In an experiment several measurements are taken using similar but different measuring instruments. (The number of measurement tools used in a single experiment could range from 2 to 500 instruments, but most have a low number (~2 - 3) of instruments used.) Since all the instruments are measuring the same effect, it is expected that they produce similar measurements, but possibly with difference sources and levels of noise. Some of the measuring tools may unknowingly be malfunctioning and produce erroneous data altogether. This means most of the measurements are somewhat correlated (> 0.8), but some could be uncorrelated or even inversely correlated. How can one summarize the measurements of the instruments in such a way as to best represent the real value of the quantity being measured?
Possible approaches to this problem might include using:
(1) a regression model to fit the measurements and then interpolate the measurement's summarized value, (2) the first component of a principle component analysis, (3) or the scores from a factor analysis.
Which method is most appropriate for dealing with the task or is another approach better for doing this summarization?