I have a big dataset with many morphological data as variables and I have lots of missing data. I will perform an nMDS and as it does not allow the presence of missing data, then I need to be able to eliminate the missing data by eliminating some variables or some samples. To do this in a consistent way while keeping most of the data, I eliminated all the samples with missing data, performed a PCA and in R I obtained the contribution of the variables. I then added back all those samples that were eliminated and considered only the variables that had a contribution above the average. But a friend pointed out that by doing this I am throwing away lots of data,some even independently very informative. So, I am now trying to figure out how I can use the results of the contribution of the variables to balance excluding characters and individuals to maximize the information in my dataset. How can I check for the independence of the variables? Would correlation be the best way? Or angle between variables in the PCA? I know the cosine of the angle is equal the correlation between the variables, so both correlation and the angle would be telling me the similar information? Any suggestion on other methods are also welcome.
There are a number of R packages which address the issue of missing data in multivariate data-sets. One possibility for instance is missMDA. Is there any reason why you avoided using them? I have not used the package myself but it seems to help with your situation.