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Related Experiment Video

Updated: Dec 5, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Causal graphical views of fixed effects and random effects models.

Yongnam Kim1, Peter M Steiner2

  • 1Department of Education, Seoul National University, Seoul, South Korea.

The British Journal of Mathematical and Statistical Psychology
|October 16, 2020
PubMed
Summary

Fixed effects (FE) and random effects (RE) models address unmeasured confounding differently. Causal graphs reveal RE models mimic randomized trials, while FE models handle time-invariant confounding by creating opposing paths to offset bias.

Keywords:
bias offsettingcausal graphdemeaningfixed effectgain scorerandom effect

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Area of Science:

  • Econometrics
  • Biostatistics
  • Epidemiology

Background:

  • Fixed effects (FE) and random effects (RE) models are widely used but their mechanisms for eliminating unmeasured confounding bias remain unclear.
  • Understanding these mechanisms is crucial for accurate causal inference in observational studies.

Purpose of the Study:

  • To provide intuitive graphical explanations of how FE and RE models eliminate unmeasured confounding bias.
  • To compare the data-generating processes and bias-offsetting mechanisms of FE and RE models.

Main Methods:

  • Translating algebraic formalizations of FE and RE models into causal graphs.
  • Augmenting causal graphs with computational structures of FE and RE estimators.
  • Utilizing a pretest-posttest design in a linear setting.

Main Results:

  • Causal graphs illustrate that RE models assume a data-generating process similar to randomized controlled trials.
  • FE models accommodate unobserved time-invariant treatment-outcome confounding.
  • Both FE and RE estimators offset bias by creating new non-causal paths, differing subtly in their implementation.

Conclusions:

  • FE and RE models employ distinct strategies to address unmeasured confounding.
  • Graphical representations clarify the bias-offsetting processes and highlight potential differences leading to varied biases in observational data.