Model selection and multimodel inference: a practical information-theoretic approach
Gespeichert in:
| Vorheriger Titel: | Burnham, Kenneth P. Model selection and inference |
|---|---|
| Beteiligte Personen: | , |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2002
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009901812&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XXVI, 488 S. Ill., graph. Darst. |
| ISBN: | 0387953647 9780387953649 9781441929730 |
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| 245 | 1 | 0 | |a Model selection and multimodel inference |b a practical information-theoretic approach |c Kenneth P. Burnham ; David R. Anderson |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2002 | |
| 300 | |a XXVI, 488 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1819250754289926144 |
|---|---|
| adam_text | Titel: Model selection and multimodel inference
Autor: Burnham, Kenneth P.
Jahr: 2002
Contents
Preface vii
About the Authors xxi
Glossary xxiii
1 Introduction 1
1.1 Objectives of the Book ................... 1
1.2 Background Material .................... 5
1.2.1 Inference from Data, Given a Model........ 5
1.2.2 Likelihood and Least Squares Theory ....... 6
1.2.3 The Critical Issue: What Is the Best Model
to User....................... 13
1.2.4 Science Inputs: Formulation of the Set of
Candidate Models.................. 15
1.2.5 Models Versus Full Reality............. 20
1.2.6 An Ideal Approximating Model........... 22
1.3 Model Fundamentals and Notation............. 23
1.3.1 Truth or Full Reality/............... 23
1.3.2 Approximating Models g¡(x 9)........... 23
1.3.3 The Kullback-Leibler Best Model g,(x d0)..... 25
1.3.4 Estimated Models g¡(x 6).............. 25
1.3.5 Generating Models................. 26
1.3.6 Global Model.................... 26
xiv Contents
1.3.7 Overview of Stochastic Models in the
Biological Sciences................. 27
1.4 Inference and the Principle of Parsimony.......... 29
1.4.1 Avoid Overfitting to Achieve a Good Model Fit . . 29
1.4.2 The Principle of Parsimony............. 31
1.4.3 Model Selection Methods.............. 35
1.5 Data Dredging, Overanalysis of Data, and
Spurious Effects....................... 37
1.5.1 Overanalysis of Data................ 38
1.5.2 Some Trends .................... 40
1.6 Model Selection Bias.................... 43
1.7 Model Selection Uncertainty................ 45
1.8 Summary........................... 47
2 Information and Likelihood Theory: A Basis for Model
Selection and Inference 49
2.1 Kullback-Leibler Information or Distance Between
Two Models......................... 50
2.1.1 Examples of Kullback-Leibler Distance...... 54
2.1.2 Truth,/, Drops Out as a Constant......... 58
2.2 Akaike s Information Criterion: 1973............ 60
2.3 Takeuchi s Information Criterion: 1976........... 05
2.4 Second-Order Information Criterion: 1978......... 66
2.5 Modification of Information Criterion for Overdispersed
Count Data.......................... 67
2.6 AIC Differences, A,..................... 70
2.7 A Useful Analogy...................... 72
2.8 Likelihood of a Model, C(g¡ data) ............. 74
2.9 Akaike Weights, w¡ ..................... 75
2.9.1 Basic Formula.................... 75
2.9.2 An Extension.................... 76
2.10 Evidence Ratios....................... 77
2.11 Important Analysis Details ................. 80
2.11.1 AIC Cannot Be Used to Compare Models of
Different Data Sets................. 80
2.11.2 Order Not Important in Computing AIC Values . . 81
2.11.3 Transformations of the Response Variable..... 81
2.11.4 Regression Models with Differing
Error Structures................... 82
2.11.5 Do Not Mix Null Hypothesis Testing with
Information-Theoretic Criteria........... 83
2.11.6 Null Hypothesis Testing Is Still Important in
Strict Experiments.................. 83
2.11.7 Information-Theoretic Criteria Are Not a Test . . 84
2.11.8 Exploratory Data Analysis............. 84
Contents xv
2.12 Some History and Further Insights............. 85
2.12.1 Entropy....................... 86
2.12.2 A Heuristic Interpretation.............. 87
2.12.3 More on Interpreting Information-
Theoretic Criteria .................. 87
2.12.4 Nonnested Models ................. 88
2.12.5 Further Insights................... 89
2.13 Bootstrap Methods and Model Selection Frequencies n¡ .. 90
2.13.1 Introduction..................... 91
2.13.2 The Bootstrap in Model Selection:
The Basic Idea.................... 93
2.14 Return to Flather s Models ................. 94
2.15 Summary........................... 96
Basic Use of the Information-Theoretic Approach 98
3.1 Introduction......................... 98
3.2 Example 1: Cement Hardening Data ............ 100
3.2.1 Set of Candidate Models.............. 101
3.2.2 Some Results and Comparisons........... 102
3.2.3 A Summary..................... 106
3.3 Example 2: Time Distribution of an Insecticide Added to a
Simulated Ecosystem.................... 106
3.3.1 Set of Candidate Models.............. 108
3.3.2 Some Results.................... 110
3.4 Example 3: Nestling Starlings................ Ill
3.4.1 Experimental Scenario ............... 112
3.4.2 Monte Carlo Data.................. 113
3.4.3 Set of Candidate Models.............. 113
3.4.4 Data Analysis Results................ 117
3.4.5 Further Insights into the First Fourteen
NestedModels ................... 120
3.4.6 Hypothesis Testing and Information-Theoretic
Approaches Have Different
Selection Frequencies................ 121
3.4.7 Further Insights Following Final
Model Selection................... 124
3.4.8 Why Not Always Use the Global Model
for Inference?.................... 125
3.5 Example 4: Sage Grouse Survival.............. 126
3.5.1 Introduction..................... 126
3.5.2 Set of Candidate Models.............. 127
3.5.3 Model Selection................... 129
3.5.4 Hypothesis Tests for Year-Dependent
Survival Probabilities................ 131
xvi Contents
3.5.5 Hypothesis Testing Versus AIC in
Model Selection................... 132
3.5.6 A Class of Intermediate Models .......... 134
3.6 Example 5: Resource Utilization of Anolis Lizards..... 137
3.6.1 Set of Candidate Models.............. 138
3.6.2 Comments on Analytic Method........... 138
3.6.3 Some Tentative Results............... 139
3.7 Example 6: Sakamoto et al. s (1986) Simulated Data .... 141
3.8 Example 7: Models of Fish Growth............. 142
3.9 Summary........................... 143
4 Formal Inference From More Than One Model:
Multimodel Inference (MMI) 149
4.1 Introduction to Multimodel Inference............ 149
4.2 Model Averaging ...................... 150
4.2.1 Prediction...................... 150
4.2.2 Averaging Across Model Parameters........ 151
4.3 Model Selection Uncertainty................ 153
4.3.1 Concepts of Parameter Estimation and
Model Selection Uncertainty............ 155
4.3.2 Including Model Selection Uncertainty in
Estimator Sampling Variance............ 158
4.3.3 Unconditional Confidence Intervals ........ 164
4.4 Estimating the Relative Importance of Variables...... 167
4.5 Confidence Set for the K-L Best Model........... 169
4.5.1 Introduction..................... 169
4.5.2 A,, Model Selection Probabilities,
and the Bootstrap.................. 171
4.6 Model Redundancy..................... 173
4.7 Recommendations...................... 176
4.8 Cement Data......................... 177
4.9 PineWoodData....................... 183
4.10 The Durban Storm Data................... 187
4.10.1 Models Considered................. 188
4.10.2 Consideration of Model Fit............. 190
4.10.3 Confidence Intervals on Predicted
Storm Probability.................. 191
4.10.4 Comparisons of Estimator Precision........ 193
4.11 Flour Beetle Mortality: A Logistic Regression Example . . 195
4.12 Publication of Research Results............... 201
4.13 Summary........................... 203
5 Monte Carlo Insights and Extended Examples 206
5.1 Introduction......................... 206
5.2 Survival Models....................... 207
Contents xvii
5.2.1 A Chain Binomial Survival Model......... 207
5.2.2 An Example..................... 210
5.2.3 An Extended Survival Model............ 215
5.2.4 Model Selection if Sample Size Is Huge,
or Truth Known................... 219
5.2.5 A Further Chain Binomial Model.......... 221
5.3 Examples and Ideas Illustrated with Linear Regression . . . 224
5.3.1 All-Subsets Selection: A GPA Example...... 225
5.3.2 A Monte Carlo Extension of the GPA Example . . 229
5.3.3 An Improved Set of GPA Prediction Models .... 235
5.3.4 More Monte Carlo Results............. 238
5.3.5 Linear Regression and Variable Selection ..... 244
5.3.6 Discussion...................... 248
5.4 Estimation of Density from Line Transect Sampling .... 255
5.4.1 Density Estimation Background .......... 255
5.4.2 Line Transect Sampling of Kangaroos at
Wallaby Creek.................... 256
5.4.3 Analysis of Wallaby Creek Data.......... 256
5.4.4 Bootstrap Analysis................. 258
5.4.5 Confidence Interval on D.............. 258
5.4.6 Bootstrap Samples: 1,000 Versus 10,000...... 260
5.4.7 Bootstrap Versus Akaike Weights: A Lesson
onQAIQ...................... 261
5.5 Summary........................... 264
Advanced Issues and Deeper Insights 267
6.1 Introduction......................... 267
6.2 An Example with 13 Predictor Variables and
8,191 Models ........................ 268
6.2.1 Body Fat Data.................... 268
6.2.2 The Global Model.................. 269
6.2.3 Classical Stepwise Selection............ 269
6.2.4 Model Selection Uncertainty for AICC and BIC . . 271
6.2.5 An A Priori Approach................ 274
6.2.6 Bootstrap Evaluation of Model Uncertainty .... 276
6.2.7 Monte Carlo Simulations.............. 279
6.2.8 Summary Messages................. 281
6.3 Overview of Model Selection Criteria............ 284
6.3.1 Criteria That Are Estimates of K-L Information . . 284
6.3.2 Criteria That Are Consistent for K......... 286
6.3.3 Contrasts ...................... 288
6.3.4 Consistent Selection in Practice:
Quasi-true Models.................. 289
6.4 Contrasting AIC and BIC.................. 293
6.4.1 A Heuristic Derivation of BIC........... 293
xviii Contents
6.4.2 A K-L-Based Conceptual Comparison of
AICandBIC .................... 295
6.4.3 Performance Comparison.............. 298
6.4.4 Exact Bayesian Model Selection Formulas..... 301
6.4.5 Akaike Weights as Bayesian Posterior
Model Probabilities................. 302
6.5 Goodness-of-Fit and Overdispersion Revisited....... 305
6.5.1 Overdispersion c and Goodness-of-Fit:
A General Strategy................. 305
6.5.2 Overdispersion Modeling: More Than One c . . . . 307
6.5.3 Model Goodness-of-Fit After Selection....... 309
6.6 AIC and Random Coefficient Models............ 310
6.6.1 Basic Concepts and Marginal
Likelihood Approach................ 310
6.6.2 A Shrinkage Approach to AIC and
Random Effects................... 313
6.6.3 On Extensions.................... 316
6.7 Selection When Probability Distributions Differ
by Model........................... 317
6.7.1 Keep All the Parts.................. 317
6.7.2 A Normal Versus Log-Normal Example...... 318
6.7.3 Comparing Across Several Distributions:
An Example..................... 320
6.8 Lessons from the Literature and Other Matters....... 323
6.8.1 Use AICC, Not AIC, with Small Sample Sizes ... 323
6.8.2 Use AICC) Not AIC, When K Is Large....... 325
6.8.3 When Is AIQ Suitable: A Gamma
Distribution Example................ 326
6.8.4 Inference from a Less Than Best Model...... 328
6.8.5 Are Parameters Real?................ 330
6.8.6 Sample Size Is Often Not a Simple Issue...... 332
6.8.7 Judgment Has a Role................ 333
6.9 Tidbits About AIC...................... 334
6.9.1 Irrelevance of Between-Sample Variation
of AIC........................ 334
6.9.2 The G-Statistic and K-L Information........ 336
6.9.3 AIC Versus Hypothesis Testing: Results Can Be
Very Different.................... 337
6.9.4 A Subtle Model Selection Bias Issue........ 339
6.9.5 The Dimensional Unit of AIC............ 340
6.9.6 AIC and Finite Mixture Models........... 342
6.9.7 Unconditional Variance............... 344
6.9.8 A Baseline for u)+(i)................ 345
6.10 Summary........................... 347
Contents xix
7 Statistical Theory and Numerical Results 352
7.1 Useful Preliminaries..................... 352
7.2 A General Derivation of AIC................ 362
7.3 General K-L-Based Model Selection: TIC......... 371
7.3.1 Analytical Computation of TIC........... 371
7.3.2 Bootstrap Estimation of TIC............ 372
7.4 AICf : A Second-Order Improvement............ 374
7.4.1 Derivation of AICC ................. 374
7.4.2 Lack of Uniqueness of AICC ............ 379
7.5 Derivation of AIC for the Exponential Family
of Distributions ....................... 380
7.6 Evaluation oftri/iöoM/^)] 1) and Its Estimator..... 384
7.6.1 Comparison of AIC Versus TIC in a
Very Simple Setting................. 385
7.6.2 Evaluation Under Logistic Regression....... 390
7.6.3 Evaluation Under Multinomially Distributed
Count Data ..................... 397
7.6.4 Evaluation Under Poisson-Distributed Data .... 405
7.6.5 Evaluation for Fixed-Effects Normality-Based
Linear Models.................... 406
7.7 Additional Results and Considerations........... 412
7.7.1 Selection Simulation for Nested Models...... 412
7.7.2 Simulation ofthe Distribution of Ap........ 415
7.7.3 Does AIC Overfit? ................. 417
7.7.4 Can Selection Be Improved Based on
All the A,? ..................... 419
7.7.5 Linear Regression, AIC, and Mean Square Error . . 421
7.7.6 AICC and Models for Multivariate Data....... 424
7.7.7 There Is No True TICC ............... 426
7.7.8 Kullback-Leibler Information Relationship to the
Fisher Information Matrix.............. 426
7.7.9 Entropy and Jaynes Maxent Principle........ 427
7.7.10 Akaike Weights w¡ Versus Selection
Probabilities n¡ ................... 428
7.8 Kullback-Leibler Information Is Always 0........ 429
7.9 Summary........................... 434
8 Summary 437
8.1 The Scientific Question and the Collection of Data..... 439
8.2 Actual Thinking and A Priori Modeling........... 440
8.3 The Basis for Objective Model Selection.......... 442
8.4 The Principle of Parsimony................. 443
8.5 Information Criteria as Estimates of Expected Relative
Kullback-Leibler Information................ 444
8.6 Ranking Alternative Models................. 446
xx Contents
8.7 Scaling Alternative Models................. 447
8.8 MMI: Inference Based on Model Averaging........ 448
8.9 MMI: Model Selection Uncertainty............. 449
8.10 MMI: Relative Importance of Predictor Variables ..... 451
8.11 More on Inferences ..................... 451
8.12 Final Thoughts........................ 454
References 455
Index 485
|
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| id | DE-604.BV014564042 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:05:02Z |
| institution | BVB |
| isbn | 0387953647 9780387953649 9781441929730 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009901812 |
| oclc_num | 264995692 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-11 DE-706 DE-703 DE-188 DE-578 DE-473 DE-BY-UBG |
| owner_facet | DE-384 DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-11 DE-706 DE-703 DE-188 DE-578 DE-473 DE-BY-UBG |
| physical | XXVI, 488 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Burnham, Kenneth P. Anderson, David Raymond 1942- Model selection and multimodel inference a practical information-theoretic approach Modellwahl (DE-588)4304786-5 gnd Biologie (DE-588)4006851-1 gnd Datenanalyse (DE-588)4123037-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4304786-5 (DE-588)4006851-1 (DE-588)4123037-1 (DE-588)4114528-8 (DE-588)4056995-0 |
| title | Model selection and multimodel inference a practical information-theoretic approach |
| title_auth | Model selection and multimodel inference a practical information-theoretic approach |
| title_exact_search | Model selection and multimodel inference a practical information-theoretic approach |
| title_full | Model selection and multimodel inference a practical information-theoretic approach Kenneth P. Burnham ; David R. Anderson |
| title_fullStr | Model selection and multimodel inference a practical information-theoretic approach Kenneth P. Burnham ; David R. Anderson |
| title_full_unstemmed | Model selection and multimodel inference a practical information-theoretic approach Kenneth P. Burnham ; David R. Anderson |
| title_old | Burnham, Kenneth P. Model selection and inference |
| title_short | Model selection and multimodel inference |
| title_sort | model selection and multimodel inference a practical information theoretic approach |
| title_sub | a practical information-theoretic approach |
| topic | Modellwahl (DE-588)4304786-5 gnd Biologie (DE-588)4006851-1 gnd Datenanalyse (DE-588)4123037-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Modellwahl Biologie Datenanalyse Mathematisches Modell Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009901812&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT burnhamkennethp modelselectionandmultimodelinferenceapracticalinformationtheoreticapproach AT andersondavidraymond modelselectionandmultimodelinferenceapracticalinformationtheoreticapproach |