I'm working on seal olfaction and did a PCA on a matrix of 220 scent compounds from 82 individuals. Is there a good way to figure out how many PCs may be relevant? I already did a scree plot and there are 3 'elbows' at PC´s 2,7,9. Also eigenvalues may be a criterion.
Dear Martin,
As far as my field of study is concerned, we only consider the PCs with eigen values greater than 1.
Using the DAPC tutorial I remember there is part of the code that identifies the number of optimal PCs using some 'alpha score': http://adegenet.r-forge.r-project.org/files/adegenet-dapc.pdf
Dear Martin,
As far as my field of study is concerned, we only consider the PCs with eigen values greater than 1.
Dear Martin,
The number of individuals (cases) must be at least 5 times larger than the number of variables (scent compounds), in order to conduct PCA. Otherwise, the coefficents will be less valid so will be the answers. Speaking about number of extracted components, it has been shown that the rule eigenvalue over 1 isn't good criterion. You can rather use Cattell's scree test, or (which is much better) parallel analysis (PA). There are free softwares and syntax-records on the Internet for parallel analysis.
PC with eigenvalue larger than 1 explains the variation more than any single input variable and hence can be useful since PCA is to reduce variable space
It seems to vary depending on who you ask, but this is a 20 year old Ecology paper that evaluated the performance of several different methods. I use the broken stick method.
http://www.esajournals.org/doi/abs/10.2307/1939574
thanks all!
@ Jackie and James: I´ll definitly have a look on the papers.
@ Javaid and Levan: I heard of Eigenvalues > 1. But my primary goal is not to reduce variable space, but rather to find variables that are similar in the multivariate space (and thus may encode relatedness or heterozygosity).
@ Selman: I think what R does with the prcomp() function is a Singular Value Decomposition (which is similar but not equal to PCA). Its definitly used in the field of semiochemical analyses. But actually I am not sure about the validity of the analysis, becauser of the reason you mentioned.
You could then look at the "weightings" (or "loadings") - the fractions of the original varianbles included into to "principal components" (i.e. the new variables) - any new variables with similar weightings of the same old variables will have similar properties. This would tend to be associated with the determinant of the original covariance matrix being very close to zero, indicating that there is almost a linear dependency between some of the original variables.
Actually, that would also correspond to some eigenvalues being very close to zero (any exactly zero would give linear dependence, and hence a zero determinant, in whihc case singular value decomposition WOULD apply).
Dear Martin,
You can aggregate your scent compounds, i.e. group them according to logical connection between them and make clusters of scents. After that, you can reduce these manifest variables (indicators) via factor analysis (PCA or similar) to less number of latent variables. By this process, you will probably get prerequisites to apply PCA. Can you write values of KMO and Bartlett's test of sphericity? They show whether you can conduct PCA or not.
Dear Martin,
I agree with Selman. Before performing a PCA you have to ensure you are accomplishing some prerequisites. A very important one is the need of a sufficient sample size. In your case some 1100 individuals. I guess you are exploring your data, so you can perform your PCA with important interpretation restrictions. To reduce the number of variables, you can look into the diagonal of the Anti-image Correlation matrix in SPSS output (R gives you these data in a separate matrix), where individual items' measures of sampling adequacy are displayed, and drop those with values below (say) .7 (Tabachnick & Fidell 2001). You can also study the reliability results (Alpha if item deleted...) and delete those items pulling your alpha down. Also you can visually analyze correlation graphs from R output to drop vaiables with light blue or white lines/columns.
Once you have a good proportion of cases per variable a parallell analysis is a good choice.
Dear all,
Actually I do not know why is there a 5 cases per variable rule, as input data in FA and PCA is the correlation matrix (always containing (m^2 - m)/2 correlations, where m is the number of items to analyze). I gues it is a matter of power.
Dear Martin,
From a graphical point of view, you see how many components you can extract. For that, you represent the decreasing of the eigenvalues of the correlation matrix X^TX. When you observe a bend, you select the eigenvalues before that bend and thus the associated components.
Use "fa.parallel" function (for continuous or "fa.parallel.poly" for categorical data) from 'psych´ R package. You will get FA and PCA from your actual and simulated data.
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