Dear Holger Steinmetz, I would like to recommend this work:

An Examination of Firm, Industry, and Time Effects on Performance Using Random Coefficients Modeling

Jeremy C. Short, David J. Ketchen, Jr., Nathan Bennett and Mathilda du Toit

Organizational Research Methods 2006; 9; 259

DOI: 10.1177/1094428106287572

Best regards and take care

Are the county rates also measured weekly? I am somewhat confused by what you see as the problem. I see it as a three level model: repeated measures within families within counties. The changing county values can only possibly account for that bit of the mood that differs at county level. It may be important to have random slopes for a key family exposure and cross-level interaction to try and account for those changing differentials.

Dear Kelvyn and Alexandre,

as these are county-level infection rates, I guess the goal would be to aggregate them on the week-level.

And yes, a three level-model was in my mind too, until someone noted that the county-variable implies a special problem as counties are in a more or less local proximity to each other and this would have to be reflected (I wonder whether this represents some form of spatial autocorrelation).

My hunch is that this could be somehow modelled in a GAMM with a Markov random field smoother and an interaction between the county level variable and the time-variable....What do you think? But still I don't know how to reflect both--the county-ID and the county-variable in the R code. There is one example by Gavin Simpson (https://fromthebottomoftheheap.net/2017/10/19/first-steps-with-mrf-smooths/) where the MRF smoother is used to model the y-variable directly (in that case, variations in education level across US counties).

Best,

Holger

In general it is the response given the predictors that should not contain spatial dependence - so in your case it is the residual geography of mood that is important. see the Final chapter of this to see how you can model spatial dependence with time Book Developing multilevel models for analysing contextuality, he...

The Bayes X software has GAMM facilities with spatial dependency and there is a R version I understand

https://www.uni-goettingen.de/de/what+is+bayesx/550520.html

https://cran.r-project.org/web/packages/BayesX/BayesX.pdf

Great, thanks. That sounds a fruitful way.

I, too, was puzzled that the person you warned me (an epidemiologist who is experienced) noted the proximity as a thing.

For the case, you are interested, I copied his mail below.

But many thanks anyway

All the best,

--Holger

Holger, the county part/level is not just a higher level, it is spatially structured one by itself too: neighboring counties will have similar #s (especially with infection numbers).

The proper way to do these spatial + longitudinal + mediation (SEM) components is still done with different tools, I will post here references I know of; but there might be a simpler workaround by =generating spatially lagged variables for any effect in the model, and using them in the regular data afterwards for say SEM longitudinal models (which can have a mixed, multilevel, or more to my liking, a latent growth hat on, they are equivalent, see: http://evaluatehelp.blogspot.com/2020/06/lmmmlmlgm.html). See a brief description here:

https://www.samsi.info/working-groups/ the Working Group VI: Spatial Mediation and Longitudinal Modeling in Program on Data Science in the Social and Behavioral Sciences (Spring 2021)

Anselin, L. (2013). Spatial econometrics: methods and models (Vol. 4): Springer Science & Business Media.

Anselin, L., & Rey, S. J. (2014). Modern spatial econometrics in practice: A guide to GeoDa, GeoDaSpace and PySAL: GeoDa Press LLC.

LeSage, J. P. (1999). Applied econometrics using MATLAB: Dept. of Economics, University of Toronto http://www.mysmu.edu/faculty/yujun/Econ623/Matlab_book_LeSage.pdf

The counties are indeed spatially structured , so it depends how strong you think the dependency in the mood outcome is likely to be. The Samsi stuff and blog looks useful. I find that the multilevel approach for longitudinal data is much more natural for panel data than SEM , and more flexible in that it can use continuous time , especially in the fixed part (this matters when you have 25 readings per person) see

http://eprints.lse.ac.uk/52203/1/Steele_multilevel_models_longitudinal_2008.pdf

for a comparison, but I am biased, and came out of one tradition and not the other!

A continuing problem with spatial models is defining the connectivity - the spatial weights - contiguity is not necessarily the best way to go. If I was modelling COVID in the current hotspot of the South Wales, I would define the connectivity up and down the valley based on transport routes and not across the interfluves. This paper (and in another context) tries to model alternative weighting schemes to see what scale the spatial pattern comes into focus.

Article Modelling residential segregation as unevenness and clusteri...

Yes, despite being an SEM fanboy, a multilevel perspective is much more efficient both regards to data management (I even format codebooks or even invitation lists as long-format nested structures :) with individuals to be invited nested in their departments :))

I will take a look in the material. I currently learn about spatial data and modelling possibilities. A completely new world for me as a psych!

Thanks for your support,

Best,

--Holger