Internal medicine

Random effects model

Key (lock)

Mathematics

Meta-analysis

Data mining

Statistics

Psychoanalysis

Machine learning

Econometrics

Psychology

Economics

Chemistry

Geometry

Computer science

Management science

Confusion

Point (geometry)

Argument (complex analysis)

Longitudinal data

Computer security

Fixed effects model

Multilevel model

Biochemistry

Panel data

Medicine

Random error

Quality & Quantity

This paper assesses the options available to researchers analysing multilevel (including longitudinal) data, with the aim of supporting good methodological decision-making. Given the confusion in the literature about the key properties of fixed and random effects (FE and RE) models, we present these models' capabilities and limitations. We also discuss the within-between RE model, sometimes misleadingly labelled a 'hybrid' model, showing that it is the most general of the three, with all the strengths of the other two. As such, and because it allows for important extensions—notably random slopes—we argue it should be used (as a starting point at least) in all multilevel analyses. We develop the argument through simulations, evaluating how these models cope with some likely mis-specifications. These simulations reveal that (1) failing to include random slopes can generate anti-conservative standard errors, and (2) assuming random intercepts are Normally distributed, when they are not, introduces only modest biases. These results strengthen the case for the use of, and need for, these models.

Fixed and random effects models: making an informed choice