Weights and Component Loadings

Another measure of association is the multiple correlation between linear combinations from each set and the object scores. If no variables in a set are multiple nominal, you can compute this measure by multiplying the weight and component loading of each variable within the set, adding these products, and taking the square root of the sum.

Figure 1. Weights
Table of weights with variables grouped by set in the rows and dimensions in the columns
Figure 2. Component loadings
Table of component loadings with variables grouped by set in the rows and dimensions in the columns

These figures give the weights and component loadings for the variables in this example. The multiple correlation (R) is as follows for the first weighted sum of optimally scaled variables (Age in years and Marital status) with the first dimension of object scores:

R = [0.701 x 0.841 + (-0.273 x -0.631)]1/2 = 0.873

For each dimension, 1 – loss = R 2. For example, from the Summary of analysis table, 1 – 0.238 = 0.762, which is 0.873 squared (plus some rounding error). Consequently, small loss values indicate large multiple correlations between weighted sums of optimally scaled variables and dimensions. Weights are not unique for multiple nominal variables. For multiple nominal variables, use 1 – loss per set.

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