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The Curious Case of the Cross-Sectional Correlation
1Methodology and Statistics, Faculty of Social and Behavioural Sciences, Utrecht University, Utrecht, The Netherlands.
Multivariate Behavioral Research
|January 4, 2023
Summary
Cross-sectional correlation in psychology is re-examined, revealing it depends on both between-person and within-person correlations when ergodicity is absent. This clarifies its meaning and utility for general psychological laws.
Area of Science:
- Psychology
- Statistics
- Multilevel Modeling
Background:
- Cross-sectional correlation is a foundational measure in psychological research.
- Concerns exist regarding its interpretation, particularly Peter Molenaar's work on ergodicity, when seeking generalizable laws.
Purpose of the Study:
- To clarify the meaning of cross-sectional correlation in the absence of ergodicity.
- To provide a deeper understanding of its utility for discovering general psychological laws.
Main Methods:
- Utilized Cattell's databox framework.
- Adopted a multilevel perspective to analyze correlations.
- Derived an analytical expression for cross-sectional correlation.
Main Results:
- The cross-sectional correlation is shown to be a function of between-person and within-person correlations.
- Two key curiosities are identified: the distinction between within-person and average person-specific correlations, and the nature of cross-sectional correlation as a weighted sum.
Conclusions:
- The study clarifies the interpretation of cross-sectional correlation when ergodicity is not met.
- Provides a nuanced understanding of how between-person and within-person dynamics influence this measure.
- Offers R code for researchers to explore these complex relationships further.
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