# Factor Analysis with Varimax Rotation # Factor Analysis with Varimax Rotation

It is a statistical analysis that investigates the interrelations between a set (more or less large) of variables and tries to explain them in terms of their latent common dimensions, called factors. It is a technique of information reduction that does not consider the variables as dependent or independent, since all are considered simultaneously.

The Exploratory Factor Analysis of a battery of items is one of the statistical techniques most frequently applied in studies related to the validity of a questionnaire. It is usually used in Master, Thesis, Abstract, mainly to identify the underlying structure of the items in a Test.

Starting from that a high value is obtained in the KMO Test (greater than 0.8, from 0.5 it is considered convenient) and the Barlett Test is significant (p-value associated with the contrast statistic or Sig. less than 0.05), it is considered convenient to undertake an Exploratory Factor Analysis, either on a battery of items that underlie some components or dimensions, on notes, scores, scores, that is, variable values ​​measured in ordinal scale. In our example, with the criterion of preserving those factors or components whose eigenvalues ​​are greater than 1 (Total column), it is verified that with only the first component 74.67% of the variability is explained. If what is given preference, on the contrary with the other criterion, is the percentage of cumulative variability, it is observed that if we keep 2 Factors, 59.57% of accumulated variance is explained (example table), as an example, so that it results both illustrative of this statistical analysis. The proportion of total variability collected by each component is the quotient of the Lambda autovalue (own value), divided by the sum of the eigenvalues. From a graphic point of view, the factors can be conserved from `where the Scree Plot graph (main graph where this post begins) makes ‘elbow’, that is, we could maintain 2 or 3 factors (even 4), if relevance is given to the latter criterion.

## Varimax Rotation With the Varimax Rotation of all the factors a better result is obtained, since when doing an orthogonal rotation, it presses a similar variable with an axis. This facilitates the meaning of the interpretation of the selected components. It is the smallest rotation, it is also taken into account when the objective is the reduction to a smaller number of incorrect variables. Consider the solution rotated when almost all the factorial loads are stronger (greater weight), towards one of the components (factors), taking into account that the other has the sufficient amount of variation explained.

Interpreting the table of the SPSS output, in the Component Matrix it is observed that, in the case of keeping 2 factors, all the variables have a higher score on the first factor. On the contrary, in the case of carrying out the rotation, the variables as a whole have more weight in the second component, while the rest have more score in absolute value with respect to the primary factor.

Some authors proceed to study the factorial structure of the scale, composed of items, by means of a Parallel Horn Analysis as an exploratory method to examine the validity of factorial when it comes to dichotomous items, that is, with 2 response categories, which resulting recursive in a significant number of questionnaires (yes/no).