Factor loadings (factor or component coefficients) : The factor loadings, also called component loadings in PCA, are the correlation coefficients between the variables (rows) and factors (columns). Analogous to Pearson’s r, the squared factor loading is the percent of variance in that variable explained by the factor.

The matrix V is usually called the loadings matrix, and the matrix U is called the scores matrix. The loadings can be understood as the weights for each original variable when calculating the principal component. The matrix U contains the original data in a rotated coordinate system.

#### Can you use Factors in PCA?

The mathematics of factor analysis and principal component analysis (PCA) are different. Factor analysis explicitly assumes the existence of latent factors underlying the observed data. PCA instead seeks to identify variables that are composites of the observed variables.

Use the loading plot to identify which variables have the largest effect on each component. Loadings can range from -1 to 1. Loadings close to -1 or 1 indicate that the variable strongly influences the component. Loadings close to 0 indicate that the variable has a weak influence on the component.

As a rule of thumb, your variable should have a rotated factor loading of at least |0.4| (meaning ≥ +. 4 or ≤ –. 4) onto one of the factors in order to be considered important. In addition, a variable should ideally only load cleanly onto one factor.

### Should I use factor analysis or PCA?

If you assume or wish to test a theoretical model of latent factors causing observed variables, then use factor analysis. If you want to simply reduce your correlated observed variables to a smaller set of important independent composite variables, then use PCA.

#### What is the use of factor analysis?

Factor analysis is a powerful data reduction technique that enables researchers to investigate concepts that cannot easily be measured directly. By boiling down a large number of variables into a handful of comprehensible underlying factors, factor analysis results in easy-to-understand, actionable data.

How do you evaluate PCA results?

To interpret each principal components, examine the magnitude and direction of the coefficients for the original variables. The larger the absolute value of the coefficient, the more important the corresponding variable is in calculating the component.

The sum of the squared loadings of each variable with a given factor (the column sum of the squared loadings matrix) will equal the factor’s eigenvalue. Hence the eigenvalue summarizes how well the factor correlates with (i.e., summarizes or can stand in for) each of the variables.

That would imply you should delete that variable from the analysis, or drop the whole factor from the solution. Hi, PCA is used for reducing/summarizing many input variables to a few PCs. The factor loading is simply the correlation of the specific variable on the respective PC.