# Finding a good parametric form for a model

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

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...