I want to compare the strength of the association between time-varying variables with the association between those same variables at the aggregate (mean) level to demonstrate the attenuating effect of aggregation. Does anybody have a reference for how this is done? Thank you!
Could you do it in SEM with a bivariate latent-trait model? These models wouldn't be nested, but might get you on the right track
In this idea, you'd have to use standardized variables and correlations, rather than covariances. Otherwise, the time-varying model would have different correlations fluctuating with the time-specific variances. Perhaps someone else will have a variant that doesn't require this.
Time-varying model:
A1 B1, A2 B2, etc., to At Bt. The covariances are constrained to equality over time, and show the correlation at the within-time level. Other covariances (i.e., across time) are freely estimated.
Aggregate model:
FA indicated by A1...At with all loadings constrained to equality and FA's variance fixed to 1.
FB indicated by B1...Bt likewise.
FA FB is the correlation of the aggregate.
That will get you point estimates and SEs for each of the two correlations of interest. If you want to test the difference between them, you'd probably have to bootstrap a confidence interval of the difference between the two coefficients.
Pat
This article discusses how to estimate the extent to which longitudinal and cross-sectional effects are different in an overall random-effects model
Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data Andrew Bell, Kelvyn Jones
https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_modelling_of_Time-Series_Cross-Sectional_and_Panel_Data?ev=prf_pub
Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...
Hi Anne,
Although not a paper on how to do this, the following could be of interest and provide some ideas
https://www.researchgate.net/publication/235009185_The_impact_of_fluctuating_workloads_on_well-being_and_the_mediating_role_of_work-nonwork_interference_in_this_relationship
Article The Impact of Fluctuating Workloads on Well-Being and the Me...
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