PCA components cluster correlated input variables, with component weights essentially proportional to number of inputs corresponding to it. If you put 10 health indicators, 2 economy indicators, and 2 education indicators—your principal component will be health-based. If you put 10 education indicators, 2 economy, 2 health, your principal component will be education-based etc. In no case will it be meaningfully “welfare”.
That’s how you get 5-factor models in psychology—you just know what kind of questions to put on the questionnaire, and as long as you don’t stray too far from it, you’ll get exactly the 5 factors you want.
PCA can only be insightful if all inputs are equally important—something that people using PCA rarely bother sanity-checking.
The Big Five personality model was originally developed by researchers who raided dictionaries for every personality trait term that they could find, had people rate themselves (or others) on hundreds or even thousands of them, and kept finding this five factor solution that explained a lot of variance. Studies in other languages and cultures typically find similar results, although it doesn’t always replicate perfectly (e.g., a missing factor, an extra factor or two, a slightly different meaning for one factor). In some ways it reflects people’s lay theories of personality more strongly than actual personality, so it might share some widespread blind spots or misconceptions, but it was constructed in a thorough, systematic way (and there is evidence that each factor predicts behaviors, so it can’t be too wildly off).
PCA components cluster correlated input variables, with component weights essentially proportional to number of inputs corresponding to it. If you put 10 health indicators, 2 economy indicators, and 2 education indicators—your principal component will be health-based. If you put 10 education indicators, 2 economy, 2 health, your principal component will be education-based etc. In no case will it be meaningfully “welfare”.
That’s how you get 5-factor models in psychology—you just know what kind of questions to put on the questionnaire, and as long as you don’t stray too far from it, you’ll get exactly the 5 factors you want.
PCA can only be insightful if all inputs are equally important—something that people using PCA rarely bother sanity-checking.
Thanks for this comment, taw. I’d been wondering whether PCA is solid evidence that the Big Five personality traits carve reality at the joints.
The Big Five personality model was originally developed by researchers who raided dictionaries for every personality trait term that they could find, had people rate themselves (or others) on hundreds or even thousands of them, and kept finding this five factor solution that explained a lot of variance. Studies in other languages and cultures typically find similar results, although it doesn’t always replicate perfectly (e.g., a missing factor, an extra factor or two, a slightly different meaning for one factor). In some ways it reflects people’s lay theories of personality more strongly than actual personality, so it might share some widespread blind spots or misconceptions, but it was constructed in a thorough, systematic way (and there is evidence that each factor predicts behaviors, so it can’t be too wildly off).
Good point, thanks.