What do the loadings of a PCA tell us?

The loadings in L tell us the proportion of each score which make up the observations in D. In PCA, L has the eigenvectors of the correlation or covariance matrix of D as its columns. These are conventionally arranged in descending order of the corresponding eigenvalues.

What does a low eigenvalue mean?

An Eigenvalue lower than one means that the factor does not “amplify” the effect of each component and thus it explains less than the components. You can preliminarily check whether the Cronbach Alpha can be improved by dropping some components and then, re-run your factor analysis with a reduced number of components.

How do you read a loading plot?

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.

What does a large eigenvalue mean?

The largest eigenvalue is the maximum pole of the system (in terms of magnitude). If the system is described in its state-space form. the eigenvalues are the roots (in the variable domain) of the equation where the polynomial corresponding to the determinant becomes equal to zero, that is.

What are loading plots?

The loadings plot shows the relationship between the PCs and the original variables. You can use the graph to show how the original variables relate to the PCs, or the other way around. For example, the graph indicates that the PetalWidth and PetalLength variables point in the same direction as PC1.

What is the difference between scores and loadings?

The two matrices V and U are orthogonal. 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.