Bill Shipley explores the logical and methodological relationships between correlation and causation. He presents a series of statistical methods that can test, and potentially discover, cause-effect relationships between variables in situations where it is not possible to conduct randomized, or experimentally controlled, studies. Many of these methods are quite new and most are generally unknown to biologists. Besides describing how to conduct these statistical tests, he also puts the methods into historical context and explains when they can and cannot justifiably be used to test causal claims. Hb ISBN (2000); 0-521-79153-7
Author(s): Bill Shipley
Publisher: Cambridge University Press
Year: 2000
Language: English
Pages: 329
Contents......Page 7
Preface......Page 11
1.1 The shadow’s cause......Page 13
1.2 Fisher’s genius and the randomised experiment......Page 19
1.3 The controlled experiment......Page 26
1.4 Physical controls and observational controls......Page 28
2.1 Translating from causal to statistical models......Page 33
2.2 Directed graphs......Page 37
2.3 Causal conditioning......Page 40
2.4 d-separation......Page 41
2.5 Probability distributions......Page 44
2.6 Probabilistic independence......Page 45
2.7 Markov condition......Page 47
2.8 The translation from causal models to observational......Page 48
2.9 Counterintuitive consequences and limitations of d-separation: conditioning on a causal child......Page 49
2.10 Counterintuitive consequences and limitations of d-separation: conditioning due to selection bias......Page 53
2.11 Counterintuitive consequences and limitations of d-separation: feedback loops and cyclic causal graphs......Page 54
2.12 Counterintuitive consequences and limitations of d-separation: imposed conservation relationships......Page 55
2.13 Counterintuitive consequences and limitations of d-separation: unfaithfulness......Page 57
2.14 Counterintuitive consequences and limitations of d-separation: context-sensitive independence......Page 59
2.15 The logic of causal inference......Page 60
2.16 Statistical control is not always the same as physical control......Page 67
2.17 A taste of things to come......Page 75
3.1 A bit of history......Page 77
3.2 Why Wright’s method of path analysis was ignored......Page 78
3.3 d-sep tests......Page 83
3.4 Independence of d-separation statements......Page 84
3.5 Testing for probabilistic independence......Page 86
3.6 Permutation tests of independence......Page 91
3.7 Form-free regression......Page 92
3.8 Conditional independence......Page 95
3.9 Spearman partial correlations......Page 100
3.10 Seed production in St Lucie’s Cherry......Page 102
3.11 Specific leaf area and leaf gas exchange......Page 106
4 Path analysis and maximum likelihood......Page 112
4.1 Testing path models using maximum likelihood......Page 115
4.2 Decomposing effects in path diagrams......Page 135
4.3 Multiple regression expressed as a path model......Page 138
4.4 Maximum likelihood estimation of the gas-exchange model......Page 142
5 Measurement error and latent variables......Page 148
5.1 Measurement error and the inferential tests......Page 150
5.2 Measurement error and the estimation of path coefficients......Page 152
5.3 A measurement model......Page 155
5.4 The nature of latent variables......Page 164
5.5 Horn dimensions in Bighorn Sheep......Page 169
5.6 Body size in Bighorn Sheep......Page 170
5.7 Name calling......Page 173
6 The structural equations model......Page 174
6.1 Parameter identification......Page 175
6.2 Structural underidentification with measurement models......Page 176
6.3 Structural underidentification with structural models......Page 183
6.4 Behaviour of the maximum likelihood chi-squared statistic with small sample size......Page 185
6.5 Behaviour of the maximum likelihood chi-squared statistic with data that do not follow a multivariate normal distribution......Page 191
6.6 Solutions for modelling non-normally distributed variables......Page 199
6.7 Alternative measures of ‘approximate’ fit......Page 201
6.8 Bentler’s comparative fit index......Page 204
6.9 Approximate fit measured by the root mean square error of approximation......Page 206
6.10 An SEM analysis of the Bumpus House Sparrow data......Page 207
7 Nested models and multilevel models......Page 211
7.1 Nested models......Page 212
7.2 Multigroup models......Page 214
7.3 The dangers of hierarchically structured data......Page 221
7.4 Multilevel SEM......Page 233
8.1 Hypothesis generation......Page 249
8.2 Exploring hypothesis space......Page 250
8.3 The shadow’s cause revisited......Page 253
8.4 Obtaining the undirected dependency graph......Page 255
8.5 The undirected dependency graph algorithm8......Page 258
8.6 Interpreting the undirected dependency graph......Page 262
8.7 Orienting edges in the undirected dependency graph using unshielded colliders assuming an acyclic causal structure......Page 266
8.8 Orientation algorithm using unshielded colliders......Page 268
8.9 Orienting edges in the undirected dependency graph using definite discriminating paths......Page 272
8.10 The Causal Inference algorithm......Page 274
8.11 Equivalent models......Page 276
8.12 Detecting latent variables......Page 278
8.13 Vanishing Tetrad algorithm......Page 283
8.14 Separating the message from the noise......Page 284
8.15 The Causal Inference algorithm and sampling error......Page 290
8.16 The Vanishing Tetrad algorithm and sampling variation......Page 296
8.17 Empirical examples......Page 299
8.18 Orienting edges in the undirected dependency graph without assuming an acyclic causal structure......Page 306
8.19 The Cyclic Causal Discovery algorithm......Page 311
8.20 In conclusion . . .......Page 316
Appendix......Page 317
References......Page 320
Index......Page 328
