How do I analyse principal component scores? [duplicate]

Question

I have carried out a principal component analysis on 10 emotions I have observed in animals e.g. happy, playful, aggressive etc (5 positive emotions and 5 negative). Each animal is given a score for each emotion from 1 to 100. E.g. an extremely happy animal receives a "happy" score of 100. My PC1 is positively correlated with positive emotions and negatively correlated with negative emotions. Thus, I have labelled the PC "Good welfare". I have component scores for each animal for PC1. I want to assign each animal to a poor or good welfare category based on these PC scores but how do I go about this? The scores range from 3.12673 to -2.23454. Could I take animals with a minus score as having poor welfare and those with a positive score had good welfare? I don't know how to interpret the component scores. Thanks!

Answer 1

In this case, higher PCA1 scores will mean "good welfare" as you've labeled it. But PCA doesn't explicitly provide you with a classification threshold like that. Zero may be a fine discriminator between the two classes you've named, but that threshold may be better chosen differently. Plot the component scores to see if there is a natural break between your good and bad welfare animals.

Added detail: The PCA process reprojects your data along a number of new axes that correspond to the greatest amount of variance in your data, provided that each new axis of rotation is orthogonal to the ones that preceded it. This means that your PC1 axis is the single axis along which the variance of the data is maximized. You may be able to cleanly distinguish between clusters or groups of animals along that single axis, or you may need to bring in PC2,3, etc. In some cases, there will be an explainable relationship to an individual component. You found that PC1 correlated with the positive emotion scores, so you may find that PC2 corresponds with the negative emotions. Your implementation of PCA should give you the cumulative variance that is explained by adding more principal components. Add enough that you are comfortable with the amount of variance you are explaining with these new variables, but not so many that you are adding variance due to noise.