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Could someone please explain me how I should decide which variables to keep in my analysis based on loadings from PCA. The output is:

    Comp.1     Comp.2    Comp.3  Comp.4     Comp.5
a   0.0281003 0.37882295 0.2935517 0.02025596 0.11199220
b   0.2019940 0.21168386 0.2398182 0.37883484 0.03540004
c   0.2545871 0.20163264 0.1459563 0.07187896 0.39797528
d   0.2774044 0.05867002 0.1859529 0.06134311 0.41428056
e   0.2379143 0.14919053 0.1347208 0.46768713 0.04035192

Importance of components:
                      Comp.1    Comp.2    Comp.3     Comp.4     Comp.5
Standard deviation     1.5809667 1.0987927 0.8806842 0.63815856 0.33218647
Proportion of Variance 0.4998911 0.2414691 0.1551209 0.08144927 0.02206957
Cumulative Proportion  0.4998911 0.7413602 0.8964812 0.97793043 1.00000000

Does this mean that variable a is not important and I can drop it? Is there any method for making this decision?

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    $\begingroup$ Too scarce information (and effort). Keep for what? "Interpretation" - in what sense? Important - how? Please pardon me for an advice for you to read some textbook on PCA first. $\endgroup$
    – ttnphns
    Mar 3, 2015 at 12:39
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    $\begingroup$ It's hard to give advices without knowing why you want to drop any variables at all. But note that variable a contributes strongly to PC2, which has variance comparable to PC1. $\endgroup$
    – amoeba
    Mar 3, 2015 at 15:17

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Generally this depends on what type of data you are looking at. I would find similar studies in your field and cite them as examples of where to choose loading cutoffs. In environmental data which is very noisy, these limits tend to be lower whereas in controlled laboratory experiments they will be higher. Generally a loading cutoff should eliminate several of the variables from a PC but you don't have that many to begin with.

Based on the standard deviation it looks like PC1 and PC2 could be considered significant, with a contributing strongly to PC2 (relative to the other variables). Let's say you chose your cutoff as $.25$ - PC1 would be related to variables c and d, while PC2 would be related to variable a alone. In other words, you should not throw a away - it looks like it has a potentially strong association with PC2 and has the highest loading value of any variable on the first two PCs.

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Without any other information, yes, if you need to drop a variable, that would be $a$.

However, in order to really know, you need e.g. confidence intervals. You could obtain those from a jack-knifing procedure. If your confidence intervals cross zero, you have reason to remove those corresponding variables.

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