Factor analysis (PCA) in action Thought for the day: “Does one learn better by understanding the abstract definition or by actually doing the activity?” My answer: Both together works best

Demonstration of the process I’d like to show you how to do an EFA on a dataset. Further, I’d like to show you how messy it can be. A bit like finger painting. This dataset has to do with individualism and collectivism.

I and C Harry Triandis’s book, Individualism and collectivism (1995), is a classic in that it defines I and C and summarizes several decades of research concerning these constructs. He says that a “subjective culture” becomes organized around a central theme and this is the basis for I and C. It’s a way of thinking about the self in relation to others.

Definition of Collectivism Collectivism is: 1) emphasis on the views, needs, and goals of the ingroup rather than the self; 2) emphasis on behaviour determined by social norms and duties rather than by pleasure or personal advantage; 3) common beliefs that are shared by the ingroup; and 4) willingness to cooperate with the ingroup.

Definition of Individualism Individualism is a social pattern that consists of: 1) loosely linked individuals who view themselves as independent of collectives; 2) are primarily motivated by their own preferences, needs, rights, and contracts; 3) give priority to their personal goals over the goals of others; and 4) emphasize rational analyses of the advantages and disadvantages of associating with others.

A huge amount of research I and C were initially laid down by Hofstede in his cross-cultural study of business people around the world in Still, the I/C distinction has proven useful in cross- cultural research. Psychometrically, what do we know? –Few good measures exist. –There is an assumption now that I and C are orthogonal. –Triandis wanted to combine I and C with another dimension (see the next page).

Vertical vs. horizontal Triandis conceptualized I and C as crossed with V and H. He borrowed the categorization from Markus and Kitayama (1991). M & K described a two-by-two categorical system of the self: –Independent vs. interdependent; and –Same vs. different. In the same way, Triandis thinks of V & I this way: –In collectivist societies, horizontal refers to a sense of social cohesion; and vertical refers to serving the ingroup. –In individualist societies, horizontal refers to treating others as individuals; and vertical refers to competition being healthy. In short, verticality refers to inequality and the importance of rank; and horizontality refers to basic equality.

Triandis’s taxonomy collectivism individualism verticality horizontality I prefer to be direct and forthright with people. Winning is everything. Group harmony is important. I sacrifice my self-interest for the sake of the group.

Key things to notice First point: no item is pure I, C, V, or H. All items are combinations of either I/C and V/H. Not the usual way to do it. It looks as though I and C are opposites, i.e., not orthogonal. Is that true? Is looks as though V and H are opposites too. Is that true? Will we find in an EFA the pattern described above? Good question. Note that I’m actually doing something “wrong” here, i.e., doing an EFA on a previously identified factor structure. I should do a CFA (later).

Let’s try the first run It identifies 9 eigenvalues greater than 1.0. And that is completely useless. Notice that it did not converge—bad sign. An examination of the scree plot suggests either 3 or 4 factors. Let’s begin with 4 factors.

4-factor solution Notice that it actually converged (in 10 iterations-- which is so-so). Accounts for 38% of the variance. A scan of the obtained factor loadings shows the following: –1 st factor: 7 HC; 2 HI; 1 VC –2 nd factor: 7 VI –3 rd factor: 5 VC; 1 HC 1 HI (rev) –4 th factor: 4 HI; 1 HC Some order here, but it’s still sort of messy.

3-factor solution Accounted for 33% and converged in 12 iterations. Percent variance is a bit low. Let’s look at the factors: –1 st factor: 6 HC; 6 VC –2 nd factor: 8 VI –3 rd factor: 5 HI Seems like we have a single collectivism factor whereas the two individualisms are distinguished from each other. Not a bad result for a Western sample.

2-factor solution Accounts for 24.5% of the variance and converged in 3 iterations. –1 st factor: 7 HC; 5 HI; 1 VC –2 nd factor: 8 VI; 3 VC Umm, what does this mean? Seems like we have a horizontal factor and a vertical factor. It doesn’t split by I and C.

Okay, so what’s the best solution? Remember that I check the Cronbach’s alphas and correlations. 4-factor solution:  s =.75;.79;.66;.49 3-factor solution:  s =.73;.79;.70 2-factor solution:  s =.78;.78 1-factor solution:  =.75 So which is best? I like the 3-factor solution. Let’s check the correlations.

Are there any high correlations? Factor 2 Factor 3 Factor 1.15*.12 Factor 2.03 So, the 3-factor solution looks pretty good. 2-factor: r =.06.

Nothing is perfect Several things to notice: –The FA programme does not tell you what the optimal factor solution is, one has to discern it from the various signs. –Involves a number of FA runs. Then you follow up with Cronbach’s alphas and correlations. –The final solution is debatable. Other researchers might choose different factor structures.