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Hello I am trying to model the relationship between two variables, say x and y. I have a number of subjects - for each subjectm I have a number of x and corresponding y, both of which are always positive. This data tends to be very sparse. There are some problem specific constraints: 1) y(0) = 0 (or very close to it) 2) y is increasing as a function of x 3) y' is decreasing as a function of x

This is rather nebulous, but I have a feeling that the most important difference between subjects is in the height of the curve, not in the slope. Because of the sparsity, I think I can get away with forcing each subject to have the same "slope" (perhaps at a specified x), but allowing the height to vary. I have been playing around with various sorts of logistic functions, but the asymptote isn't really justifiable. I have also been looking at things like a*log(x+b), but this doesn't really conform to the intuition delineated above. Does anyone have any suggestions?

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As non-expert said, if we could look at the graph we might be able to help more. –  Ross Millikan Feb 1 '11 at 5:22
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(This is supposed to be a comment.)

I would say that without knowing the physical process(es) that generated the $y$'s for each corresponding $x$'s, any number of functions would be admissible. Barring that, one usually graphs the data first before even thinking about models...

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thank you for your reply. I don't really know much about the physical process. I have plotted the data, but for each subject it is extremely noisy. This is why I am trying to just get something off the ground. To clarify a bit - I am looking for a model that has maybe 1 parameter that controls steepness, 1 that controls height, and maybe one or two others. –  grg s Jan 2 '11 at 5:17
    
Maybe you can edit your post to show that noisy graph you speak of, and then we can start from there. –  non-expert Jan 2 '11 at 5:32
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