of the NL tree 577
14.5 Handling degenerate branches in NL models 583
14.6 Three-level NL models 587
14.7 Elasticities and partial effects 590
14.8 Covariance nested logit 593
;xlf Contents
14.9 Generalized nested logit 597
14.10 Additional commands 600
15 Mixed logit estimation 601
15.1 Introduction 601
15.2 The mixed logit model basic commands 601
15.3 Nlogit output: interpreting the ML model 608
15.3.1 Model 2: mixed logit with unconstrained distributions 611
15.3.2 Model 3: restricting the sign and range of a random
parameter 621
15.3.3 Model 4: heterogeneity in the mean of random parameters 626
15.3.4 Model 5: heterogeneity in the mean of selective random
parameters 629
15.3.5 Model 6: heteroskedasticity and heterogeneity in the
variances 633
15.3.6 Model 7: allowing for correlated random parameters 636
15.4 How can we use random parameter estimates? 643
15.4.1 Starting values for random parameter estimation 645
15.5 Individual-specific parameter estimates: conditional parameters 646
15.6 Conditional confidence limits for random parameters 651
15.7 Willingness to pay issues 652
15.7.1 WTP based on conditional estimates 652
15.7.2 WTP based on unconditional estimates 658
15.8 Error components in mixed logit models 660
15.9 Generalized mixed logit: accounting for scale and taste
heterogeneity 672
15.10 GMX model in utility and WTP space 676
15.11 SMNL and GMX models in utility space 697
15.12 Recognizing scale heterogeneity between pooled data sets 704
16 Latent class models 706
16.1 Introduction 706
16.2 The standard latent class model 707
16.3 Random parameter latent class model 711
16.4 A case study 714
16.4.1 Results 715
16.4.2 Conclusions 722
16.5 Nlogit commands 724
16.5.1 Standard command structure 724
xiii Contents
16.5.2 Command structure for the models in Table 16.2 725
16.5.3 Other useful latent class model forms 733
17 Binary choice models 742
17.1 Introduction 742
17.2 Basic binary choice 742
17.2.1 Stochastic specification of random utility for binary choice 745
17.2.2 Functional form for binary choice 747
17.2.3 Estimation of binary choice models 750
17.2.4 Inference-hypothesis tests 752
17.2.5 Fit measures 753
17.2.6 Interpretation: partial effects and simulations 754
17.2.7 An application of binary choice modeling 756
17.3 Binary choice modeling with panel data 767
17.3.1 Heterogeneity and conventional estimation: the cluster
correction 768
17.3.2 Fixed effects 769
17.3.3 Random effects and correlated random effects 771
17.3.4 Parameter heterogeneity 772
17.4 Bivariate probit models 775
17.4.1 Simultaneous equations 111
17.4.2 Sample selection 782
17.4.3 Application I: model formulation of the ex ante link between
acceptability and voting intentions for a road pricing scheme 784
17.4.4 Application II: partial effects and scenarios for bivariate
probit 800
18 Ordered choices 804
18.1 Introduction 804
18.2 The traditional ordered choice model 805
18.3 A generalized ordered choice model 807
18.3.1 Modeling observed and unobserved heterogeneity 810
18.3.2 Random thresholds and heterogeneity in the ordered choice
model 812
18.4 Casestudy 817
18.4.1 Empirical analysis 820
18.5 Nlogit commands 830
19 Combining sources of data 836
19.1 Introduction 836
Contents
19.2 The nested logit “trick” 844
19.3 Beyond the nested logit “trick” 848
19.4 Case study 853
19.4.1 Nlogit command syntax for Table 19.2 models 858
19.5 Even more advanced SP-RP models 860
19.6 Hypothetical bias 868
19.6.1 Key themes 871
19.6.2 Evidence from contingent valuation to guide choice
experiments 874
19.6.3 Some background evidence in transportation studies 880
19.6.4 Pivot designs: elements of RP and CE 886
19.6.5 Conclusions 893
Part IV Advanced topics 897
20 Frontiers of choice analysis 899
20.1 Introduction 899
20.2 A mixed multinomial logit model with non-linear utility functions 899
20.3 Expected utility theory and prospect theory 905
20.3.1 Risk or uncertainty? 906
20.3.2 The appeal of prospect theory 908
20.4 Case study: travel time variability and the value of expected travel time
savings 912
20.4.1 Empirical application 914
20.4.2 Empirical analysis: mixed multinomial logit model with
non-linear utility functions 917
20.5 NLRPLogit commands for Table 20.6 model 923
20.6 Hybrid choice models 927
20.6.1 An overview of hybrid choice models 927
20.6.2 The main elements of a hybrid choice model 931
21 Attribute processing, heuristics, and preference construction 937
21.1 Introduction 937
21.2 A review of common decision processes 943
21.3 Embedding decision processes in choice models 946
21.3.1 Two-stage models 946
21.3.2 Models with “fuzzy” constraints 947
21.3.3 Other approaches 952
Contents
XV
21.4 Relational heuristics 955
21.4.1 Within choice set heuristics 955
21.4.2 Between choice set dependence 958
21.5 Process data ,963
21.5.1 Motivation for process data collection 963
21.5.2 Monitoring information acquisition 963
21.6 Synthesis so far 966
21.7 Case study I: incorporating attribute processing heuristics through
non-linear processing 968
21.7.1 Common-metric attribute aggregation 970
21.7.2 Latent class specification: non-attendance and dual
processing of common-metric attributes in choice analysis 977
21.7.3 Evidence on marginal willingness to pay: value of travel time
savings 979
21.7.4 Evidence from self-stated processing response for
common-metric addition 981
21.8 Case study II: the influence of choice response certainty, alternative
acceptability, and attribute thresholds 987
21.8.1 Accounting for response certainty, acceptability of
alternatives, and attribute thresholds 989
21.8.2 The choice experiment and survey process 993
21.8.3 Empirical results 997
21.8.4 Conclusions 1008
21.9 Case study III: interrogation of responses to stated choice
experiments - is there sense in what respondents tell us? 1009
21.9.1 The data setting 1013
21.9.2 Investigating candidate evidential rules 1015
21.9.3 Derivative willingness to pay 1023
21.9.4 Pairwise alternative “plausible choice” test and dominance 1025
21.9.5 Influences of non-trading 1029
21.9.6 Dimensional versus holistic processing strategies 1035
21.9.7 Influence of the relative attribute levels 1051
21.9.8 Revision of the reference alternative as value learning 1052
21.9.9 A revised model for future stated choice model estimation 1054
21.9.10 Conclusions 1057
21.10 The role of multiple heuristics in representing attribute processing as
a way of conditioning modal choices 1058
Appendix 21 A: Nlogit command syntax for NLWLR and RAM
heuristics 1062
Contents
Appendix 2IB: Experimental design in Table 21T5 1066
Appendix 21C: Data associated with Table 21.15 1066
22 Group decision making 1072
22.1 Introduction 1072
22.2 Interactive agency choice experiments 1073
22.3 Case study data on automobile purchases 1079
22.4 Case study results 1082
22.5 Nlogit commands and outputs 1091
22.5.1 Estimating a model with power weights 1091
22.5.2 Pass 1, round 1 (agent 1) and round 2 (agent 2) ML model 1091
22.5.3 Pass 1, round 1 (agent 1) and round 2 (agent 2) agree model 1093
22.5.4 Sorting probabilities for two agents into a single row 1094
22.5.5 Creating cooperation and non-cooperation probabilities for
the pairs 1094
22.5.6 Removing all but line 1 of the four choice sets per person
in pair 1094
22.5.7 Getting utilities on 1 line (note: focusing only on overall
utilities at this stage) 1095
22.5.8 Writing out new file for power weight application 1096
22.5.9 Reading new data file 1096
22.5.10 Estimating OLS power weight model (weights sum to 1.0) 1096
22.5.11 Pass #2 (repeating same process as for pass#l) 1098
22.5.12 Pass #3 (same set up as pass#l) 1103
22.5.13 Group equilibrium 1108
22.5.14 Joint estimation of power weights and preference parameters 1113
Select glossary 1116
References 1128
Index 1163
|
any_adam_object | 1 |
author | Hensher, David A. 1947- Rose, John M. Greene, William 1951- |
author_GND | (DE-588)142773298 (DE-588)130335355 (DE-588)124700551 |
author_facet | Hensher, David A. 1947- Rose, John M. Greene, William 1951- |
author_role | aut aut aut |
author_sort | Hensher, David A. 1947- |
author_variant | d a h da dah j m r jm jmr w g wg |
building | Verbundindex |
bvnumber | BV042236059 |
classification_rvk | QH 233 QH 234 |
classification_tum | WIR 017f |
ctrlnum | (OCoLC)912014817 (DE-599)BVBBV042236059 |
dewey-full | 519.5/42 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.5/42 |
dewey-search | 519.5/42 |
dewey-sort | 3519.5 242 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik Wirtschaftswissenschaften |
edition | 2. ed. |
format | Book |
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id | DE-604.BV042236059 |
illustrated | Illustrated |
indexdate | 2024-07-10T01:16:02Z |
institution | BVB |
isbn | 9781107465923 9781107092648 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027674278 |
oclc_num | 912014817 |
open_access_boolean | |
owner | DE-M382 DE-83 DE-11 DE-634 DE-945 DE-355 DE-BY-UBR DE-824 DE-N2 DE-91 DE-BY-TUM DE-19 DE-BY-UBM |
owner_facet | DE-M382 DE-83 DE-11 DE-634 DE-945 DE-355 DE-BY-UBR DE-824 DE-N2 DE-91 DE-BY-TUM DE-19 DE-BY-UBM |
physical | XXX, 1188 S. Ill., graph. Darst. |
publishDate | 2015 |
publishDateSearch | 2015 |
publishDateSort | 2015 |
publisher | Cambridge Univ. Press |
record_format | marc |
spelling | Hensher, David A. 1947- Verfasser (DE-588)142773298 aut Applied choice analysis David A. Hensher ; John M. Rose ; William H. Greene 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2015 XXX, 1188 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Decision making / Mathematical models Probabilities / Mathematical models Choice Mathematisches Modell Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 Rose, John M. Verfasser (DE-588)130335355 aut Greene, William 1951- Verfasser (DE-588)124700551 aut Erscheint auch als Online-Ausgabe 978-1-316-13623-2 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027674278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Hensher, David A. 1947- Rose, John M. Greene, William 1951- Applied choice analysis Decision making / Mathematical models Probabilities / Mathematical models Choice Mathematisches Modell Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
subject_GND | (DE-588)4077850-2 |
title | Applied choice analysis |
title_auth | Applied choice analysis |
title_exact_search | Applied choice analysis |
title_full | Applied choice analysis David A. Hensher ; John M. Rose ; William H. Greene |
title_fullStr | Applied choice analysis David A. Hensher ; John M. Rose ; William H. Greene |
title_full_unstemmed | Applied choice analysis David A. Hensher ; John M. Rose ; William H. Greene |
title_short | Applied choice analysis |
title_sort | applied choice analysis |
topic | Decision making / Mathematical models Probabilities / Mathematical models Choice Mathematisches Modell Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
topic_facet | Decision making / Mathematical models Probabilities / Mathematical models Choice Mathematisches Modell Statistische Entscheidungstheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027674278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT hensherdavida appliedchoiceanalysis AT rosejohnm appliedchoiceanalysis AT greenewilliam appliedchoiceanalysis |