[R] Maximum likelihood fitting of a functional relationship (MLFR)

[Turgut Durduran]

Hello all,

Evidently my previous message met some filter due to subject line. I am re-sending my message. I apologize if this was sent out twice.

Based on "Ripley & Thompson, Analyst, 1987
 ", I am trying to do a regression of my data which assumes a linear 
relationship between measurements by two modalities of the same 
physiological parameter. The complication is that my errors are 
heterogeneous, i.e. not only both X & Y variables have significant 
variances, their ratio and individual values differ greatly between 
subjects. I believe a simple linear regression (which ignores the 
variances) is underestimating the slope of the relationship while a 
method like deming regression is overestimating (or underestimating 
depending on what I give as the ratio) since it assumes a constant ratio
 of the variable. Therefore, I have concluded that I need to do the full
 MLFR type of analysis suggested in that paper.

Looking through 
archives and such, I could not find a direct implementation for R. I 
think a related method is that implemeted in "leiv" package which 
implements errors-in-variables methods.

Admittedly, I am bit lazy
 and I did not dig into "leiv" implementation to figure out the 
differences and whether giving the ratio of the standard errors of Y to 
those of X for each point actually is correct.


I am wondering if anyone has implemented this method in R and has an example that I can look that. 


While at it,  I am wondering what is the way to estimate the 95% confidence interval in the results both for "leiv" and "MLFR".


Thanks,

Turgut