Dear Andem

Pl see for PCA and Factor Analysis. May be of some use.

Chapter A note on the Factor Analysis in Forestry Sciences

It is possible that neither approach is correct. You could just search for principle component analysis (PCA) and curvilinear component analysis (CCA) to get a simple definition. PCA is linear, CCA is curvilinear.

If you are looking for a method, you might start with defining your goals. Do you have a data set with 20 correlated variables and you want 2 or 3 uncorrelated variables that capture most of the variability in the data? Do you have treatments? Something like plankton from 8 locations and you are interested in looking at how these locations differ, or more classical treatments where you released something into the water and are measuring the effect. Are you assuming that there is some unknown variable that you can't measure, but you figure that you can estimate this unknown variable? So things like Factor analysis, or Discriminant analysis may also be appropriate. You might also look at optimal designs: see articles at http://odajournal.com/.

Thanks ......Timothy Ebert and Rajiv pandey

Have a look: http://documents.irevues.inist.fr/bitstream/handle/2042/12339/AR18_4.pdf?...1

I suggest you see "Archetypal Analysis".

Its a multivariate method used to reduce the dimensionality of the data.

Hello Andem,

You have to know very well your data set and the theory/theories that guide your research. Even if you were a pioneer in the field and no theory is available yet, you still need to formulate hypotheses for your research and they  should guide you on the analytical design. You also need a theory to interpret the results of data reduction no matter what method you choose to do that. A good start in knowing and understanding your data consists of descriptive analyses, scales psychometrics, and the variables' correlation. The factor analysis and reliability test show you the measurements that fit statistically your data while multicolinearity can be a good criterion for identifying unnecessary measurements. Parceling is another "economic" option for scales with large number of items in regard to the number of observations.   

best

My favourite approach is Correspondence Analysis. There should be any number of publications using this on Researchgate. Try using PAST, a free statistical program that is easy and quick to use and has a variety of multivariate techniques enabling you to compare results. Available here: http://folk.uio.no/ohammer/past.

To Timothy. Giving advices in Multivariate methods, you should at list know its correct names. There is no 'principle component analysis', only Principal Component Analysis. Seems, you know the method from very secondary sources.

Anna

Hello, Andem,

Are your data real numbers taking values from a continuous scale? 

Then I would advise you to start from PCA. This would give information, how much your measured variables are interdependent, and what  approximatlely is the intrinsic dimensionality of the data. PCA is in included in practically any statistical package dealing  dealing with multivariate data

Next I would try a clustering procedure, for example Kohonen's self-organizing map (SOM), which give a  2-D representation  of the internal structure of the data. If you have Matlab  in its basic version, then you may  use the free Matlab SOM Toolbox dowloadable from HUT (Helsinki University of Technology) .    The package (authored by Vesanto et al) contains also tools for PCA .

 If you have no Matlab, then this method is not for you, and you have to search for other methods permitting to visualize multivariate data. 

By the way:  Writing CCA, had you in mind Canonical Correlation analysis  or Curvilinear Component Analysis?  The last is also included into the Matlab SOM Toolbox from HUT.

Wishing success in your analysis

Anna

Dear Anna,

Your inference based on a spelling error is unusual in the implication of a cause effect relationship. In this regards, I wonder what I should infer based on your mistake of using list rather than least in the first sentence.

However, you are correct that I have not read the primary sources as in Pearson (1901) "On lines and planes of closest fit to systems of points in space", nor Hotelling (1933) "Analysis of a complex of statistical variables into principal components."

While I am annoyed at they way you chose to point out the error, thank you for pointing out the mistake.

I can guess at what kinds of data are present. There will be continuous values for measurements of water quality and temperature. There will be integer values based on counts of each species collected. There may be problems like some counts are nearly always zero. There may be a wide range of other problems, depending on the way in which the data were collected. Also, a few species will dominate the total population, but there will be a large number of uncommon to rare species. The rare species can be biologically important though the represent a minute portion of the total population. Larval sea urchins, crabs, and so forth may be relatively uncommon relative to diatoms, yet they settle out of the plankton to become key organisms later in life (a salt water example). This is the simple version. It is possible that the data could also be a time series (samples once every two weeks in an 8 month field season and repeated for four years).

You have the possibility to reduce your data using a two dimensional plot. 

CCA allows you to correlate external (explanatory/environmental) variables on your ordination plot of plankton. It has a different process of creating an ordination plot to PCA and is prone to the horseshoe effect if you have long gradients. Good luck with it

CA apparently does not depend on your data being normally distributed which PCA does.

Andem

When you use the abbreviation CCA are you referring to Canonical Correspondence Analysis or Canonical Correlation Analysis? 

That's one of the problems with statistical jargon...too many overlapping abbreviations.

Fortunately, PCA at least as far as I know only stands for one thing i.e. Principal Component Analysis unless you meant Porsche Club of America which I sincerely doubt... :-)

Please can someone sent me the original setup for R and Primere software's for me to install because I can only download the trial version of the software which doesn't last long........thanks