Can someone explain the differences between Varimax and Quartimax rotations on SPSS? I get quite different results depending on which one I choose when validating components using PCA. I am getting 7 components as the result - some of which have only 2 items from about 30 items. Thanks in advance.
The aim of rotations in factor analysis is to better clustering variables in few factors. In both methods the resulting factors remain uncorrelated.
More generally, Varimax focuses on factors whereas Quartimax rotation concentrates on variables.
More especially,
(1) Varimax rotation maximizes the variance of the squared loadings of a factor; i.e., Varimax tries to simplifies the columns of loading matrix. Each factor will tend to have either large or small loadings of any particular variable.
(2) Quartimax rotation maximizes the variance of the squared factor loadings in each variable, i.e., simplifies the rows of loading matrix. In other words, Quartimax minimizes the number of factors needed to explain each variable. By Quartimax rotation, often a huge number of variables include in the first rotated factor, and hence, usually this method can not be helpful in many researches.
The aim of rotations in factor analysis is to better clustering variables in few factors. In both methods the resulting factors remain uncorrelated.
More generally, Varimax focuses on factors whereas Quartimax rotation concentrates on variables.
More especially,
(1) Varimax rotation maximizes the variance of the squared loadings of a factor; i.e., Varimax tries to simplifies the columns of loading matrix. Each factor will tend to have either large or small loadings of any particular variable.
(2) Quartimax rotation maximizes the variance of the squared factor loadings in each variable, i.e., simplifies the rows of loading matrix. In other words, Quartimax minimizes the number of factors needed to explain each variable. By Quartimax rotation, often a huge number of variables include in the first rotated factor, and hence, usually this method can not be helpful in many researches.
I am completely agree with Heydar Ali, around 80 of 100 factor analyses we use Varimax rotation, simply based on its merit.
Wow. Fantastic answers thank you so much. I guess both are valid and I should pick one based on the result groupings to see how they fit. Hope this approach is ok!
What should I say about a column that has only one variable? Should that be discarded because it seems unrelated to the rest of the questionnaire? Thank you for your advice.
> I should pick one based on the result groupings to see how they fit
The goodness-of-fit of a factor model is not changed by rotating it. Rotation does only change the way observed variance is partitioned but does not change the amount of explained variance and, thus, fit of the model. It is a way to find a "simple structure" in your data, according to the heuristic: The more zeros or neglectably small values in the loading matrix, the simpler.
Both rotation principles are heuristics and not based on a statistical principle. This is why their appropriateness/simplicity/interpretability has to be evaluated by the researcher and her/his knowledge about the data.
Hello Mr Leong, I did a PCA at Uni Melb on a dataset with SPSS and I only recall using varimax In that I don't think I've heard of the other - or not that I can recall but it was a while ago now. Sorry Cheers, Deborah
Dear Rupert
The goal of rotation in FA is two fold- to get is simple structure and positive manifold. The un rotated factors are often difficult to interpret because one may find several factors having significant loadings on only few variables and some (generally the first) having too many variables with significant loadings. Further, some variables may be loading negative while others positive on the same factor. The rotation helps to redistribute the total variance extracted by a given number of factors in such a way that each factor is represented by several variables with, as far as possible, positive loadings. The simple structure is defined as a factor structure in which the variables loading on factor have lower loadings on the other factors and each factor has significant or higher loadings on some variables but not on the others.
As Hyder Ali has explained the said two objectives of the simple structure are obtained by the two methods of rotation.
Form your original post and subsequent replies, I guess that you have probably not used any method for determining the number of factors to be retained for subsequent rotation as a result you are getting some factors with fewer variables - only two or one variable with significant loadings.
My suggestion would be to use any method or a set of methods such as scree test, parallel analysis etc. to determine the number of factors to be retained. Then to apply what ever rotation you want. It is often recommended that one should first perform oblique rotation and see the correlation among factors. If the factors are not correlated with each other then to apply any orthogonal rotation method such as varimax.
Remember, that the total variance explained remains the same both before and after rotation. What differs is the amount of variance attributable to each factor. It is possible that the variance explained by a given factor before rotation may be different than that what one obtains after rotation.
hope this helps
Could I suggest to forget rotations and maintain plain PCA so to keep the physical meaning of what you get ????
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