Demetri Pananos
New blog post about justifying interpreting a difference in means on the log scale as a relative difference in means on the natural scale
https://dpananos.github.io/posts/2022-11-25-taylor-series/
Demetri Pananos Ph.D - Way Too Many Taylor Series

Let \(Y(a)\) be a potential outcome for a continuous measure under treatment status \(A=a\), which for the purpose of this blog post can be considered a binary treatment. When is

Nov 27, 2022 at 8:55pmMastodon for iOS
Show threadCarlos ScheideggerNov 27, 2022
@Phdemetri I *love* the equation coloring. I wonder if there's a way we could make that work nicely with the quarto themes.
Show threadDemetri PananosNov 27, 2022
@scheidegger would love to hear ideas! This was a PAIN to write up
Show threadCarlos ScheideggerNov 27, 2022
@Phdemetri Yeah, I don't really know how to do it. But I'd love for it to be easier for other folks too! We would have to teach MathJax a macro that knows to expand into a CSS variable that is tied to the quarto bootswatch themes.
Show threadElio CampitelliNov 27, 2022
@Phdemetri What a teaser. I can't wait for the sequel!
Show threadCollin EdwardsDec 15, 2022

@Phdemetri Pretty sure that since the Taylor series is only locally a good approximation, this is predicated on "small" variances (wrt non-linearities in the log function). Which is maybe your point in the next blog post?

But with this in mind, the takeaway should be "difference in log means is a close approximation to the relative differences of the means, when variances are small", I think?

Show threadCollin EdwardsDec 15, 2022
@Phdemetri A critique I've seen leveled at some evolutionary models is that evolution depends on genetic variation, but the use of Taylor series approximation in those models depends on genetic variation being so small that fitness functions are effectively linear.
Show threadDemetri PananosDec 16, 2022
@collinedwards yea next step would be to say something about the variance.