[R-sig-eco] PCA question

[Jari Oksanen]

Ana,


On 01/04/2014, at 18:03 PM, Ana Serronha wrote:

> Hi everyone,
> 
> I have read that,  loadings (from pca) more than .5 are typically
> considered strong; loadings between .3 and .5 are acceptable; and loadings
> less than .3 are typically considered weak, am I correct?
> However, I can't find a credible reference to use. Can you suggest me a
> book or a paper to use as a reference?

I don't this kind of guidelines are usually given in *community* ecology: (1) they only make sense with correlation matrices, and (2) the results are usually plotted and not inspected numerically. If you are not analysing communities, but some other kinf of data, using correlations makes sense and then looking at loadings may be meaningful. These kind of guidelines are not usual with PCA, but they are used with Factor Analysis (FA). Many people (even distinguished scientists and instructors) mix these or do not make a distinction, and there may be a carry over of FA principles to PCA. FA results are often not plotted nor even regarded graphically, but only inspected numerically. They are also standardly rotated to something that is called "simple structure". In simple structure, the loadings tend either to zero or to one so that you can say that a factor is measurement model or combination of certain and only certain analysed variables. In confirmatory FA we even explicitly select the variables that form the measurement model for the factor (i.e., are used as observations to find a priori factor). That's the reason why R has formula interface for factor analysis and also for PCA. For these purpose people use these guidelines of loading threshold. For instance, the default output of rotated factor analysis in R will print blanks for loadings below some absolute value threshold (|0.2| I think). PCA is not FA, and it tries not to produce a simple structure, and if it is rotated, it no longer is PCA. However, if the thing you really wanted to do was FA, but you picked up PCA instead, then you can use limits like that. I suggest you check any ook on factor analysis (starting from Harman 1977, going to Jöreskog, or anything you find in your local library).

Cheers, Jari Oksanen