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#mediation #stats question: if a mediator (obesity) explains a major portion (32%) of the association of X (change over time) with Y (pain) but the model explains at most 3% of variance in Y, is it still substantively meaningful to interpret mediation?
@ndporter Probably a non-helpful comment, but I'd be disinclined to treat pseudo-R2 as talking about % of variance explained. It's analogous to R2 but it isn't calculated in terms of variance.
(Obvs your observation that your model doesn't explain much is true.)
@bthalpin for sure. I know it's not precisely true. The question is (with ballpark figures): if the rates increase 30% over time, obesity explains 32% of the relationship with time on an individual level, but the model improve our prediction of pain 3% or less, can obesity really be said to mediate the difference (e.g. account for anywhere close to 1/3 of the change or 10% of the total pain)?
@ndporter There are 2 different views of models: the relationships they make visible in the coefficients & their corresponding hypothesis tests, versus their predictive power. As long as we make the (sometimes heroic) assumption that the processes not included in the model (omitted vars etc) are not correlated with the variables in the model, the relationships are well estimated (even if they don't make a huge difference). Obvs the poorer the fit the more room for omitted variable bias.
@ndporter (Also, if pain_scale is ordinal, you might get more power from ologit)
@bthalpin it is a 3-point ordinal scale and this part of the analysis is modeled on someone else's, so I'm sticking with their choice of mlogit. When I extend, I'll probably use ologit.
@bthalpin Thanks, this is the kind of thing I was looking for. In this case, the assumption is probably not warranted but may be approximately ok - as long as there's some transparency in the discussion, I guess.