PCA are often mentioned as a form of factor analysis, but it is not.

In PCA all variance are used and distributed among the components.

I factor analysis the common variance is used to define the factor and the unique variances are parted out (amd called error variance).

While there is discussion about this, I think the best understanding is that proper factor analysis can be used for defining measurement of latent factors.

PCA can be used for prediction in specific contexts, but not for developing measurement, despite it is often used for this purpose in psychology.

An example: The psychological test DAPP was developed with the purpose of establishing scales to complement the categorical psychiatric diagnostic system. However, unfortunately, the PCA was used which compromised the scales. As an example the Antisocial scale include questions about drinking. while drinking is not a defining characteristic of antisocial personality. As another example questions of sexual behavior is included in a scale of interpersonal problems.

While it is true that drunkennes may further antisocual acts, and sexual problems may further interpersonal problems, antisocial personality does not necessarily include alcohollim, and persons with interpersonal problems may not necessairly also have the specified sexual problems.

A consequence of the fact that PCA includes all variance in the data set is that often the analysis results in more components than when using factor analytic methods.

Thank you for your response. I understand that in psychometrics, the difference between PCA and factor analysis is crucial for measuring latent factors. In my case, I’m more focused on environmental topics, where PCA is widely used to reduce the dimensionality of complex environmental data. Do you think the differences between PCA and FA are just as relevant in other fields beyond psychometrics?

The differences between the methods also pertains to the difference between reflexive and formative models.

In a reflexive model (built by proper factor analysis) you presuppose that the latent factor is a really existing entity which determines the indicators (the observed measurements), like a state of depression in a patient determines how the patient answers the questions in a depression questionnaire.

For a formative model (built by regression analyses and PCA) you chose the indicators you think are relevant predictors for some outcome of interest, like a socioeconomic index, which can be designed to represent the best indicator for some outcome. Like, should you only include economic measures, or also the status the person is ascribed by others? For some uses one is best for predication for other maybe the other.

A measure of gross domestic product is another example of a formative model. In fact, currently there is discussions about if in addition to economic indicators, environmentalt factors should also be included in such an index, the argument being that in that case you get a better indication on the nations standing, but an index whithout such information may be better to predict pure econimic outcomes.

However, the indicators to be included in a formative model needs themselves to represent good measurement, and, depending on the area of interest, these may be developed using factor analysis.