Correlations

The correlation tab will calculate the correlation matrix for the currently selected fitting parameters at their current value. This allows us to estimate if any parameters are strongly correlated.

(NOTE: After a fit has completed, the  final correlation matrix will be determined for the best fit values automatically and displayed on the "Fitting Details" tab. The "EPR Parameters...Correlations" tab allows us to estimate correlations from the starting values before fitting). 

The correlations are displayed as a matrix containing all possible pairwise parameter combinations. The values are in the range from -1 to 1, where 0 means no correlation, "-1" means 100% negatively correlated, and "1" means 100% correlated. The background color has a red tint proportional to the absolute correlation value.

Troublesome correlations show in dark red!

Any fitting parameter is correlated to some degree with all other parameters so a correlation of zero typically does not occur.

What are correlated parameters?

A correlation shows how much the change in one parameter can be compensated by a change in another parameter for a nearly equally good fit.

For example, if we have two parameters (A1, A2) and are trying to solve A1 + A2 = 10, there is an infinite number of solutions because the two parameters are 100% negatively correlated. Any change in A1 can be fully compensated by a change in A2 for a perfect solution. Since an increase in A1 can be compensated by a decrease in A2, the correlation is -1. IF we fix A1, there is one unique solution for A2.

What causes EPR parameters to be correlated?

All parameters are correlated to some degree. For example an increase in rate increases the amplitude of the central line that can be somewhat (but not perfectly!) compensated by a decrease in scale. Rate and scale are thus correlated with a negative value.  Even a relatively strong correlation might be OK, but If two parameters are highly correlated (e.g. |r|>0.95), one of them needs to be fixed at a reasonable value to successfully fit for the other.

In EPR, a very strong correlation exists between the isotropic g value (g1) and the shift parameter, because they both move the spectrum left or right without changing the lineshape much. The correlation between "g1" and "shift" will be close to 1.0.

Correlation might depend on the values of other parameters. For example Ax, Ay, Az are highly correlated to each other for fast motion, but uncorrelated for slow motion. For fast motion, only fit for A1, i.e. the isotropic average.

Use the correlation tool to potentially identify correlations between the parameter estimates, but note that the correlations could be different at the best fit values. The correlations will be most meaningful if the parameter estimates are reasonable.