Definition of Factor Analysis

Factor analysis is an analysis technique that is frequently used in the field of development and validation of tests, allows exploring how the factors or latent variables are structured from the responses to the items of a test.

To obtain adequate measurement scales, researchers have resorted to the technique known as factorial analysis, which makes it possible to identify the structure that underlies the items of a measurement scale. This technique explores how a Latent Factor, which we could also call unobserved variable They explain the pattern of responses given to the items or items on a test.

Next, a brief introduction to factor analysis will be provided, including but not limited to: the differences between factor analysis and the principal component analysis, exploratory and confirmatory factor analysis and finally the elements that make up these.

Factor analysis and principal component analysis

When reviewing the literature around the development and validation of instruments, we can realize that among academics there are There is some confusion around the indiscriminate use of Factor Analysis (FA) and Principal Component Analysis (PCA). This indiscriminate use may be due to the fact that for a long time technological resources made the application of AF difficult and to compensate for this, they included ACP. Although both techniques are similar, since they reduce the items to smaller dimensions (factors and components), they also present some specific differences that lead to very different.

The FA seeks to identify how many and how the factors (latent variables) are structured; these factors would explain the common variance of the group of items analyzed. On the contrary, in the PCA, it is intended to determine how many components are necessary to summarize the scores of a group of observed variables, that is, explaining the greatest amount of variance observed. Another difference is that while in the AF the observed variables are considered as the dependent variables, in ACP these are the independent ones.

Exploratory and confirmatory factor analysis

Once the difference in AF and ACP has been established, it is necessary to make a new difference between the Exploratory Factor Analysis (EFA) and the Confirmatory Factor Analysis (AFC). Both analyzes have been considered as two parts of a continuous process. The AFE seeks to determine how many factors make up our scale, while the AFC is characterized by confirm those factors, but also determine how the factors and the items of the scale. Another way of defining them is that the AFE "builds" the theory while the AFC would confirm it.

AF Elements

Sample size

This is one of the most discussed topics, not only in FA, but also in data analysis in general. Determining the appropriate sample size for the analysis is a discussion that seems endless, the classic recommendations is that the greater the number of items, the greater the number of participants in our sample should be, with a minimum of 200 being the most recommended. However, the classic recommendations tend to lack a clear foundation, today many elements must be taken into account to determine how many participants are necessary, such as the number of items per factor, the matrix used for the analysis, and even how many response options the participants have. items. Thus, studies that use simulations under these conditions have determined that a minimum of 300 participants is an adequate figure.

Number of items to include in the analysis and in each factor

Regarding the number of items to be included in the analysis, these must be selected from the theory, however, it is necessary to point out that these should not be redundant, as this would cause these items to share the variance and therefore have bad estimate. Therefore, care must be taken to select only those items that truly represent the construct we are trying to assess. On the other hand, it is recommended to have at least three items for each factor; however, this amount can be modified depending on the matrix used and the sample size.

Matrix used

In classical FA designs there is an assumption that the variables are related in a linear fashion, They also present adequate normality indices, so the Pearson Correlation matrix was typically the one used. Today it is suggested to take into account the assumption of normality and the response format of the items. In addition to the above, the development of new tools for the development of PA has led to the use of new techniques such as the matrix of polychoric and tetrachoric correlations, however, both matrices require a larger sample size compared to the matrix of pearson.

Factor estimation

The most commonly used estimation methods are 2:

• Maximum likelihood: This method is the most common to use due to its advantages over other methods such as the ability to contrast the adjustment and quantification of errors. However, this method requires compliance with the normality of the data, having continuous scales and using the Pearson correlation matrix.

• Ordinary least squares. Actually this method refers to a family of estimation methods. These methods have proven to be robust when the assumptions of normality and linearity are not met. In the same way, its application in conjunction with the polychoric matrix has proven to be efficient.

Item rotation

This step refers to continuously rotating the matrix to find a solution that is simple and consistent. The most widely used methods today are orthogonal rotation, more specifically the criterion varimax and oblique rotation in your method direct oblimin. Today the latter is the most recommended method for presenting a more reliable and consistent structure.

Factors to retain

The crucial element of this analysis is factor formation, but how do we know how many factors we should have in our scale? The classic recommendation was to follow Kaiser's rule, which refers to keeping eigenvalues ​​greater than 1; however, this method tends to cause an overestimation of the factors. Nowadays it is suggested to follow the recommendations of the parallel analysis and other similar methods, but it is also suggested to take into account the interpretability of the results and the basic theory.

Finally, it is necessary to highlight that the CFA tends to be estimated using structural equation models. (SEM) so the process to carry it out should be carried out based on the criteria developed for these Models.

References

Lloret-Segura, S., Ferreres-Traver, A., Hernández-Baeza, A., & Tomás-Marco, I. (2014). The exploratory factor analysis of the items: a practical guide, revised and updated Introduction Determination of the adequacy of the Analysis. Annals of Psychology, 30(3), 1151–1169.