# Fixed effects, random effects and GEE: What are the differences?

@article{Gardiner2009FixedER, title={Fixed effects, random effects and GEE: What are the differences?}, author={Joseph C. Gardiner and Zhehui Luo and Lee Anne Roman}, journal={Statistics in Medicine}, year={2009}, volume={28} }

For analyses of longitudinal repeated‐measures data, statistical methods include the random effects model, fixed effects model and the method of generalized estimating equations. We examine the assumptions that underlie these approaches to assessing covariate effects on the mean of a continuous, dichotomous or count outcome. Access to statistical software to implement these models has led to widespread application in numerous disciplines. However, careful consideration should be paid to their…

## 355 Citations

### Random-Effects, Fixed-Effects and the within-between Specification for Clustered Data in Observational Health Studies: A Simulation Study

- EconomicsPloS one
- 2014

A simulation study is conducted to compare RE, FE, and WB estimation across 16,200 scenarios and concludes that the WB approach has been underutilized, particularly for inference on marginal effects in small samples.

### Fixed effects analysis of repeated measures data.

- EconomicsInternational journal of epidemiology
- 2014

The analysis of repeated measures or panel data allows control of some of the biases which plague other observational studies, particularly unmeasured confounding, but the reduction in bias may come at the expense of precision, particularly if there is little change in exposures over time.

### To GEE or Not to GEE: Comparing Population Average and Mixed Models for Estimating the Associations Between Neighborhood Risk Factors and Health

- EconomicsEpidemiology
- 2010

It is argued in general that mixed models involve unverifiable assumptions on the data-generating distribution, which lead to potentially misleading estimates and biased inference and is concluded that the estimation-equation approach of population average models provides a more useful approximation of the truth.

### On the Unnecessary Ubiquity of Hierarchical Linear Modeling

- PsychologyPsychological methods
- 2017

This article compares and contrasts HLM with alternative methods including generalized estimating equations and cluster-robust standard errors and demonstrates the advantages of the alternative methods and also when HLM would be the preferred method.

### Effect Partitioning in Cross-Sectionally Clustered Data Without Multilevel Models

- MathematicsMultivariate behavioral research
- 2019

It is shown how generalized estimating equations (GEEs) can be used to effectively partition effects without random effects and violations of distributional assumptions adversely affect estimates with MLMs but have no effect on GEEs because no such assumptions are made.

### Fixed effects models versus mixed effects models for clustered data: Reviewing the approaches, disentangling the differences, and making recommendations.

- PsychologyPsychological methods
- 2019

The differences between mixed effects and fixed effects models for clustered data are discussed, each approach is reviewed, and a within-between specification is discussed, which blends advantageous properties of each framework into a single model.

### A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure

- EconomicsStatistical methods in medical research
- 2019

To flexibly and efficiently estimate the effect of a cluster-level exposure, two targeted maximum likelihood estimators (TMLEs) are presented and it is suggested that estimation under the sub-model can result in bias and misleading inference in an observational setting.

### A New Approach to Hierarchical Data Analysis: Targeted Maximum Likelihood Estimation of Cluster-Based Effects Under Interference

- Economics
- 2017

This work presents two targeted maximum likelihood estimators (TMLEs), which harness the hierarchical data structure to reduce bias and variance in an observational setting and increase efficiency in a trial setting, and illustrates the potential gains from incorporating the full hierarchicalData structure during estimation, while avoiding unwarranted assumptions.

### No quick fix: understanding the difference between fixed and random effect models

- EconomicsJournal of Epidemiology & Community Health
- 2010

This commentary considers the major assumption underlying the chosen fixed effects model, details how the alternative random effects approach would allow testing of this assumption and reflects on the need for a widespread understanding of the importance of the choice of model.

### Conditional assessment of the impact of a Hausman pretest on confidence intervals

- Mathematics
- 2015

In the analysis of clustered and longitudinal data, which includes a covariate that varies both between and within clusters, a Hausman pretest is commonly used to decide whether subsequent inference…

## References

SHOWING 1-10 OF 62 REFERENCES

### MEANINGFUL STATISTICAL MODEL FORMULATIONS FOR REPEATED MEASURES

- Mathematics
- 2004

This paper illustrates and exemplifies that a number of issues arise from decisions to choose a parametric statistical model, even in relatively simple settings, such as ordinal regression, linear mixed models, models for cross-classified data and generalizedlinear mixed models.

### Selection of Working Correlation Structure and Best Model in GEE Analyses of Longitudinal Data

- Computer ScienceCommun. Stat. Simul. Comput.
- 2007

A selection method called QIC is proposed which can be used to select the best correlation structure and the best subset of explanatory variables in GEE and a computing program is developed to calculate the QIC value.

### Small sample inference for fixed effects from restricted maximum likelihood.

- MathematicsBiometrics
- 1997

A scaled Wald statistic is presented, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings and has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact.

### Applied Longitudinal Analysis

- Education
- 2005

dents and as a reference for those researchers embarking on running their own designed experiment, provides thorough coverage of a wide variety of topics for a number of experimental situations. The…

### QIC Program and Model Selection in GEE Analyses

- Mathematics
- 2007

The generalized estimating equation (GEE) approach is a widely used statistical method in the analysis of longitudinal data in clinical and epidemiological studies. It is an extension of the…

### Linear Mixed Models for Longitudinal Data

- Computer ScienceTechnometrics
- 2001

This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data and attempts to target applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia.

### Econometric Analysis of Count Data

- Economics
- 1997

The book provides graduate students and researchers with an up-to-date survey of statistical and econometric techniques for the analysis of count data, with a focus on conditional distribution…

### Modeling the Drop-Out Mechanism in Repeated-Measures Studies

- Engineering
- 1995

Methods that simultaneously model the data and the drop-out process within a unified model-based framework are discussed, and possible extensions outlined.

### Multilevel and Longitudinal Modeling Using Stata

- Psychology
- 2005

Preface Linear Variance-Components Models Introduction How reliable are expiratory flow measurements? The variance-components model Modeling the Mini Wright measurements Estimation methods Assigning…

### Conditional Akaike information for mixed-effects models

- Mathematics
- 2005

This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and…