Factor Analysis in SPSS (Principal Components Analysis) - Part 4 of 6

In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 4 of 6).

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Video Transcript: what we want to do is retain the number of components that are above what's known as the scree, or where this plot tends to not drop much, when it tends to, I wouldn't say flatline, but taper off very gradually. Notice how these 4points here, these 4 eigenvalues, the rate of change, or the slope here, is quite minimal as we move across. But this value, there's a big drop from component 1 to component 2, and then from component 2 all the way through 5, there's not much of a change anymore. So according to the scree plot, we interpret the number of components above where they tend to not change much anymore. And where this name comes from, the scree plot, scree is a geological term which indicates the rubble or the stones that fall from a cliff. So if you think of a cliff, you're driving along the road, you're going to see a lot of stones, smaller sized rocks and some bigger rocks, but they're all collected along the side of the mountain, right? Well this is the scree or the rubble that is collected off the cliff. So that's where this name comes from. So we want to retain the number of components above the scree. So the scree plot would indicate to us here that we want to retain one component. Suppose there was a component right here as well. Well notice that it still drops quite a bit from here to here, and then it flat lines. So if we had a component here as well, then we would retain two components in that case. As you add components the likelihood of these two rules of thumb agreeing completely, decreases. It certainly can happen, they can agree, without question, but the likelihood tends to decrease. One of the interesting things about these two rules are that, the eigenvalue greater than one rule has been around for a very long time, as has the scree plot. The eigenvalue greater than one rule was published by Kaiser in 1960, so that's quite a long time, and it's still one of the primary methods for extraction, for determining the number of components, used today. And the scree plot, the key publication for that was in 1966 by Raymond Cattell. So this came out in 66, the publication anyway, and the publication for this came out in 1960 by Kaiser, so that's quite a long time ago, and they're still the two primary methods that are used for factor extraction. Now that being said, for those who are interested in a more advanced look at factor analysis, there are better methods that can be used, such as parallel analysis. But, unfortunately, they're not output in SPSS. You can go ahead and run a parallel analysis if you search on the web, and you can use syntax for SPSS to run it, or you can use, some websites have it all ready, where you just input the number of variables you have, your sample size, and so on, and you can get out the solution for the parallel analysis. But that's really beyond the scope of this video. If I get a chance, I'll try to make a video on how to run and interpret a parallel analysis as well. But for now, these are the two most commonly used methods of extraction. OK, so to review, in our example here, we have one component. And next we'll go ahead and look at our Component Matrix and we'll also look at our Rotated Component Matrix here. And let's start with this one. Notice it says Rotated Component Matrix only one component was extracted the solution cannot be rotated. And that's a very important point to make, and that is, when you have a one component solution in principal components analysis, then there is no rotation. Rotation only comes into play when there are two or more components. So with one component there is no rotation, and that's why we got this output, and the reason why we got this output, if you recall, when we did our factor analysis in SPSS, under rotation, we asked for Varimax. So basically SPSS is telling us, we can't do Varimax rotation because there's only one component, and rotation doesn't come into play in that case. So as one measure of the effectiveness of our solution, we noted the total variance explained by our one component. I had said that 63% of the variance was pretty good in practice. That's one way to look at it. That's the overall variance that the component accounts for. Now here on the Component Matrix