Thanks very much for your responses, Kevin, Pierre and Lasse. I finally choose to use NMDS since it is well suited to handle non-normal and non-continuous data (McCune & Grace 2002). Moreover, the axes that I obtained from these ordination were very well-related to most of my traits, providing an excellent continuous variable pooling all the binomial data. Anyway, I agree that MCoA would be another very good solution, but I found problems in finding good (and reliable) scripts to run it in R.

regarding PCA, I don´t think that it would be appropiate for non-continuous data, Lasse, at least is what many multivariate stats books say...

as a summary to the readers of this question; MCoA and NMDS are both valid and good techniques to ordinate binomial datasets, although you need to be careful in the distance used to built the ressemblance matrix depending in your question.

thanks to all who answered to this questions, I learned a lot from you!! :-)

NMDS is Ok but the main question is about the distance method used. I am not convinced by the euclidean distance in your case, a jaccard distance could be better.

Thanks very much for your responses, Alex and Jose. About the distance used, Alex. I discussed about it with one of the co-authors and we decided that Euclidean could be more appropiate because, in our case and arguably, shared zeros mean somehow similarity (i.e. species that are not woody are more similar between them). Jaccard distance was conceived to avoid the hoofprint effect, which is confounding shared zeros as similarity. That would be like thinking that, if a tropical species is nor in the desert neither in tundra, then tundra and desert are more similar between them. Anyway, we tried both distances and the results were very similar. Do you have any reference where NMDS is used for this kind of analysis?that would be really helpful

ok, i was wrong about jaccard, I agree with you on this point, I do not know NMDS ref for this kind of data. But now I remenber about multiple correspondance analysis that is may be better to screen for a structure in multiple categorical variables. Recently MCA has been used in the paper of Ruiz Labourdette (Journal of Biogeography (J. Biogeogr.) (2012) 39, 162–176). You can easily perform MCA in R with ade4 package.

Thanks!

Hallo Santiago,

if the result of your MCA looks to complex to realise a pattern just use the more easier PCA (principal component analysis). here you can use your categorical data, afterwords I would perform a mor complex MCA to see more details..

tschau

thanks for your response, Christian. Although I´m afraid PCA is not a proper approach when you have just binomial/categorical variables, it would work better with continuous variables. I think MCA would do the work just fine, even if it is more complicated

thanks anyway

I advice to use ginis method for distance and apply PCA technique. I recently applied ginis method to find a covariance matrix of GWAS data (which is binary multivariate data) and then applied SPCA (sparse canonical correlation analysis). It worked better. I advice to try it.

Hi Satish, do you have any suggested reference for it? Thanks

Thanks, Sathish...I´ll check that

I suggest you to read this "Potential risk factors associated with human encephalitis: application of canonical correlation analysis" by Jemila S Hamid, Christopher Meaney, Natasha S Crowcroft, Julia Granerod and Joseph Beyene, it was published in BMC Medical Research Methodology 2011, 11:120. Here is the link http://www.biomedcentral.com/1471-2288/11/120. Hope it is helpful. Let me know. I have different idea for finding the co-variance structure if you need it.

Hi Santiago, has your problem solved? If not yet how about if you first try Detrended Correspondence Analysis (DCA) by using "vegan" library first in R? But first you must have to transpose data matrix. DECORANA value will say you about using PCA/RDA or CCA. I do not see there will be problem with the nature of data. Yes, certainly there will be problem if you have as many number of rows (species in your case) as number of column (binomial variables) for detail see Palmer 1994. I guess you will have more species than variables. RDA will be fine if the DECORANA value is less than or equal to 1.5 Standard Deviation Unit. If greater then you can choose Canonical Correspondence Analysis (CCA). All you can perform in vegan.

Goodluck.

Hi Sathish and Chitra. Thanks so much for your responses. I´ll check all of them...i didn´t know, but there are a lot possibilities,hehehe

Hi! standard PCA uses euclidean distance, and is suitable for covariances, so I agree with Santiago that it is not the best distance for the data described (however some suggestions like ginis method that I don't know may help to deal with this...). CCA as proposed is based on unimodal distributions (chi) of species on gradients, so numeric data are also needed as far as I understand for this ordinations to perform correctly.

I guess that NMDS as you initially proposed was an adequate measure, you just need to choose an adeqaute distance. Dice, Jaccard, Kulcynjsky and Ochiai will perform on binomial data (presence/absence of the trait). If you have more categories like Hamming can do it, and if you have mixed data then try Gower. As your data are binomial Dice gives more importance to matches than to mismatches, while Jaccard isand Kulcynjsky are balanced. Ochiai I don't know very well how it performs. Finally if you need to have eigen axis to group your initial variables in new composed variables, Principal coordinates (PCoA) will do it just the same way as PCA but allowing you to change the distance measure.

Thanks, Alex....excelent response

You can also change the distance preserved in PCA, within some bounds. The original data can be scaled such that when doing a PCA, the resulting distances are something else than Euclidean. This method has been described in Legendre & Gallacher 2001 in Oecologia.

Usually ordination is performed such that the data table has species in the columns and samples in the rows. Here you have species in rows and their properties in the columns. When it comes to choosing an appropriate distance index, it should be remembered that there is no error (such that a species would not be observed in a sample although it is actually present; a plant is herb if it is a herb and that's it) associated with the information in the columns, and that double absence is as informative as double presence. In this case it can thus be very dangerous to use an index that weights different association between the categorical variables differently. Therefor I would recommend that you use PCA for the data.

I'm not quite sure of your goal, but you might want to cluster your species (row vectors) using machine learning techniques, and then study the characteristics of the clusters.

Hi,

I totally aggree with Alex Salas-López. A PCoA with jaccard on the disjonctif table should be really informative. However you lose the original link between modality of a same variable. Hence an alternative could be to do Multiple Correspondence Analysis, which is especially designed for qualitative variables (a kind of extension of corespondance analysis when you have more than two variables).

Have a look to FactoMineR::MCA. and their website http://factominer.free.fr/classical-methods/multiple-correspondence-analysis.html

Cheers,

Pierre

A common and useful way handeling categorical variables is to transform them into dummy variables and then calculate the euclidean distance between them (i.e., PCA). I do not see why you cold not just use PCA to compress the variables. This is much better than NMDS, since you directly get the amount if variation explained by the first principal component.

Thanks very much for your responses, Kevin, Pierre and Lasse. I finally choose to use NMDS since it is well suited to handle non-normal and non-continuous data (McCune & Grace 2002). Moreover, the axes that I obtained from these ordination were very well-related to most of my traits, providing an excellent continuous variable pooling all the binomial data. Anyway, I agree that MCoA would be another very good solution, but I found problems in finding good (and reliable) scripts to run it in R.

regarding PCA, I don´t think that it would be appropiate for non-continuous data, Lasse, at least is what many multivariate stats books say...

as a summary to the readers of this question; MCoA and NMDS are both valid and good techniques to ordinate binomial datasets, although you need to be careful in the distance used to built the ressemblance matrix depending in your question.

thanks to all who answered to this questions, I learned a lot from you!! :-)

There is an important work by Cox about the fact pricipal componetn analysis work well with qualitative binary data, MDS is Ok, you could use correspondence analysis as well that is particularly suited for binary data being based on chi-square metrics.