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@SolomonKurz You can easily convert back and forth:

@SolomonKurz 😂

@stephenjwild @AJThurston @MatthewBJane ...changes the state of the system (the 2nd difference). Else, it's just noise. Any "disturbance" only becomes an information, if it has an impact on the system (where the system itself decides how to react & process on that external impulse). Just my 2 cents, mostly unrelated🤪

Head over to Blue sky: Will reduce activity here...

@mzloteanu @stephenjwild You can simplify it to following quote: "bcMLM may be preferable to FE". I would probably replace "may" with "are". I recommend the cited Bell-papers (if you have - like me - some prejudices against FE) or this vignette:

@mzloteanu @stephenjwild @mattansb @landsheapes Can you post a reprex at: This is what I get (code in ALT-text)

@mzloteanu @stephenjwild @mattansb @landsheapes ... However, in unbalanced data, the conditional and marginal predicted values can largely differ." (See

@mzloteanu @stephenjwild @mattansb @landsheapes ... namely ggpredict(), ggemmeans() or ggaverage(), resp. predict_response with the different margin options)

@mzloteanu @stephenjwild @mattansb @landsheapes Are you interested in the exact predicted values? Then you should care about the margin-options. If you need group differences (pairwise comparisons, eg), then it probably matters less, because the differences between predictions are often similar across different margin options

@SolomonKurz Therefore, I would indeed use sum scores, because it's probably more informative (condensed information) than many (correlated) items.

@SolomonKurz I have tried this with my own data, and compared imputed score to score build from imputed items. Sometimes, imputed score was lower for observations than the sum of their single items that were not imputed (meaning imputing items is probably more accurate)

@mattansb @mzloteanu @landsheapes And for mixed models, see revised handling and vignette: