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

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.