Exam 1

1. Metainformation

   Tag	Value
   file	Factor-analysis_eur-factor_analysis-201-en_eur-factor_analysis-201-en
   name	eur-factor_analysis-201-en
   section	Factor analysis/Factor loadings
   type	schoice
   solution	FALSE, TRUE, FALSE, FALSE
   Type	Conceptual
   Program
   Language	English
   Level	Statistical Literacy

   Question

   A researcher conducts an explorative factor analysis and extracts 3 factors. Next, she performs a non-orthogonal rotation. The factor loadings in the pattern and structure matrix turn out to be almost identical across the three factors. What is the correct conclusion concerning this result?

   
   
   1. FALSE: There is no point in performing a rotation, because the results with and without the rotation are almost identical.
   2. TRUE: The three factors are barely correlated.
   3. FALSE: The sum of the eigenvalues is almost identical with and without rotation.
   4. FALSE: The orthogonal and non-orthogonal rotations show almost the same proportion of explained variance.
   
   

   Solution

   • The comparison between the pattern and structure matrix does not give information about the solution without rotation.
     
   • After extraction the pattern and structure matrix tell us nothing about the initial eigenvalues (these are about the explained variance of all possible factors, so the same number as there are items).
   • The statement about the proportion of explained variance is incorrect because it does not answer the question. After having extracted a certain number of factors, the proportion explained variance is always the same with and without rotation (even if the loadings in the pattern and structure matrix are very different).

   Non-orthogonal rotation means that the factors are allowed to correlate. The pattern matrix gives the corrected loadings (corrected for factors that have a higher correlation) between an item and a factor. If the loadings in the pattern and structure matrix are nearly the same, this means that the factors are barely correlated (there is no overlap between the factors to correct).

   
   
   1. False
   2. True
   3. False
   4. False