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I have a spreadsheet with seven parameters and their values for 9000 samples. I need to determine which are dependent parameters and which are independent, i.e. which parameters control the changes in the other ones.

Please let me know which algorithm might be helpful. I have thought of PCA and regression but I did not understand how I can use them to determine the independent and dependent parameters.

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    $\begingroup$ what do you mean exactly by dependent and independent? $\endgroup$ – Patrick Coulombe Aug 6 '14 at 4:24
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    $\begingroup$ by independent i mean those parameters are controlling parameters. They control the changes in the dependent parameters. $\endgroup$ – ankitha Aug 6 '14 at 4:54
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    $\begingroup$ Normally, this is determined by thinking and not by statistics. $\endgroup$ – Michael M Aug 6 '14 at 13:29
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You can try the pcalg package for R to try to automatically detect causal structure in your (observational) data.

Read the vignette for an introduction to the used concepts.

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Another useful resource for learning the causal relationships between variables is the Tetrad program. Tetrad contains implementations of many major causal structure learning algorithms, including PC, PC-Stable, GES, FCI, ICA-LiNGAM, and others.

The Tetrad website has many resources explaining how to use Tetrad, although it is still not a particularly intuitive interface. Richard Scheines has recorded a tutorial on Tetrad (and causal structure learning in general), which might be more helpful.

The choice of search algorithm depends on the assumptions you are willing to make about your data. For example, if you think there are confounding variables that you have not observed, which might produce an association between the variables you have observed, then you should use the FCI algorithm (which allows for the presence of unobserved confounders). If you think your data is (at least approximately) multivariate Gaussian, then you can apply the default conditional independence test in FCI (the Fisher-Z test). However, if you think the data are not jointly Gaussian, you should probably use an independence test that allows for non-Gaussianity, such as the Conditional Correlation test. Can you tell us a little more about your data?

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