On Nov 12, 2:01 pm, djh <halitsk...@att.net> wrote: > I. You wrote: > > ?First, the simplified model is not a legitimate replacement or > substitute for the original model, but you seem to be treating them > as interchangeable.? > > No ? not at all as ?interchangeable?, but rather as two different > alternative models which can be ?ranked? better/worse in two different > ways: > > A) the simplified model is ?better? than the original because: > > 1) if there IS a correlation between ln(c) and ln(e), we can tell > immediately whether c varies directly or inversely with e; this is not > the case when considering ln(c/L) and ln(c/e); > > 2) similarly, if there IS a correlation between ln(c) and ln(u), we > can tell immediately whether this c varies directly or inversely with > u; this is not the case when considering ln(c/L) and ln(c/e). > > 3) similarly, if there IS a correlation between ln(c) and > (ln(e),ln(u)), we can tell what?s actually going on between c and e,u > much more easily than in the case of a correlation between ln(c/L) and > (ln(c/e), ln(c/u). > > 4) since we can tell immediately how c correlates with e and u (if in > fact it correlates at all), we can determine whether there are any > cells of the model in which Jacques central hypothesis holds- namely, > that c should vary directly with e (but not necessarily vary at all > with u). > > B) the simplified model is ?better? than the original precisely > because the original model does not allow us to distinguish among the > three dicodon sets 1,2,3, whereas the simplified model does. In > particular: > > 1) using the simplified model, the p?s of all 4 three-ways (euSe, > euSu, eS, and uS) are < .05 ONLY for dicodon set 2, not for dicodon > set 1 or 3; > > 2) using the original model, NO dicodon set exhibits 3-ways whose p?s > are all < .05. > > So, in effect, use of the simplified model allows us to assert that in > a probabilistic sense, it is more likely that there is a significant > effect of e and u on c when we use dicodon set 2 rather than 1 or 3, > i.e. that the ?union of two energetically equivalent subsets? (2S = 1S > U 3S) is more likely to generate data showing a significant effect of > e and u on c than 1S or 3S alone. > > (I should note en passant that you yourself never really trusted the > original correlations to be non-tautological, because of the ratios > c/L, c/e, and c/u that appear in them.) > > II. You wrote: > > ?Second, I thought that one of your requirements was that all the 3- > way interactions had to differ significantly from zero in both the > statistical and practical senses of the term.? > > No. From my point of view, it?s only necessary that there be a p < > .05 attached to the 3-way. > > And since I know that statement will ?get on your last nerve? (as they > say down South here), please allow me to explain why I made it, even > after all the times you?ve told me that ?p?s? are more treacherously > meaningless than instructive. > > Recall why I dragged you into this whole process of evaluating various > linear regressions in the first place: > > A) first, it was to try and figure out which are the highest-quality > linear regressions to use in constructing predictors for the logistic > regressions we were using to investigate structural alignability (call > these linear regressions our ?driver? regressions.) > > B) second, it was to try and figure out which S subset(s) generate(s) > the highest-quality driver regressions: 1S but not 2S or 3S, 2S but > not 1S or 3S, 3S but not 1S or 2S, 1S and 2S, but not 3S, etc. > > C) third, it was to try and figure out whether the quality of the > driver regressions can be improved by restricting u-level to uH, or > whether results with uH are the same as those with uL. > > And it?s my admittedly naive opinion that questions (A-C) are all > ?answered?, AT LEAST SUGGESTIVELY, by the fact that the 3-ways for > dicodon set 2 all have associated p?s < .05, whereas the 3-ways for > dicodon sets 1 and 3 do not. > > That is, it doesn?t matter what the absolute size of the 3-way > difference is ? what matters for the purposes of deciding (A-C) is > only which 3-ways are associated with p?s < 0.5. > > III. You wrote: > > ?Third, are you now saying that you want a 4-way interaction, that the > 3-ways should differ across dicodon sets? Or are you saying that it's > OK to ignore dicodon sets that don't show a 3-way interaction?? > > I think this question was more or less answered by what I said in II > above. In particular, it?s not only ?OK?, but ?imperative?, to ignore > any dicodon set whose 3-ways for euSe, euSu, eS, and uS are not ALL > associated with p?s < .05. This is because if we relax this > condition, there is a far greater chance that operating with a given > ?S? dicodon subset is no better than operating with any other ?S? > dicodon subset. > > ******** > > In any event, permit me close by saying that: > > 1) on the one hand, I completely accept your opinion that we won?t > really know the full story of what?s going on until we do the kind of > trivariate distributional analysis you?ve suggested; > > 2) on the other, I don?t have the knowledge to do such an analysis > without relying on you or someone else to guide me thru each and every > step, which is probably unfeasible. > > So basically, what I?m asking is whether the result obtained for the 3- > ways using dicodon set 2 and the simplified model is ?enough? to take > our chances on submitting a paper based essentially on this result. > > If you think a referee might deem the result acceptable, then I have > reason to believe that this initial paper will turn on a funding > spigot that will allow us to: > > a) do a proper trivariate analysis of the data of the type you?ve > suggested; > > b) return, at long last, to our original investigation of structural > alignability via logistic regessions whose predictors are obtained > from the residuals of driver regressions obtained using dicodon set 2s > and u-level uH.
Although I am more comfortable with the simplified model, I'm still reluctant to endorse the interactions as sufficient to warrant publication. First, there has been no mention of the reasonableness of fitting homoscedastic linear models to those variables. That needs to be checked for every regression in every cell. That's LOTS of plots to look at. There is no other way.
There is also the Bonferroni problem. A correction to the critical p is needed, but I don't know what the factor should be, or what an upper bound for it might be. When I asked (point 3 in my post of Oct 31 @ 12:36 pm) what your decision procedure was, I was hoping that your reply would allow me to deduce a correction factor, but your post of Nov 2 @ 7:35 am overwhelmed me. The answer may turn out to be simple, but it still escapes me.
With regard to the larger picture, I'm not sure that the interactions are sufficient in principle. Some time ago, I wrote (or thought about writing -- it's been so long that I can't remember which) that I wouldn't really be able to evaluate the statistical argument until after I read the paper, at which time I might say something like "Oh, so that's what you want to show. Well, in that case, you should have done ... ." I still feel that way, and probably will until I sort out your Nov 2 post.