by Maike Rahn, PhD
When are factor loadings not strong enough?
Once you run a factor analysis and think you have some usable results, it’s time to eliminate variables that are not “strong” enough. They are usually the ones with low factor loadings, although additional criteria should be considered before taking out a variable.
As a rule of thumb, your variable should have a rotated factor loading of at least |0.4| (meaning ≥ +.4 or ≤ –.4) onto one of the factors in order to be considered important.
Some researchers use much more stringent criteria such as a cut-off of |0.7|. In some instances, this may not be realistic: for example, when the highest loading a researcher finds in her analysis is |0.5|.
Other researchers relax the criteria to the point where they include variables with factor loadings of |0.2|. Which cut-offs to use depends on whether you are running a confirmatory or exploratory factor analysis, and on what is usually considered an acceptable cut-off in your field. In addition, a variable should ideally only load cleanly onto one factor.
How many variables and observations?
Another question often asked is how many variables a researcher should use for analysis. Generally, each factor should have at least three variables with high loadings.
It is also important to have a sufficient number of observations to support your factor analysis: per variable you should ideally have about 20 observations in the data set to ensure stable results. A common minimum is the lesser of 10 observations per variable and 100 observations. However, some statisticians would go as low as five observations per variable .