The output from a factor analysis will vary depending on the type of rotation you chose. Both orthogonal and oblique rotations will contain the following sections.
• Communalities. The communality of a given item is the proportion of its variance that can be accounted for by your factors. The communality for the initial extraction is always 1. This is because the full set of factors is specifically designed to account for the variability in the full set of items.
• Total Variance Explained. Provides you with the Eigen values and the amount of variance explained by each factor in both the initial and the rotated solutions.
• Component Matrix. Presents the factor loadings for the initial solution. Factor loadings can be interpreted as standardized regression coefficients, regressing the factor on the measures. Factor loadings less than .3 are considered weak, loadings between .3 and .6 are considered moderate, and loadings greater than .6 are considered to be large.
Factor analyses using an orthogonal rotation will include the following section.
• Rotated Component Matrix. Provides the factor loadings for the orthogonal rotation. The rotated factor loadings can be interpreted in the same way as the unrotated factor loadings.
• Component Transformation Matrix. Provides the correlations between the factors in the original and in the rotated solutions.
Factor analyses using an oblique rotation will include the following sections.
• Pattern Matrix. Provides the factor loadings for the oblique rotation. The rotated factor loadings can be interpreted in the same way as the unrotated factor loadings.
• Structure Matrix. Holds the correlations between the factions and each of the items. This is not going to look the same as the pattern matrix because the factors themselves can be correlated. This means that an item can have a factor loading of zero for one factor but still be correlated with the factor, simply because it loads on other factors that are correlated with the first factor.
• Component Correlation Matrix. Provides you with the correlations among your rotated factors.
Why is normality not required for factor analysis when it is an assumption of correlation, on which factor analysis rests?
Factor analysis is a correlative technique, seeking to cluster variables along dimensions, or it may be used to provide an estimate (factor scores) of a latent construct which is a linear combination of variables. The normality assumption pertains to significance testing of coefficients. If one is just interested in clustering (correlating) factors or developing factor scores, significance testing is beside the point. In correlation, significance testing is used with random samples to determine which coefficients cannot be assumed to be different from zero. However, in factor analysis the issue of which variables to drop is assessed by identifying those with low communalities since these are the ones for which the factor model is "not working." Communalities are a form of effect size coefficient, whereas significance also depends on sample size. As mentioned in the assumptions section, it is still true that factor analysis also requires adequate sample size, in the absence of which the factor scores and communalities may be unreliable, and if variables come from markedly different underlying distributions, correlation and factor loadings will be attenuated as they will be for other causes of attenuation in correlation.
Author- Manika Luitel