Seems to make sense - although it is questionable that you really attribute twice the weight for V1 and V2 - because of the sum under the root.

It would be easier by using the block metric (Manhattan distanc) - but if you want Euklidan distance it is a way to do it.

Thanks Gerhard,

yes, me to I see the sum under the root as a problem. For sure transformations will weight, but I have no idea if the weight will be 2, or even if the weight will be constant, I mean independent on values of my variables.

Manhattan is a nice idea, rock solid, lots of thanks.

Cheers, Pierre

Dear Pierre,

another point is that the variables are each other correlated, so strictly speaking your is not a proper Euclidean space, I suggest you to use Mahalanobis indeed...

I agree with Alessandro. Calculate the distance matrix and weight afterwards.

The relationship between the adjacent variables [continuous??] is important in the equation. I am not a statistician but having worked with one for some of my experiments involving repeated measures we have always considered this point. Alessandro and Neal are right.

Dears,

Thanks you for your answers.

For the moment, let's consider that I am not interested in weighting some of my variables, I just want to compare proportions of species (variables) composing some sites (individuals). Following Anderson et al. 2011, euclidean distance on proportions is suitable. This is why I am surprised of your answer. I get the point that my variables are correlated, and Mahalanobis is the suitable distance. However, why there are discrepency on this point?

Maybe it is related to the Normality assumptions of Mahalanobis, which is usually not met with ecological data? Or maybe it is because we are using distance-based MANOVA, as in Primer6/Permanova+ or vegan::adonis() in R?

Since my data are not guassian (each variable range between 0 and 1, and each row sum up to 1, i.e. species profiles) , I think I will follow Anderson et al. by using euclidean distance and the running permanova in primer. Is it a huge mistake?

Moreover, a statisticien suggest me to use manhatan rather than euclidean when dealing with proportions. Manhatan would be more "robust". Any idea about in which sense in is more robust, and why? Is it because manhatan break down correlation?

@Tilakavati: Once I get a distance matrix, how could I weight some specific variables?

Thanks to all of you, I 'd like read your point of view.

Pierre

Anderson et al. 2011, Navigating the multiple meanings of b diversity: a roadmap for the practicing ecologist. Ecol Lett

Pierre I am going to copy this conversation to my Statistician. WIll respond back next week

Thank you Tilakavati. Good WE.

hi,

I have the same case, my question if I have three variables x,y,and z

using

Manhattan distance :

(a,b)= w1* dist(x,x')+w2*dist(y,y')+ w3*dist(z,z')

and I need to make x contribute more in that distance, does reduce the w1 or increase it?

another query

should w1+w2+w3=1 or 3?

thanks