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On the Common but Problematic Specification of Conflated Random Slopes in Multilevel Models.

Jason D Rights1, Sonya K Sterba2

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This summary is machine-generated.

Multilevel models (MLMs) with random slopes can suffer from unrecognized random conflation, leading to incorrect interpretations of between-cluster slope differences and biased standard errors. Researchers should use specific random slope specifications to avoid this issue for accurate multilevel analysis.

Keywords:
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Area of Science:

  • Statistics
  • Multilevel Modeling
  • Quantitative Psychology

Background:

  • Multilevel models (MLMs) with fixed slopes require disaggregating level-1 effects into between- and within-cluster components to avoid conflation.
  • For MLMs with random slopes, two types of conflation can occur: fixed conflation and random conflation, with the latter being less understood.

Purpose of the Study:

  • To clarify the nature and consequences of random slope conflation in multilevel models.
  • To demonstrate how commonly used models can still produce conflated random components.
  • To provide guidance on selecting appropriate random slope specifications for accurate multilevel analysis.

Main Methods:

  • The study theoretically explains fixed and random conflation in MLMs with random slopes.
  • It analyzes the contextual effect model with random slopes to show persistent random conflation.
  • It demonstrates the impact of random conflation on slope heterogeneity and standard errors through simulations or empirical examples (details not specified in abstract).

Main Results:

  • A commonly used model for disaggregating fixed effects in MLMs with random slopes still results in a conflated random component.
  • Random conflation leads to erroneous interpretations of between-cluster slope heterogeneity (under- or overestimation).
  • Random conflation can also produce inaccurate standard errors for fixed effects.

Conclusions:

  • Selecting appropriate random slope specifications is crucial to avoid random conflation in MLMs.
  • Unconflated models offer advantages in estimating and testing random slope variance (improved power, Type I error, bias) and in standard error estimation for fixed effects.
  • Recommendations are provided for choosing specific random slope models based on research objectives.