Random and Fixed Effects Papers

Useful Papers - Random and Fixed Effects in fMRI


Holmes (2000), SPM99 random effects manual TXT

Summary: An excellent summary of the distinction between random-effects and fixed-effects models in neuroimaging: what the big deal is, why you'd want to use a random-effects model in some situations, and then a great deal of detail on how to do it in SPM. Level of detail isn't so tight as to prevent its usability as a guide for other programs - an identical approach will work for any typical neuroimaging analysis package for a standard-style hierarchical analysis.

Bottom line: Required reading for group analysis in SPM or other programs.

Friston et. al (1999), "How many subjects constitute a study?," NeuroImage 10, 1-5 PDF

Summary: An interesting look in how a paper can end up being cited for reasons completely counter to why it was written. Often cited in papers describing why they used a random-effects analysis, this is actually a theoretical treatment of how fixed-effects models and conjunction analyses with relatively small numbers of subjects can be used to establish an effect as "typical" - an conceptual analogue to "average" that authors argue supports some of the same inferences as "average." This is not, on the whole, an argument that's been bought an awful lot in the literature at large.

Bottom line: Generally, it's cited because of the sideline admission by the authors that some forms of inference can only be supported by random-effects analyses. Turns out those are the kinds of inference that people actually want to make. Weird.

Miller et. al (2002), "Extensive individual differences in brain activations associated with episodic retrieval are reliable over time," Journal of Cognitive Neuroscience 14:8, 1200-1214 PDF

Summary: A fairly extensive critique of group analyses and averaging as the sole criterion of activation in a group study. Authors review a number of studies on individual variability and episodic retrieval, and demonstrate that when six subjects from a 2001 study were retested with the same paradigm, their patterns of activation were extremely consistent with those from the earlier test, suggesting that individual differences among them aren't simply noise. Some exploration of the relationship between individual brain pattern and real-life performance.

Bottom line: Just looking at your group averages isn't good enough. It's important to look at your individual subjects' data, because differences between them may be meaningful and might be related to performance in a variety of ways.


Holmes & Friston (1998), "Generalisability, random effects and population inference," NeuroImage 7, S754 PDF

Summary: Really the original paper on random-effects tests in neuroimaging. Argues that population inference can only truly be supported by random-effects analyses, and presents the strategy SPM99 and forward would take in doing group testing for random effects: the hierarchical, separable model in which each subject is modeled separately and summary images of their activations are then analyzed at a new level.

Bottom line: Turns out you need random effects for population inference; no more getting away with a whole bunch of scans on two or three people...

McGonigle et. al (2000), "Variability in fMRI: an examination of intersession differences," NeuroImage 11, 708-734 PDF

Summary: A look not at individual differences between subjects, but at difference in patterns of activation within a given subject between sessions. This paper provides a good example of how the same data can be analyzed both with fixed-effects and random-effects models, and of the different conclusions that can be drawn from activations found with each type of model. Includes a nice look at what types of variability show up with each type of model (Fig. 8, p. 729).

Bottom line: Random effects analyses raise the threshold of variability necessary for significance, but with the bonus of supporting potentially more interesting kinds of inference.

Aguirre et. al (1998), "The variability of human BOLD hemodynamic responses," NeuroImage 8, 360-369 PDF

Summary: An excellent look at the underlying assumption of identical shape of HRF across subject, day and scan session. Similar to the above McGonigle et. al in its use of fixed- and random-effects models to make different inferences about variability due to different factors.

Bottom line: Another interesting example of the usefulness of both types of models in the same study to demonstrate different effects or influences.