Afsnitsforfatter: Danielle J. Navarro and David R. Foxcroft

Principal Component Analysis

In the previous section we saw that EFA works to identify underlying latent factors. And, as we saw, in one scenario the smaller number of latent factors can be used in further statistical analysis using some sort of combined factor scores.

In this way EFA is being used as a “data reduction” technique. Another type of data reduction technique, sometimes seen as part of the EFA family, is principal component analysis (PCA). However, PCA does not identify underlying latent factors. Instead it creates a linear composite score from a larger set of measured variables.

PCA simply produces a mathematical transformation to the original data with no assumptions about how the variables covary. The aim of PCA is to calculate a few linear combinations (components) of the original variables that can be used to summarize the observed data set without losing much information. However, if identification of underlying structure is a goal of the analysis, then EFA is to be preferred. And, as we saw, EFA produces factor scores that can be used for data reduction purposes just like principal component scores (Fabrigar et al., 1999).

PCA has been popular in Psychology for a number of reasons, and therefore it is worth covering, although nowadays EFA is just as easy to do given the power of desktop computers and can be less susceptible to bias than PCA, especially with a small number of factors and variables. Much of the procedure is similar to EFA, so although there are some conceptual differences, practically the steps are the same, and with large samples and a sufficient number of factors and variables, the results from PCA and EFA should be fairly similar.

To run a PCA in jamovi, all you need to do is select Factor → Principal Component Analysis from the main jamovi button bar to open the PCA analysis panel. Then you can follow the same steps as for the EFA in jamovi in the previous section. The only differences are that what is called factors for the EFA is called components here, and that there is no choice of Extraction method and no Model fit measures.

Generally, the results are quite similar to those obtained with the EFA. There are also five components extracted, similar to the five factors extracted by the EFA. However, the five component solution accounts for a little over half of the variance in the observed data (56% vs. 46% in the EFA). We can also recognize that components loading are slightly higher, and that the uniqueness values are slightly lower. For the PCA the whole variance of each item is considered whereas for the EFA the variance is split into common variance (i.e., to what degree the variation in one questionnaire item can be predicted by the other items, and can therefore be assumed to measure some common underlying construct) and variance that is unique to that particular item.