A framework of R-squared measures for single-level and multilevel regression mixture models

Area of Science:

• Psychology
• Statistics
• Data Analysis

Background:

• Regression mixture models are widely used in psychology for both single-level and multilevel data.
• Existing research lacks comprehensive R-squared measures for regression mixture models, leading to reliance on p-values instead of effect sizes.

Purpose of the Study:

• To introduce an integrative framework for R-squared measures in single-level and multilevel regression mixture models.
• To provide researchers with tools and methods for quantifying explained variance in these complex models.

Main Methods:

• Developed 11 distinct R-squared measures based on definitions of outcome and predicted variance.
• Utilized analytical relationships and graphical illustrations to explain the measures.
• Demonstrated novel decompositions of R-squared into meaningful sources of explained variance.

Main Results:

• Presented a unified framework for R-squared measures applicable to various regression mixture models.
• Introduced new software tools for practical computation of these measures and their decompositions.
• Showcased the utility of these measures through two empirical examples.

Conclusions:

• The proposed R-squared measures enhance the interpretation of regression mixture models by providing effect size information.
• The new framework and software enable psychologists to gain deeper insights into explained variance in their data.