Here is a comment on one of Don's comments, and then a followup on part of the re-description of the problem.
On 27 May 2004 06:22:47 -0700, [EMAIL PROTECTED] (Donald Burrill) wrote: [ ... ] > less-rapidly-changing regions. At some level, you're really asking > "Which points can I expect to show me the best separation between models > that I want to distinguish between, which points will give me the best > available precision in estimating the parameters I'm currently looking > at, and which points will help me diagnose a badly fitting model?" We > may agree that today (or perhaps yesterday) it might have seemed > reasonable to try to fit sigmoidal data with a cubic, or perhaps > quintic, function in X; tomorrow it may become obvious that "Oh! That > ought to be a logistic function!", which might lead to other choices for > apparently-optimal design points.) In other words: Keep in mind your purpose. Or, figure out your purpose. If you want "a good description," then part of the purpose might be the discrimination between those alternatives of shape. > > On Wed, 26 May 2004, Xinmiao wrote in part: > > > ... I'm trying to design an experiment in which behavioral/neuronal > > response v.s. stimulus strength curves are to be measured. We know > > that the tuning curves are sigmoidal/linear, and my question was how I > > should spread out the sampling points along the stimulus dimension, > > say 4 or 7 or even more? We've also known that the error-variance, at > > least for neuronal responses, should be approximately same as mean, > > the square root of which shouldn't differ much between different > > independent variable (stimulus strength). ... > > <snip, the rest> Here is a 'sampling' issue that I touched on earlier, before this detail. That description of "neuronal response" to "stimuli strength" reminds me of only one experiment I've read. Do you: - Stick an electrode into a mass of cells; - 'stimulate' with a pulsed voltage and measure the number of cells that react; after allowing recovery time, - repeat the stimulation with the same or different voltage; - eventually stick another electrode into another location and repeat. = if yours is nothing like that, then I don't have a point = In this design, each location deserves its *own* fit if it is simple. Otherwise, location needs to be a factor in the design. The responses from one site are presumed to be correlated, and it loses power and precision to ignore that fact. I don't know what has been shown in previous experiments, but if the facts are not well-known, I figure that the peak-voltages should be randomized, and the recovery-times and order taken into account (or, examined and discounted). I'm curious as to whether the experiment is this, or anything similar. -- Rich Ulrich http://www.pitt.edu/~wpilib/index.html . . ================================================================ This list will soon be replaced by the new list EDSTAT-L at Penn State. Please subscribe to the new list using the web interface at http://lists.psu.edu/archives/edstat-l.html. ================================================================
