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Factor Analysis: Varimax Rotation

Varimax rotation is a statistical technique used at one level of factor analysis as an attempt to clarify the relationship among factors. Generally, the process involves adjusting the coordinates of data that result from a principal components analysis. The adjustment, or rotation, is intended to maximize the variance shared among items. By maximizing the shared variance, results more discretely represent how data correlate with each principal component. To maximize the variance generally means to increase the squared correlation of items related to one factor, while decreasing the correlation on any other factor. In other words, the varimax rotation simplifies the loadings of items by removing the middle ground and more specifically identifying the factor upon which data load. This entry introduces the varimax rotation and discusses its use in the statistical process, as well as its general application and limitations.

Defining Varimax Rotation

The computation of varimax rotation does not involve a change in the plot locations or coordinance of the data. Instead, what changes is the baseline or orthogonal axis relative to the coordinance of data points. The objective is to identify the alignment or rotation of the axis in a way that best represents the shared variance among various components. The expected result is identification of a model that best fits the data. In other words, the computation provides a more equal distribution, or assortment of shared variance among the components. The usefulness of the rotation is in the clarity of deciding about the relationship between data and the identifiable principal components.

Varimax rotation belongs to the family of orthogonal rotations. Orthogonal rotations lean more toward assumptions that the components or factors do not correlate with one another. That means data that indicate loading on one factor also indicate a zero loading on any other factor. The assumption is important to keep in mind for the field of communication due to the nature of observations and measurements. Typically, in social sciences the topics under examination are not perfectly uncorrelated, and this is especially true when studies focus on behavioral sets associated with states of emotion or motivational factors. Generating evidence to argue that behavioral sets are attributable to specific emotions often becomes figurative guess work—is the person crying because he or she is sad, or because he or she is happy? When varimax rotations assume factors derived from social scientific means are uncorrelated, accurate interpretation of, and thus identification of, underlying themes becomes difficult to determine. Nevertheless, maximizing the variance belongs to the assumptions associated with orthogonality in contrast to oblique rotations. Thus, the objective of varimax rotation is to ultimately identify which data belong to which factor.

Statistical Process

Following a principal components analysis to determine the probable quantity of data-driven factors, a varimax rotation becomes a viable next step. However, at this stage, examination of factor correlations also becomes necessary before applying rotation techniques of any kind. This is because determining which factor rotation to apply partially depends on the degree to which factors correlate prior to application of rotations. Typically, for varimax rotations, factors must be identified as uncorrelated. Some scholars argue that factors identified as uncorrelated should produce either a coefficient of .32 or less, or at least indicate less than 10% covariance. Other scholars argue that the purpose of rotations is to simplify data that are not so purely uncorrelated, and may initially indicate higher degrees of correlation. For such occasions, more oblique rotations become necessary. However, for varimax rotations, orthogonality of data must be determined, though the cutoff points remain arbitrary, and such determinations are dependent upon a variety of additional results including both the quantity of factors and sample sizes. Either way researchers decide, the standard statistical assumptions of varimax rotation are that the data are orthogonal. As a means to clarify interpretation of results, the more varimax rotation is applied to orthogonal data, the more accurate the statistical technique becomes to further simplify results.

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