Cross-Correlation Function (CCF)

[Drew Smith]

I am revising a manuscript which is exploring a new way of calculating a particular variable and was asked by a reviewer to calculate the cross-correlation between the two variables used in this calculation method to further investigate the validity of my new method.

I understand in principle what a CCF is but I am bit stumped as to what my CCFs are telling me as it relates to what the reviewer has suggested. I have never used CCFs before so maybe it's more obvious than I think.

If anyone reading this can help me out, I'd be very grateful. Since this may involve me sending you some files, perhaps it would be best if you contacted me via email or PM initially.

Thanks!!

[Dan Robbins]

Re: Cross-Correlation Function (CCF)

Hi Drew,

While I doubt I could help you with the analysis, I would reccomend you look at David Winters book 'Biomechanics of Motor Control and Human Movement'. There are good descriptions which may help clarrify the output from what ever software you used to perform the analysis.

HTH
Dan

[Erik Cattrysse]

Re: Cross-Correlation Function (CCF)

Hello Drew, We have been using cross-correlationfucntions to objectively describe the correlation between main and associated movements (i.c. axial roation of the cervical spine and coupeld lateral bending). In gate analysis this could be used e.g. to anlayse the relationship bewteen hip angle and knee angle...
cross-corrlelation is calculated as a pearson-correlation rho.
I will send a proceeding concerning the topic presented in 2006 at the ISB 3D-human movement analysis conference. (to large to upload on Biomch)
I hope it can be of any use to you.
Erik

[Todd Pataky]

Re: Cross-Correlation Function (CCF)

Hi Drew,
Although I can't be certain, it sounds like the reviewer is asking only for a quantification of the similarity of the new and old metrics. I think it would be sufficient to conduct linear regression on (new metric) vs. (old metric). "Cross-correlation" would only be relevant, I believe, if the metrics were functions of time, space, and/or some other continuous independent variable. But if the metric is scalar, then I believe that the reviewer has incorrectly referred to this as "cross-correlation".
Cheers,
Todd

[Drew Smith]

Re: Cross-Correlation Function (CCF)

Hello Drew, We have been using cross-correlation fucntions to objectively describe the correlation between main and associated movements (i.c. axial roation of the cervical spine and coupeld lateral bending). In gate analysis this could be used e.g. to anlayse the relationship bewteen hip angle and knee angle...
cross-corrlelation is calculated as a pearson-correlation rho.
I will send a proceeding concerning the topic presented in 2006 at the ISB 3D-human movement analysis conference. (to large to upload on Biomch)
I hope it can be of any use to you.
Erik

Erik, I received your paper.

Thank you for your help!

[Drew Smith]

Re: Cross-Correlation Function (CCF)

Hi Drew,
Although I can't be certain, it sounds like the reviewer is asking only for a quantification of the similarity of the new and old metrics. I think it would be sufficient to conduct linear regression on (new metric) vs. (old metric). "Cross-correlation" would only be relevant, I believe, if the metrics were functions of time, space, and/or some other continuous independent variable. But if the metric is scalar, then I believe that the reviewer has incorrectly referred to this as "cross-correlation".
Cheers,
Todd

Todd,

Thanks for your help. I think that there may be some misunderstanding operating here but sometimes it is difficult to point that out to a reviewer, especially if one doesn't have enough experience with these types of statistical analyses.

[Allan Carman]

Re: Cross-Correlation Function (CCF)

Hello Drew

If you want to establish validity between a new method and a criterion or that two devices/methods are producing the same results then you will want to measure the 'agreement' between repeated measures of the two methods.

A good reference for this is Bland and Altman, 1986, The Lancet, 307-310. They describe the same scenario that you have described, and point out that correlation does not indicate agreement. A high correlation does mean a good linear relationship between the two variables but this line could be any line and not necessarily the line representing unity.

A later reference is Bland and Altman, 1999, Statistical Methods in Medical Research, 135-160.

Another consideration with repeated measures, although getting away from the present discussion, are period and interaction effects, see Hills and Armatage, 1979, Br.J.Clinical Pharmac.,7-20.

In summary, the correlation coeficient (r) is not the correct statistic to show agreement.

Cheers
Allan Carman
School of Physiotherapy
University of Otago

[Drew Smith]

Re: Cross-Correlation Function (CCF)

Hello Drew

If you want to establish validity between a new method and a criterion or that two devices/methods are producing the same results then you will want to measure the 'agreement' between repeated measures of the two methods.

A good reference for this is Bland and Altman, 1986, The Lancet, 307-310. They describe the same scenario that you have described, and point out that correlation does not indicate agreement. A high correlation does mean a good linear relationship between the two variables but this line could be any line and not necessarily the line representing unity.

A later reference is Bland and Altman, 1999, Statistical Methods in Medical Research, 135-160.

Another consideration with repeated measures, although getting away from the present discussion, are period and interaction effects, see Hills and Armatage, 1979, Br.J.Clinical Pharmac.,7-20.

In summary, the correlation coeficient (r) is not the correct statistic to show agreement.

Cheers
Allan Carman
School of Physiotherapy
University of Otago

Thanks, Allan. I'll be sure to have a look at those references. I appreciate your contribution to this discussion.

[Yunus Ziya Arslan]

Re: Cross-Correlation Function (CCF)

Dear Dr. Smith,

You may have a look at the reference by Wren et al. (J Biomech. 2006;39(14):2714-8). A clear and condensed evaluation of cross-correlation method in measuring the similarity in shape and timing between two curves can be found in this paper.

Regards.
Yunus Ziya

[Drew Smith]

Re: Cross-Correlation Function (CCF)

Dear Dr. Smith,

You may have a look at the reference by Wren et al. (J Biomech. 2006;39(14):2714-8). A clear and condensed evaluation of cross-correlation method in measuring the similarity in shape and timing between two curves can be found in this paper.

Regards.
Yunus Ziya

Thank you, Yunas. I will get a copy of this paper.

[Andre Rodacki]

Re: Cross-Correlation Function (CCF)

Drew:
I have used CCFs and built up some experience. It is used to relate whether two signals (phenomenon) are in phase or not. It shifts one signal while the other remains "stationary. It calculates the correlation between these variables for each shift (lag) and plots you a graph showing these correlations. Well.. it works well for phase shift, but it does not work to observe magnitude of the signals (Y axis). If you are looking into movement phase shifts it is a nice approach. Several softwares run this sort of analysis such as Statistica. It is very each to run. If you have any doubts, let me know. For sake of curiosity what are you using CCFs for, i.e., what are you analyzing?

[Drew Smith]

Re: Cross-Correlation Function (CCF)

Drew:
I have used CCFs and built up some experience. It is used to relate whether two signals (phenomenon) are in phase or not. It shifts one signal while the other remains "stationary. It calculates the correlation between these variables for each shift (lag) and plots you a graph showing these correlations. Well.. it works well for phase shift, but it does not work to observe magnitude of the signals (Y axis). If you are looking into movement phase shifts it is a nice approach. Several softwares run this sort of analysis such as Statistica. It is very each to run. If you have any doubts, let me know. For sake of curiosity what are you using CCFs for, i.e., what are you analyzing?

Thank you, Andre, for your response. I basically have the same understanding of CCF, although I am not sure how to interpret relative large correlations at lags other than zero. We are looking at a different way to calculate a common variable and a reviewer suggested using CCF as a secondary indication of agreement. We have since chosen another technique but I do appreciate you taking the time to respond.