I'm trying to interpret the results of Co-correspondence analysis (CoCA) with the R package cocorresp. The descriptive paper is rather unclear about how to interpret the results. I've performed the symmetric coca analysis with the result
Eigenvalues: COCA 1 COCA 2 COCA 3 COCA 4 COCA 5 COCA 6 COCA 7 COCA 8 COCA 9 COCA 10 0.2428 0.1915 0.1135 0.0929 0.0418 0.0355 0.0298 0.0144 0.0131 0.0110 COCA 11 COCA 12 COCA 13 COCA 14 COCA 15 COCA 16 COCA 17 COCA 18 COCA 19 COCA 20 0.0098 0.0087 0.0055 0.0034 0.0018 0.0015 0.0011 0.0010 0.0009 0.0006 Inertia: X Y Total: 5.8493448 2.39 Explained: 5.8491524 2.39 Residual: 0.0001924 0.00
and then I also used a crossvalidation with the crossval function
Cross-validatory %fit of Y to X: COCA1 COCA2 COCA3 COCA4 COCA5 COCA6 COCA7 COCA8 COCA9 COCA10 COCA11 0.760 1.939 2.562 3.928 3.943 4.287 4.443 4.619 5.407 5.366 5.500 COCA12 COCA13 COCA14 COCA15 COCA16 COCA17 COCA18 COCA19 COCA20 5.468 5.154 4.913 3.989 -0.466 -2.043 -4.813 -7.198 -9.662
I'm not quite sure what to do with this information or how to interpret the results. If I'm looking at a poor fit of 0.76% and 1.9% to the first two axes, I don't think these are strongly corresponding to each other. Am I correct in this conclusion? Is this equivalent to the correlation coefficient discussed in the paper? If not, how can I find this correlation value? Also, any idea in how i can find the p-values for this analysis?
Thank you!
Hi Samuel,
Maybe I'm answering too late? Also, I'm not an expert in this.
In any case, a cross-validatory test is used for predictive purposes because this test leaves one sample out and tries to predict the composition of that sample, and then compares the prediction with the actual data. It does that for every sample and obtain a prediction level. So in this case you have a response community and a predictor community.
In the symmetric CoCA, there is no response or predictor, but rather it correlates the communities. Your CoCA results give you the co-variation fit between the communities. You have the variation explained (5.84...), the total variation (5.84...) and the residual (0.000019...). So it looks like your two communities are highly correlated.
Two, imo, clear and well explained examples of symmetric and predictive CoCA using the R package cocorresp was published here (one of the authors is the original developer of CoCA):
Article Investigating microbial associations from sequencing survey ...
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