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 interval-censored - that is, the age is an estimate with a range between T(L) < U < T(R) where the true age U is some estimate between the left and right values. 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 imputation methods involving kernel density, midpoint approximation, and various other maximizing techniques.
Any suggestions on how to handle interval-censored explanatory data when fitting data to a logarithmic (or any) model such as the one described above.