Autor des Abschnitts: Danielle J. Navarro and David R. Foxcroft

Hauptkomponentenanalyse

Im vorigen Abschnitt haben wir gesehen, dass die EFA dazu dient, die zugrunde liegenden latenten Faktoren zu ermitteln. Und wie wir gesehen haben, kann in einem Szenario die geringere Anzahl latenter Faktoren in einer weiteren statistischen Analyse unter Verwendung einer Art von kombinierten Faktorwerten verwendet werden.

Auf diese Weise wird die EFA als „Datenreduktions“-Technik eingesetzt. Eine andere Art der Datenreduktionstechnik, die manchmal als Teil der EFA-Familie angesehen wird, ist die Hauptkomponentenanalyse (PCA). Bei der PCA werden jedoch keine zugrunde liegenden latenten Faktoren ermittelt. Stattdessen wird eine Linearkombination erstellt, die eine größere Menge von gemessenen Variablen repräsentiert.

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.