> 2. You wrote: > > ?3. I think I remember you saying that Arthur's program won't/can't/ > shouldn't be asked to handle segments whose lengths are too > different, and that's why you divided the lengths into intervals. > However, I wonder if it might not be better to make the predictions > based on the two actual lengths (or their mean and difference) > instead of the interval midpoint. For things that change regularly > with L, all we need to do is include the product of L with that > predictor. (Whether it's L or ln[L] is a separate question; I'm > using just plain L et al for convenience.) ? > > This would be both possible and appropriate when we use a version of > the logistic regression model in which each cell is a single input > pair and n0+n1 = 1. > > But if you decide that we should ALSO continue using a model in which > each cell is the 00,01,10,11 residual subset obtained from the x1 and > x2 drivers for a given length interval, then what you?re suggesting > would obviously be impossible (because at the cell level, we?re > ?above? the pair level and have therefore lost the actual L?s > associated with elements of the pairs.) >
I neglected to add the obvious possibility that we could do a model with single-pair input cells (rather than residual subset cells) and the following predictors
avg L of the two elements of a pair (or ln thereof) avg e of the two elements of a pair (or ln thereof) avg u of the two elements of a pair (or ln thereof) avg c of the two elements of a pair (or ln thereof) avg c/u of the two elements of a pair (or ln thereof) avg c/e of the two elements of a pair (or ln thereof) avg c/L of the two elements of the pair (or ln thereof) residual subset of the pair (00,01,10,11) w' for the residual subset of the pair (this is the "fancy" weighting factor using the covariance of 00/01/10/11) that you specified)
This would take some minor reprogramming of the housekeeping around how I submit pairs to Arthur's program and keep input/output tallies, but it might be worth it because the above set of predictors does combine all elements currently thought to be potentially predictive.
I won't be getting to the logistic regressions for another month or so, so there's plenty of time for you to think about this possibility.