What does fixed effects and random effects mean?
For economists, fixed effects means The fixed effects model is a linear regression of y on x, that adds to the specication a series of indicator variables. For example, one could include a series of country dummies in comparative time series cross-sectional data to account for unexplained country-to-country variation that does not change over time.
In the random effects model, the groupings (e.g., counties)are instead assumed to follow a probability distribution [typically normal with mean μα and variance (σα)2], with parameters estimated from the data.
Biostatisticians, particularly those who focus on meta-analysis use the terms are used a bit differently. For instance, consider an indirect comparison study of many trials that measure treatment A’s efficacy relative to a placebo. Fixed effects models assume that the true treatment effect is constant across trials. In other words, the fixed effects model assumes that only within-study sampling error exits. On the other hand, random effects models assume that the differences in trial-specific treatment effectiveness are not identical but come from a common distribution.
The fixed and random effects essentially weight the trial results on the basis of the inherent uncertainty of each estimate. Under the fixed effects model, the weights placed on each study’s results are proportional to the inverse of study variance.
Whereas fixed effects measures variance based only on within-trial variability, the random effects weight is equal to the inverse of the sum of the within-trial variance and the residual between-trial variance.
This may seem like mumbo jumbo to many of you. But not to worry…the healthcare economist has an spreadsheet example to demonstrates how to do this calculation.
- HT: Michael Borenstein, Larry Hedges, Hannah Rothstein (2011). Meta-Analysis: Fixed effect vs. random effects. Meta-Analysis.com.