In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 5 of 6).
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Video Transcript: this tells us some information about how each of the individual items do in terms of getting at that component. So what we have here is, notice we have our 5 items, SWLS1 through 5, and then we have this column for Component, and we have these different values here. And in a one-component solution, it's pretty nice, as this works out very cleanly. And what I mean by that is that these are called Component Loadings, or people might call them factor loadings, and they tell you how strong the relationship is between the item and the component in our solution. And if you look at these values here, they can be interpreted, in a principal components analysis with a one-component solution, these are literally just the Pearson correlation of the item with the component, or we can think of as factor. so SWLS1 correlates or loads, people will say, .747 on the component. SWLS2 loads or correlates, in this case, .8 on the component, and so on. And if we look here, our highest loading item is SWLS3, which loads or correlates, if we round here, .89 on that component, which is very high. So whatever SWLS3 is measuring, and as a reminder, that question said "I am satisfied with my life," this loads or correlates the highest on the component of any of the items. Now that being said, it should be noted here that all of these items correlate or load very highly on the component. It's just that SWLS3 loads the highest. But SWLS2 and 4 load very high as well. And so does SWLS5 and 1, for that matter as well. SWLS5 has the lowest loading, but .71 is still quite good in practice. And in fact there are some rules that people use here in terms of trying to interpret whether or not an item loads in a meaningful way on a component. And in this case, like I said, all of these do. But people will use, I've seen a variety of rules, varying from if these are .3 or higher, all the way to .5 or higher, as being important or noteworthy. So, in other words, if SWLS1 was, let's say .24, for example, then using the rule of .3, I would say this item does not load meaningfully on the component. If it was .25. But it's not, it's .75, so it loads quite high on the component. And all of these do. But there are variety of rules, .3, .4, .5, sometimes people will calculate what the significance should be an alpha of .05 for these loadings and interpret them that way, and so on. But here ours are all very high. This is a very clean solution, it's a pretty straightforward solution, which I wanted to use here for your first look at principal components analysis, as I think it's best to use a simple solution and then build from there to more complex ones. I'm going to go ahead and take this component matrix and go ahead and move it up here to just below the Commonalities. So let's go and take a look at that. And that'll allow us to look at these side-by-side, which will be a bit easier. So I want to take a look at this Commonalities table. And the commonalities, I talked about that our solution indicated that we accounted for 63% of the variance for our one component solution, that that was pretty good. And we saw our factor loadings, or component loadings, that is, the Pearson correlation between an item and the component, that these are all quite good. Now in a one component solution, this is pretty straightforward, which is nice. The correlations here, or the component loadings, if we square them, that gives us the commonalities. So if we look at SWLS2, .8, if we square that, that gives us .64. And if we square these other ones, that will give us the values you see here. And if you recall from regression, if you're familiar with regression, R-squared is, in simple regression, it's literally just the correlation squared. And the correlation squared, or R-squared, indicates the amount of variance that was accounted for. Well, the same thing here in factor analysis. So for SWLS2, we have .8, that square is .64, and that indicates the amount of variance that our one component accounted for in SWLS2. So in other words, 64% of the variance in SWLS2 is accounted for, or explained, by the component that we retained.
