Cause and Correlation in Biology: A User’s Guide to Path Analysis, Structural Equations and Causal Inference with R

Preface
Preface to the second edition
1. Preliminaries
1.1 The shadow's cause
1.2 Fisher's genius and the randomised experiment
1.3 The controlled experiment
1.4 Physical controls and observational controls
2 From cause to correlation and back
2.1 Translating from causal to statistical models
2.2 Directed graphs
2.3 Causal conditioning
2.4 D-separation
2.5 Probability distributions
2.6 Probabilistic (conditional) independence
2.7 The Markov condition
2.8 The translation from causal models to observational models
2.9 Counter-intuitive consequences and limitations of d-separation: conditioning on a causal child
2.10 Counter-intuitive consequences and limitations of d-separation: conditioning due to selection bias
2.11 Counter-intuitive consequences and limitations of d-separation: feedback loops and cyclic causal graphs
2.12 Counter-intuitive consequences and limitations of d-separation: imposed conservation relationships
2.13 Counter-intuitive consequences and limitations of d-separation: unfaithfulness
2.14 Counter-intuitive consequences and limitations of d-separation: context-sensitive independence
2.15 The logic of causal inference
2.16 Statistical control is not always the same as physical control
2.17 A taste of things to come
3 Sewall Wright, path analysis and d-separation
3.1 A bit of history
3.2 Why Wright's method of path analysis was ignored
3.3 D-sep tests
3.4 Independence of d-separation statements
3.5 Testing for probabilistic independence
3.6 Permutation tests of independence
3.7 Form-free regression
3.8 Conditional independence
3.9 Spearman partial correlations
3.10 Seed production in St Lucie cherry
3.11 Generalising the d-sep test
4 Path analysis and maximum likelihood
4.1 Testing path models using maximum likelihood
4.2 Decomposing effects in path diagrams
4.3 Multiple regression expressed as a path model
4.4 Maximum-likelihood estimation of the gas exchange model
4.5 Using lavaan to fit path models
5 Measurement error and latent variables
5.1 Measurement error and the inferential tests
5.2 Measurement error and the estimation of path coefficients
5.3 A measurement model
5.4 Fitting a measurement model in lavaan
5.5 The nature of latent variables
5.6 Horn dimensions in bighorn sheep
5.7 Body size in bighorn sheep
5.8 The worldwide leaf economic spectrum
5.9 Name calling
6 The structural equation model
6.1 Parameter identification
6.2 Structural under-identification with measurement models
6.3 Structural under-identification with structural models
6.4 Representing composite variables using latents
6.5 Behaviour of the maximum-likelihood chi-square statistic with small sample sizes
6.6 Behaviour of the maximum-likelihood chi-square statistic with data that do not follow a multivariate normal distribution
6.7 Solutions for modelling non-normally distributed variables
6.8 Alternative measures of ‘approximate’ fit
6.9 Bentler's comparative fit index (CFI)
6.10 Approximate fit measured by the root mean square error of approximation (RMSEA)
6.11 Missing data
6.12 Reporting results in publications
6.13 An SEM analysis of the Bumpus house sparrow data
7 Multigroup models, multilevel models and corrections for the non-independence of observations
7.1 Nested models
7.2 Dealing with causal heterogeneity: multigroup models
7.3 The dangers of hierarchically structured data
7.4 Multilevel SEM
8 Exploration, discovery and equivalence
8.1 Hypothesis generation
8.2 Exploring hypothesis space
8.3 The shadow's cause revisited
8.4 Obtaining the undirected dependency graph
8.5 The undirected dependency graph algorithm
8.6 Interpreting the undirected dependency graph
8.7 Orienting edges in the undirected dependency graph using unshielded colliders assuming an acyclic causal structure
8.8 The orientation algorithm using unshielded colliders
8.9 Orienting edges in the undirected dependency graph using definite discriminating paths
8.10 The causal inference algorithm
8.11 Equivalent models
8.12 Detecting latent variables
8.13 Vanishing tetrad algorithm
8.14 Separating the message from the noise
8.15 The causal inference algorithm and sampling error
8.16 The vanishing tetrad algorithm and sampling variation
8.17 Empirical examples
8.18 Orienting edges in the undirected dependency graph without assuming an acyclic causal structure
8.19 The cyclic causal discovery algorithm
8.20 In conclusion…
Appendix: A cheat-sheet of useful R functions
References
Index