direction of pgls

[mwpennell]

do we want to have sla ~ leafn or the other way around (shouldn't make a difference obviously but theoretically could be different)

[wcornwell]

There is a lot of discussion on this point in the ecology literature. Because the variables are not cause-and-effect framework--it'd be nice to have a symmetric way to handle error--ideally we'd do the pgls equivalent of sma, see

http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2011.00153.x/abstract

Dan Falster has published quite a bit on this, so it'd be good to chat with him on it at some point...

[richfitz]

Though doing this will raise the ire of Hanson at least. For example: http://sysbio.oxfordjournals.org/content/61/3/413.long See also: https://www.nescent.org/wg/academy/images/6/6d/AdaptationandtheComparativeMethod.pdf

[wcornwell]

Interesting. I didn't realize the Hansen versus Warton tension. Hansen certainly doesn't hold back...

I think Hansen is right about SMA if you want a predictive model. But where there is no clear predictor-response structure to the two variables, and you're not using the slope of the line for prediction, then there is still an argument for using a symmetric model like SMA. Maybe you just shouldn't call it "regression"

For us seems like the biological questions could be: 1) are simple evolutionary models more adequate for modeling variation in leafN at a given SLA compared to the leafN by itself? 1a) the reverse 2) are simple evolutionary models more adequate for modeling 1) SLA 2) LeafN, or 3) the major axis of variation for the two traits (this is what Wright et al. called the leaf economic spectrum)?

I sort of think 2 is more interesting biology, but maybe 1/1a is a more general question for comparative methods?

[lukejharmon]

This is interesting stuff. But worth pointing out that the adequacy part of the picture changes with something like SMA. We are using residuals (in Y) to test adequacy. For sma-type models, one might use orthogonal residuals. I suppose those should be mvn too?

On Oct 18, 2013, at 1:31 AM, Will Cornwell notifications@github.com wrote:

Interesting. I didn't realize the Hansen versus Warton tension. Hansen certainly doesn't hold back...

I think Hansen is right about SMA if you want a predictive model. But where there is no clear predictor-response structure to the two variables, and you're not using the slope of the line for prediction, then there is still an argument for using a symmetric model like SMA. Maybe you just shouldn't call it "regression"

For us seems like the biological questions could be: 1) are simple evolutionary models more adequate for modeling variation in leafN at a given SLA compared to the leafN by itself? 1a) the reverse 2) are simple evolutionary models more adequate for modeling 1) SLA 2) LeafN, or 3) the major axis of variation for the two traits (this is what Wright et al. called the leaf economic spectrum)?

I sort of think 2 is more interesting biology, but maybe 1/1a is a more general question for comparative methods?

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[mwpennell]

I think for the purposes of assessing model adequacy, we shouldn't go down the SMA rabbit hole.

[wcornwell]

Matt,

On Friday Rich and I were chatting about why simple models are more adequate for PGLS compared to the univariate analysis. We didn't come up with much (maybe because it was Friday evening after climbing in a pub) but two quick thoughts:

1) check if in a simple simulation whether a simple link between two simulated traits makes models for each trait individually inadequate? (I might be mis-representing this idea, Rich?)

2) Run this result by someone really analytically smart (e.g. Felsenstein?) and see if there is something that we're not seeing.