Q: Evaluating quality of sources using factor analysis Assume I have entities $e_i$ (let's say, persons) and am trying to approximate their numerical attribute $q_i$ (let's say, their age). For this, I'm using imperfect data from $3$ sources $S_1, S_2, S_3$. Source $S_i$ is defined on a domain $D_i\subseteq \{e_1,\ldots, e_N\}$ and gives me an approximation of the real value for any $e\in D_i$. Assume that $D_i\cap D_j$ is nonempty for each $i,j$.
Without having much other information, how can I evaluate the quality of my sources?
One idea I have in mind is to construct a "correlation matrix" $C$ having 


*

*$1$ on the diagonal, and

*a Pearson correlation of sources $S_i$ and $S_j$ on the intersection $D_i\cap D_j$ where both sources are defined, on positions $(i,j)$ and $(j, i)$.


Then the C-eigenvector corresponding to the largest eigenvalue should correspond -- I guess -- to something like an "approximation of the true value", assuming that factors in the factor analysis are interpretable. 
If this first factor is, let's say, $0.8\times S_1 + 0.3\times S_2 + 0.6\times S_3$, can I interpret it so that source $S_1$ is "better" and source $S_2$ is the worst?
Any feedback or references to this idea? -- does it make sense?

A: Yes. But you should probably use principal components analysis
A similar approach is used in intelligence testing - general intelligence (g) is defined as the first unrotated principal component from a PCA of a bunch of intelligence tests. The higher the loading, the more the test is assumed to represent general intelligence, and this is called its 'g-loading'. 
There's information on the wikipedia page: https://en.wikipedia.org/wiki/G_factor_(psychometrics)
You can find more papers with your favorite search engine. Here's one: https://www.sciencedirect.com/science/article/abs/pii/0160289686900097 
