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

by Bill Shipley

• ISBN13: 9780521529211
• ISBN10: 0521529212
• Edition: 1st
• Format: Paperback
• Copyright: 2002-09-02
• Publisher: Cambridge University Press

Summary

This book goes beyond the truism that 'correlation does not imply causation' and explores the logical and methodological relationships between correlation and causation. It presents a series of statistical methods that can test, and potentially discover, cause-effect relationships between variables in situations in which it is not possible to conduct randomised or experimentally controlled experiments. Many of these methods are quite new and most are generally unknown to biologists. In addition to describing how to conduct these statistical tests, the book also puts the methods into historical context and explains when they can and cannot justifiably be used to test or discover causal claims. Written in a conversational style that minimises technical jargon, the book is aimed at practising biologists and advanced students, and assumes only a very basic knowledge of introductory statistics.

Author Biography

Bill Shipley teaches plant ecology and biometry in the Department of Biology at the Universite de Sherbrooke, Quebec, Canada

Table of Contents

Preface	xi
Preliminaries	1	(20)
The shadow's cause	1	(6)
Fisher's genius and the randomised experiment	7	(7)
The controlled experiment	14	(2)
Physical controls and observational controls	16	(5)
From cause to correlation and back	21	(44)
Translating from causal to statistical models	21	(4)
Directed graphs	25	(3)
Causal conditioning	28	(1)
d-separation	29	(3)
Probability distributions	32	(1)
Probabilistic independence	33	(2)
Markov condition	35	(1)
The translation from causal models to observational models	36	(1)
Counterintuitive consequences and limitations of d-separation: conditioning on a causal child	37	(4)
Counterintuitive consequences and limitations of d-separation: conditioning due to selection bias	41	(1)
Counterintuitive consequences and limitations of d-separation: feedback loops and cyclic causal graphs	42	(1)
Counterintuitive consequences and limitations of d-separation: imposed conservation relationships	43	(2)
Counterintuitive consequences and limitations of d-separation: unafaithfulness	45	(2)
Counterintuitive consequences and limitations of d-separation: context-sensitive independence	47	(1)
The logic of causal inference	48	(7)
Statistical control is not always the same as physical control	55	(8)
A taste of things to come	63	(2)
Stewall Wright, path analysis and d-separation	65	(35)
A bit of history	65	(1)
Why Wright's method of path analysis was ignored	66	(5)
d-sep tests	71	(1)
Independence of d-separation statements	72	(2)
Testing for probabilistic independence	74	(5)
Permutation tests of independence	79	(1)
Form-free regression	80	(3)
Conditional independence	83	(5)
Spearman partial correlations	88	(2)
Seed production in St Lucie's Cherry	90	(4)
Specific leaf area and leaf gas exchange	94	(6)
Path analysis and maximum likelihood	100	(36)
Testing path models using maximum likelihood	103	(20)
Decomposing effects in path diagrams	123	(3)
Multiple regression expressed as a path model	126	(4)
Maximum likelihood estimation of the gas-exchange model	130	(6)
Measurement error and latent variables	136	(26)
Measurement error and the inferential tests	138	(2)
Measurement error and the estimation of path coefficients	140	(3)
A measurement model	143	(9)
The nature of latent variables	152	(5)
Horn dimensions in Bighorn Sheep	157	(1)
Body size in Bighorn Sheep	158	(3)
Name calling	161	(1)
The structural equations model	162	(37)
Parameter identification	163	(1)
Structural underidentification with measurement models	164	(7)
Structural underidentification with structural models	171	(2)
Behaviour of the maximum likelihood chi-squared statistic with small sample sizes	173	(6)
Behaviour of the maximum likelihood chi-squared statistic with data that do not follow a multivariate normal distribution	179	(6)
Solutions for modelling non-normally distributed variables	185	(3)
Alternative measures of `approximate' fit	188	(4)
Bentler's comparative fit index	192	(1)
Approximate fit measured by the root mean square error of approximation	193	(2)
An SEM analysis of the Bumpus House Sparrow data	195	(4)
Nested models and multilevel models	199	(38)
Nested models	200	(2)
Multigroup models	202	(7)
The dangers of hierarchically structured data	209	(12)
Multilevel SEM	221	(16)
Exploration, discovery and equivalence	237	(68)
Hypothesis generation	237	(1)
Exploring hypothesis space	238	(3)
The shadow's cause revisited	241	(2)
Obtaining the undirected dependency graph	243	(3)
The undirected dependency graph algorithm	246	(4)
Interpreting the undirected dependency graph	250	(4)
Orienting edges in the undirected dependency graph using unshielded colliders assuming an acyclic causal structure	254	(2)
Orientation algorithm using unshielded colliders	256	(4)
Orienting edges in the undirected dependency graph using definite discriminating paths	260	(2)
The Causal Inference algorithm	262	(2)
Equivalent models	264	(2)
Detecting latent variables	266	(5)
Vanishing Tetrad algorithm	271	(1)
Separating the message from the noise	272	(6)
The Causal Inference algorithm and sampling error	278	(6)
The Vanishing Tetrad algorithm and sampling variation	284	(3)
Empirical examples	287	(7)
Orienting edges in the undirected dependency graph without assuming an acyclic causal structure	294	(5)
The Cyclic Causal Discovery algorithm	299	(5)
In conclusion ...	304	(1)
Appendix	305	(3)
References	308	(8)
Index	316