This is related with this question.
What is the best strategy/package in R/python/Mathematica to fit a non-linear model to data with uncertainty measures in both variables?
Elaborating:
For every data point, I have several measures of two variables, $X$ and $Z$. The different measures can be treated as independent replicates. I compute $\tilde{X}$ and $\tilde{Z}$ for every data point and then calculate a third variable $Y = \tilde{Z}-\tilde{X}$. I have a non-linear model that computes $Y$ ~ f($\tilde{X}$,$p_{1}$,...). (I'm testing also different models, that's why I did not specify the number of parameters, as they change).
Now, how to do this fitting but taking into account the uncertainty in both $\tilde{X}$ and $Y$? As stated in the linked question, I'm not interested only in weighting the points, I want to propagate the uncertainty to parameter estimation.
More doubts: For different data points I have different number of measures for $X$ and $Z$. What should be used as the uncertainty of $X$ and $Z$? The standard deviation or the standard error of the mean?
The error on $Y$ should be $Y_{err}=\sqrt{X_{err}^{2}+Z_{err}^{2}}$ right?
What is an acceptable measure of goodness of fit? Adjusted R squared?
How to compare different models? I feel like I could use BIC, but for that I need to compute the log likelihood...
