How do we ascertain how many factors/dimensions there are in our data? Well, there are several different ways to do this. It is nevertheless important to keep in mind that we want to aim for a balance between simplicity and accuracy: as few factors as possible, that explain as much of the variance as possible.

Determining the number of factors

Eigenvalue > 1	Eigenvalues are indicators of the variance explained by a factor. Using the rule “eigenvalue is greater than one” is very common. The reasoning behind this rule is that a factor should account for at least as much variance as any single variable. Thus, the average of all eigenvalues is one, and the factor analysis should thus extract factors that have an eigenvalue greater than this average value.
Scree plot	In a scree plot, factors have their eigenvalues plotted alongside the y-axis (i.e. vertical axis) in the order or magnitude. Factors explaining large amounts of variable appear to the left, whereas factors explaining little variance are aligned to the right. The somewhat weird task is here to “locate the elbow”. This means to identify the number of factors stated before the line starts becoming flat.
Communalities and uniqueness	Communality refers to how much variance of each variable that can be reproduced by the factor extraction. A general rule of thumb is that the extracted factors should explain at least 50% of the variables’ variance (i.e. the communalities should be between 0.5 and 1). Stata, however, reports on the opposite of communalities: uniqueness (which is 1-communality). The similar threshold applies here, i.e. the uniqueness should be between 0 and 0.5.