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I am using PCA to validate and research a set of 13 suppliers of products against a set of about 50 variables and performance indicators against an ideal "wish"-Supplier, mostly based on G. Jankers Book on Factor Analysis for Supplier a Rating System. While using R Studio I use my data to perform the PCA with prcomp.

My question is regarding practical statements of the outcomes of the PCA and its factors. My Goal is to identify the perfomance indicators, in which a supplier needs to improve, in order to improve another outcome. For example, maybe a supplier needs to improve reaction speed in order that the amount of price requests rise as well. Or to identify groups of suppliers with similar performance indicators.

PC1 accounts for about 50% of all variances, PC2 for 15%, PC3 for 10% and so on. If I now have a look on PCAs against the loadings for each of the 50 performance indicators and check the PCAs against the Suppliers, I result in having a few questions. Also to make sure I did understand correctly.

  1. Lets say Supplier 1 loads really low on PC1, like -6,23569. PC1 loads really high on the first 5 performance indicators. Can it be said that: "Supplier 1 does move against PC1"? So Supplier 1 would have really low loadings on the first 5 Performance indicators? Anything that loads high on PC1 would turn negative on Supplier 1 and vice versa?

  2. If a certain group of Performance indicators load significantly high on a PC, can it be said that a Supplier, that loads high on that PC as well does generally move with the PC and has generally higher emphasis on that group of performance indicators?

  3. PC1 is said to count for 50% of the information. If a performance indicator loads REALLY LOW on PC1, does that mean that this one performance indicator holds significantly more value in the whole spectrum because PC1 has such a high emphasis on it, which also means that this performance indicator might be the most important one in the specturm? Going further down the PCs, if PC10 has a very high loading on another one which didnt stand out on any of the PCs before, does this mean this indicator has just less value overall?

My Goal is to identify which performance indicators actually make a difference and then check which supplier needs to improve which area or which are the ones that needs to be focussed on.

Just imagine you are in a shoe store and sell addidas, nike, puma etc, and you want to figure out which of those is your times worth and you get the best out of and how to push them to become your ideal supplier.

Some Inputs of PCA Savy people are appreciated.

Supplier vs. PCs Performance Indicators vs. PCs

Edit: Ok so I understood Question 1 and 2. Am I correct in assuming that if a Factor loads high very early in the ranks of PCs that this must be something of bigger importance towards the whole factor spectrum? I have analysed the accumulation of explanation per indicator. (Sum of the Squareroots of the loadings per PC). Why am I not reaching 100% on the last PC on neither factor? highest I did get was 76% Explanation.

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  • $\begingroup$ Okay I have understood Question 1 and 2 now. Since PC1 = Loading1 * Performance indicator1 + Loading2 * performance indicator2... and so on. $\endgroup$
    – Zilfalon
    Commented Oct 22, 2021 at 17:47

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Principal Component Analysis (PCA) is not very useful for that type of interpretation.

Just imagine you are in a shoe store and sell addidas, nike, puma etc, and you want to figure out which of those is your times worth and you get the best out of and how to push them to become your ideal supplier.

It would be more useful to frame it as a supervised learning problem and find the feature and instances that are most associated with the target values.

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