I have been performing a relatively routine fit on data for some time. I fit the data to a fairly simple semi-empirical function. For each data point I perform repeated experiments to build a histogram and then fit using standard methods.
However the situation is slightly more complicated than this, technically the variable x is a product of lots of values (~60-70) which I combine to create a single variable for the fit. There is in principle no reason that I could not fit to the full expression the only disadvantage being that I could no longer bin the data as each data point would be unique. I do know my experimental uncertainties quite well so I could quite easily fit with a Gaussian maximum likelihood.
If I do this I increase my number of variables from one to 60-70. My question is this: are there any interesting effects/pitfalls that occur when fitting with a large number of variables? Although the number of free parameters does not change I feel like I am going from well sampling 1-D space to barely sampling a very high dimensional space, albeit it a very highly correlated one. The fit contains only two free parameters and I would have many hundred data points. If nothing else it would be interesting to see how the fit is biased by my combined variable.