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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.

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How exactly are you fitting the data and how do you combine all the variables into 1? Is your purpose prediction or identifying the important variables? –  Glen Jan 7 '12 at 0:18
    
I am currently fitting the histogram with chi-squared fitting. If I were to fit using individual data points I would still use chi-squared fitting/gaussian maximum likelihood as the data are more or less normally distributed. The x values are multipled together with a certain weighting (each element is between 0 and 1), which has come from experience. My aim is really just that I am wondering why use an approximate value when I can use the full expression. The purpose is to find the best fit parameters to use the model as a predictive tool. Although I may do some PCA out of curiosity. –  Bowler Jan 7 '12 at 0:32

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