I have a series of human growth data that I wish to fit to a 3 parameter logarithmic growth curve:
s(i) = Beta0 + B1*T + B2*ln(t), where s is a length and t is an age.
The only problem is that this age is not a point estimate. Rather, I have an upper and lower boundary to an age distribution based on tooth development. The age estimation technique returns a lognormal age distribution with an upper and lower 95% PI. I'd like to account for this "estimation" in my model, as opposed to a just plugging in a biased mean point estimate in OLS. I'd like to do this in R, but I am struggling with the best way to model and/or 'maximize' this interval so as to return a fitted curve based on the interval values. I have thought through deconvulution, simulation, Bayesian techniques, ODR, and other maximizing techniques to find the parameters that best-fit the data.
Any suggestions on how to handle such "error" in an explanatory variable, when fitting data to a logarithmic (or any) model such as the one described above??