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I ran a PCA on survey data asking whether respondents trust different levels of government, where they rank their level of trust from 0-7.

Whilst I can interpret PC1 as a weighted average of individual scores for each variable (Local, Regional, National, International), I can't understand how to interpret PC2.

Would it be correct to assume that positive scores on PC2 indicate higher trust in Regional and National governments whilst negative scores indicate higher trust in International Governments?

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PC2 measures relative trust. A person can have a fairly high (positive) PC2 with middling trust in Local, Regional and National, but simultaneously extremely low trust of European and international.

But a person can have an equally high (positive) PC2 if they have middling European and international trust, but simultaneously extremely high trust of Local, Regional and National.

Your answer would be right if it were qualified. "Higher" does not mean "Higher than average"; rather it means "Higher relative to the other group of variables".

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  • $\begingroup$ Ah, I think I see what you mean. For example, if we were to compare two respondents, m which had a score of 3 and n which had a score of 4. We can say that n had a greater trust in local, regional and national government relative to international governments compared with m, who had a lower relative amount of trust between the two groups. Would that be correct? $\endgroup$
    – SoniaG
    Feb 18 '20 at 14:42
  • $\begingroup$ Right. But you could not say that "n" had greater overall trust in local, regional and national governments than "m"; "n" could have less. To see this clearly, suppose the z-values for "m" are 2,2,2,-1,-1. Then m's PC2 is 2.78. Suppose also that the z-values for "n" are 1,1,1,-3,-3. Then n's PC2 is 3.84. Here, "n" has lower trust in local etc. than "m", but a greater relative difference in how s/he views (local etc.) vs (international etc.) $\endgroup$ Feb 18 '20 at 18:54

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