Dear Sarah,

as always, there is no straightforward answer to your question. Allow me to give you a few pieces of advice:

1. If you assume your factors to be correlated, do not choose varimax and orthogonal rotation but rather principal-axis-factoring and oblique rotation.

2. How many factors do you expect based on your hypothesis? You often end up with too many if you just follow the eigenvalues.

3. Are there substantial (>.3) cross-loadings of one item on more than one factor? Check for multicollinearity and, if necessary, delete the item.

4. Once you have "constructed" your factors, check the inter-item-correlation and Cronbach's alpha.

5. Depending on the nature of your data, 46 % explained variance is fine in the Social Sciences.

I would be happy to answer any more questions that might arise.

Beste wishes from Germany

Marcel

You must also take into account the theory of the model that you try to propose, if you try to promponer a factorial model is very important to justify theoretically, if you have a history should look at some similar model. If there is no similar model from a previous study, I recommend a confirmatory analysis or SEM.

Hello Sarah,

In addition to the comments made by Cristian Ramos-Vera and Marcel Grieger , I would add that, it is quite possible that 46%-52% of the common variance may be as good a factor solution as is possible for the variables you are working with. However, I would add that parallel analysis is probably a more dependable method for determining the number of factors to extract than is the "eigenvalue > 1" criterion.

At the front end, though, it's fair game to ask some additional questions:

1. Do these variables have some logical, empirical, or theoretical basis for your assuming that they will share some common motivating factor(s)?

2. Are the measures of the variables that you used as technically strong with respect to established evidence for score reliability and validity as possible?

3. Did you run cursory checks on the "fitness" of the data set for factoring, such as KMO, Bartlett's test (which is such a low bar that, should a variable set fail this, just walk away from it!), and inspection of all bivariate correlations?

4. Are you using suitable correlation measures? For dichotomous/polytomous variables, polychoric correlations might be better than ordinary Pearson correlations.

As Marcel suggests, it's probably safer to start with non-orthogonal rotations (e.g. promax, oblimin) under the assumption that often factors do correlate in the real world. However, if you find that the estimated interfactor correlations are all small, it is certainly true that you could justify an orthogonal rotation as being part of a more parsimonious solution.

Good luck with your work.