 Factor analysis answers the question of what indicators have in common. In an exploratory factor analysis, you start by first extracting all common variants from the data, and then you take that out from the data, then you extract another factor and so on. This process leads to a factor analysis solution that is often uninterpretable, because most of the indicators will load highly on the first factor, and then have a mixture of positive and negative loadings on the remaining factors. To make the factor analysis results more interpretable, we do a factor rotation. What the factor rotation achieves is that it takes the indicators first. So let's assume that we have here six indicators, and items one, two, three vary together. Items four, five and six vary together. So this is the score of person number one, and this is the score of person number two here. And when we do a factor analysis first, we extract first factor, then the factor analysis starts from the origin here, and it asks the question to which direction the data are, and it will indicate that all the data are to that direction here. So all the data are to the right and down a bit. Then the next thing that we do is that we eliminate the influence of this factor. So we basically shift all these observations sideways, so that they have a zero value on this variation, this factor, and then we extract another factor asking which direction the observations are, or the variables are. Then the answer is that they are either up or down. So they are orthogonal to this factor here, and with two persons we can use these two factors to pinpoint the location of each indicator. So this indicator item one is this much along the first factor, and then that much along the second factor. This also indicates that the first factor shows the overall direction, and the second factor is usually a positive or a negative, depending on which direction we go to that factor. Do we go up or down? And the problem of course is that if we want to summarize this data, then we would say that this group of indicators in this direction, and the other group is in that direction. So the factor analysis really doesn't reflect that dimensionality, even if it allows us to summarize these indicators, give them our coordinates. So the problem is that the first factor explains a little bit of every indicator, and then the second factor has positive and negative loadings, and they don't really explain where the data are in a way that is easier to interpret. The purpose of a factor loading is that we try to reorient the factor analysis solution so that indicators load highly on one factor and one factor only. So we try to maximize each indicator's largest factor loading, and minimize all other factor loadings. It also makes the variances more equal. So here the first factor explains more variation than the first factor, because all the indicators are in this direction. So there are different techniques, and the techniques are in two variants. We have oblique and orthogonal rotation. Oblique rotation maintains the factors that they're uncorrelated. So we kind of take the factor solution here, and then we rotate it around the zero axis like that. So we rotate those two arrows so that they point more toward the clusters of the observations, like so. So we rotate it a bit and about 45 degrees or a bit less, and then now the first factor points to the direction of the first. Items 1, 2, 3, and the second factor points to items 4, 5, and 6. But these factors still don't point exactly to where the items are, because we are constraining that the factors must be uncorrelated. So this is a 90-degree angle. When we relax that assumption, we can actually draw the line so that the factors are correlated. When this factor is higher, then this factor can be higher as well. And now the arrows point that the first three items are in this direction, the second three items are in that direction. And that's the idea of factor rotation. So you reorient the factor analysis to make it more simpler to interpret. So do you have to understand what exactly the factor rotation does? The answer is no, because there is a simpler rule of thumb that you can apply. The rule of thumb is that always use our oblivion rotation, because it's the theoretical the most appealing for many scenarios, and particularly it is an oblique rotation. If your factors are supposed to represent constructs that are correlated, which is the case if we make a theory about those constructs, then constraining the factors to be uncorrelated doesn't make any sense. Varymax rotation is often the default, and it's an oblique rotation, so you should never use that one. The reason why Varymax is the default is because of history. Factor analysis has decades of history, and when the factor analysis was introduced, we really didn't have computers, so people were doing hand calculations, and the Varymax rotation is much simpler to calculate than the oblimin rotation. But nowadays the computer will do this, both of these for you instantaneously, so the amount of computation is a non-issue. You should really go with the direct oblimin instead of anything else. And when you look at articles, they actually report that oblimin is used. So this is a pretty nice way of reporting a factor analysis from this information systems research paper. So they authors report that they conducted exploratory factor analysis, they did oblimin rotation, and they also explained why they did oblimin rotation because they want to have the factors to be correlated. And you only need one sentence and two lines for that. So that's really a nice way of reporting that you actually did factor analysis correctly.