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How to create an index from all principal components?
Another answer here mentions weighted sum or average, i.e. w X X i + w Y Y i with some reasonable weights, for example – if X, Y are principal components – proportional to the component st. deviation or variance. But such weighting changes nothing in principle, it only stretches & squeezes the circle on Fig. 2 along the axes into an ellipse.
How to create composite index from multiple components?
If your variables are themselves already component or factor scores (like the OP question here says) and they are correlated (because of oblique rotation), you may subject them (or directly the loading matrix) to the second-order PCA/FA to find the weights and get the second-order PC/factor that will serve the “composite index” for you.
How to create a single index using PCA?
I am using Principal Component Analysis (PCA) to create an index required for my research. My question is how I should create a single index by using the retained principal components calculated through PCA. For instance, I decided to retain 3 principal components after using PCA and I computed scores for these 3 principal components.
What is the answer to the question Composite Index?
This answer is deliberately non-mathematical and is oriented towards non-statistician psychologist (say) who inquires whether he may sum/average factor scores of different factors to obtain a “composite index” score for each respondent.
Which is an example of retaining principal components?
If the scree plot contains an “elbow” (a sharp change in the slopes of adjacent line segments), that location might indicate a good number of principal components (PCs) to retain. For this example, the scree plot shows a large change in slopes at the second eigenvalue and a smaller change at the fourth eigenvalue.
How to select the second principal component in PCA?
More formally, select e 11, e 12, …, e 1 p that maximizes subject to the constraint that The second principal component is the linear combination of x-variables that accounts for as much of the remaining variation as possible, with the constraint that the correlation between the first and second component is 0