> The critique is that the existence of the Big 5 itself is the result of misapplication of PCA for a task where a latent variable model would be required, the

> The critique is that the existence of the Big 5 itself is the result of misapplication of PCA for a task where a latent variable model would be required, the identification of personality traits. As stated, that critique is wrong in this sense: for a given population of, say, new employees at a business, PCA is sufficient to establish correlations between things that are easy to measure (Big 5 assessment test scores) and things that are much more expensive to measure but which the business cares about (how the employee will perform if assigned to a certain team). In this way, mere correlational data, without the construction of a latent variable model, is operationally useful. Objections that the tests don't really "detect personality" "directly" are semantical in this context. Yes, if the business starts using (implicitly or explicitly) a causal model of latent personality variables to make claims or predictions that take them outside the population distribution for which the correlations have been measured, then they could be making a mistake. But this does not invalidate the use of Big 5 assessments in general. > Using PCA to detect personality traits is like using a thermometer to measure atmospheric pressure. What's worse, psychometrists seem to have taken the reading on the thermometer and proclaimed "Atmostperhic pressure is 25 [degrees Celsius]!". Given a fixed population (in this case, a population of weather events) where temperature and pressure are well correlated, it is completely reasonable to use a thermometer to estimate pressure, and to take concrete action based on this. By all means, criticize people for being insufficiently precise (e.g. for not stating what their error bars or what the relevant population is), but don't pretend that this completely invalidates everything and Big 5 should be ignored.