Hi Valerie, thank you for providing some more context.

I have considered a similar problem, but unfortunately not yet pursued it to conclusion. In the system that I have considered, we have several agents that all impact a single plant (mostly insects, but also pathogens). They are all measured with different units. Unfortunately, even knowing the abundance does not necessarily give a good measure of impact! 

The solution that I was considering was to estimate for each agent whether their impact was negligible, minor or major (or similar). The output variable then becomes "impact". 

If you can measure or estimate relative impact (using literature or expert knowledge) and express it in units/density (e.g., reduction biomass, reduction reproduction per adult per m2), then you can express them all as impact.

Impact = relative impact x density

Hope this helps.... easy in theory, hard in practice!

As for the last question. I think Factor analysis (almost the same idea as PCA) is preferable as you can decide for one or several factors depending on how much information is lost.

Do you mean different taxonomic traits/variables measured in different units?

For different taxonomic traits/variables measured in different units, a  simple way could be by converting each of them to relarive numbers with regard to tthe respective maximun observed or potential value of the different traits/variables..

Thank you for these answers. My variables are all abundances, but the units of measurement differ. I have individuals pro square meter, individuals pro gram of soil, and individuals pro trap. z-transformation might be an option. The "problem" is that I will get values that are both negatie and positive and for my next analyses I would need to get only positive values.

I do not recommend doing PCA on such a dataset, unless data are standardized (somehow) beforehand.

For some standardization\transformations useful for multivariate analysis you may check: Legendre P, Gallagher ED. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129: 271-280.

However, Pedro Alcolado's suggestion seems reasonable to me. In your specie x sites matrix of abundances, just divide each cell for either the row total (i.e. the sum of all the observation for that species), or for the row maximum (i.e. the maximum abundance observed for that species).

Thanks. Yes, I think Pedro' suggestion fits my needs. However, what about combining relative variables? By dividing by the sum of all observation for a given species, I obtained a scale-free variable, isn't it? Should I then take the mean of the variables that I want to put in the same group? I do not think I can sum them?

One way is to take de máximum potential value or the máximum existing  limit  of the variable as 100, for example (or 5, as another possibility), and then relativize each of the obtainded values of the variable with respect to that maximum for each variable by dividint each value by 100 (or 5). Then multiply by 100 (or 5 accordingly), to obtain the new values that will vary betweeen 0 and 100 ,(or between 0 and 5) for all variables.

Good points to take into account, those from Sean Haughian!

Good points to take into account, those from Sean Haughian!

Thank you Sean, that's a good point.

I would be interested to know if someone has used composite variables that I think are especially used in the social sciences?

You could input all of your data to PRIMER, then make a draftman plot, according to this plot, you could choose how tobtransform your data, and then try to make PCA in PRIMER.

Identify the principal component the affect the abundance of  a particular species. Different species are affected by different variable.

If your purpose is to come up with a single variable that would describe abundance of different organisms or collected from different measurements, standardization (proportions or relative to maximum) seems to be OK.

Other approach can be categorizing your data giving scores (e.g., 0=absent to 5=dominant) for each of your organism/measurements.

If your purpose includes the use of multivariate methods such as PCA, than in plant communities it has been found that “Species presence/absence sometimes represents a plant community as well as species abundances do, or better” see Bastow Wilson, J. (2012).. Journal of Vegetation Science, 23(6), 1013-1023.

Measuring different taxonomic groups in different units means what? pl explain more about the different units so that I can understand the problem.

Dear G.S. Solanki,

I thought I mentionned it earlier. I have abundance data. Some units are individual pro square meter, others are individuals pro gram of soil and finally I have individuals pro trap. Thus three different units of measurement.

If you could give some more information, it would be helpful. But my first guess is that a mixed effect model should resolve your issue. What are the units and the variables, and what question are you asking?

I think that you need to be very clear about what is the purpose of the composite variable. Is it to measure the impact of a range of pests? Is it to give a biodiversity value to a system? There are many possibilities. Once you know what is the purpose of the variable, then you need to be transparent to the reader how you have constructed it. Then the reader can make up their own mind about whether the process you are following is reasonable or not. For me, clarity and transparency is key. Otherwise you and the reader may have difficulty with the interpretation of the results also.

Hi Louis, you are absolutely right.

In my system, several species do predate a similar prey. Thus I would like to combine these different predators species to get a single variable representing the total "predator pressure" on the prey. Each predator may be weighted according to knowledge about its efficiency, but first I have to know how to put the different predators on a common scale.

Hi Valerie, thank you for providing some more context.

I have considered a similar problem, but unfortunately not yet pursued it to conclusion. In the system that I have considered, we have several agents that all impact a single plant (mostly insects, but also pathogens). They are all measured with different units. Unfortunately, even knowing the abundance does not necessarily give a good measure of impact! 

The solution that I was considering was to estimate for each agent whether their impact was negligible, minor or major (or similar). The output variable then becomes "impact". 

If you can measure or estimate relative impact (using literature or expert knowledge) and express it in units/density (e.g., reduction biomass, reduction reproduction per adult per m2), then you can express them all as impact.

Impact = relative impact x density

Hope this helps.... easy in theory, hard in practice!

Thank you Louis, your answer is really insightful. I really like to idea of having a surrogate variable that depicts the impact of the predators, instead of the predators themselves. This allows defining this variable within each group but using a scale common to all groups. As you say, this requires good ecological knowledge about species impact, which is not as straightforward as abundance, but I might well go further with it.

either principle components analysis or factor analysis will do the job.

in my opition, it is not a problem to lose some information in order to reach a general pattern. Aiming to solve your question, you may even have to lose some indepanect variables that are not so relevant ro your response variable,  that is the way multivariates general linear model selection works. you can build a full models and drop the most unrelated or duplicated variable once a time, finally you will find the best model left in term of the change of AIC. biologically speaking, indicator species will represent other species in community, even though the number of indicator  species is much smaller than that of the whole commuinity.

other options may involve using a specific index that you think is good enough for your question, or build a new one out of your abundance variables. such as Shannon-Winner index for biodiversity, etc..

Parameter based variables may be considered as sub set  of group variables. PCA can help to know the contribution of the variables in each sub set and chances of missing the variable will also reduced.

Valerie, 

You might also consider nonlinear principal component analysis, a generalization of factor analysis/principal components analysis that works on any combination of interval/ratio, ordinal, or nominal-level variables. This multivariate technique is available in SPSS as CATPCA (Categorical Principal Components Analysis). You can find useful background information in the following references: Meulman, J., & W. J. Heiser (2012). IBM SPSS Categories 21. Chicago. Il: IBM Corporation; Linting, M., & A. van der Kooij (2012). Nonlinear Principal Components Analysis With CATPCA: A Tutorial. Journal of Personality Assessment, 94(1), 12-25; Linting, M., J. J. Meulman, P. J. F. Groenen, & A. J. van der Kooij (2007). Nonlinear Principal Components Analysis: Introduction and Application. Psychological Methods, 12(3), 336-358; and Garson, G. D. (2013a). Factor Analysis. Statistical Associates Blue Book Series. E-book. Ashboro, NC: Statistical Publishing Associates.

Dear Franklin Tjon Sie Fat,

Thank you for your suggestion. I am not a SPSS user and did not know this function. Is nonlinear principal component analysis similar to non-metric multidimensional scaling? I will have a look at the references you mentioned.

Dear Valerie,

For an overview of the relationship between the family of multivariate dimension reduction techniques under SPSS (including CATPCA and MDS) follow the link below. http://library.uvm.edu/services/statistics/SPSS22Manuals/IBM%20SPSS%20Categories.pdf. Best wishes!