---
tag: 4QQQP1Q886
kind: concept
name: Factor analysis
msc: [62H25]
specializes: [C63RVH96TF]
sources:
  - url: https://en.wikipedia.org/wiki/Factor_analysis
same_as:
  wikidata: Q726474
  wikipedia: Factor analysis
---

## Summary

Factor analysis models many observed variables as linear combinations of a few unobserved common factors plus a noise term specific to each variable.
It is a [[latent variable model|C63RVH96TF]] that explains the correlations between the observed variables through the shared factors.
The model implies that the [[covariance matrix|0V7G6WMFK0]] is a low-rank matrix plus a diagonal matrix.
It is widely used in psychology and the social sciences.

## Explanations

### L1 human

Students who do well in algebra tend to do well in geometry, and good readers tend to be good writers.
Factor analysis tries to explain such patterns by a few hidden abilities, for example a mathematical ability and a verbal ability.
Each test score is then a weighted sum of the hidden abilities plus a part special to that test.
The weights, called loadings, show which tests depend on which abilities.