Linked Questions

53 votes
4 answers
31k views

Why does inversion of a covariance matrix yield partial correlations between random variables?

I heard that partial correlations between random variables can be found by inverting the covariance matrix and taking appropriate cells from such resulting precision matrix (this fact is mentioned in ...
michal's user avatar
  • 1,288
33 votes
1 answer
47k views

Best factor extraction methods in factor analysis

SPSS offers several methods of factor extraction: Principal components (which isn't factor analysis at all) Unweighted least squares Generalized least squares Maximum Likelihood Principal Axis Alpha ...
Placidia's user avatar
  • 14.5k
15 votes
1 answer
26k views

Steps done in factor analysis compared to steps done in PCA

I know how to perform PCA (principal component analysis), but I would like to know steps that should be used for factor analysis. To perform PCA, let us consider some matrix $A$, for instance: ...
dato datuashvili's user avatar
5 votes
1 answer
18k views

What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis?

On the one hand I read in a comment here that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, ...
user1205901 - Слава Україні's user avatar
7 votes
2 answers
8k views

Can you calculate $R^2$ from correlation coefficents in multiple linear regression?

In simple linear regression, $R^2$ is equivalent to the squared correlation of a dependent and an independent variable. Is this also true for multiple linear regression? For example, I measured trait ...
E_H's user avatar
  • 341
4 votes
1 answer
4k views

High KMO but low communality in factor analysis

I'm performing a factor analysis and I have for a variable a Kaiser-Meyer-Olkin (KMO) measurement of .710 and a communality of ...
Frederik's user avatar
4 votes
1 answer
7k views

What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
Ponjul Zwalda's user avatar
2 votes
0 answers
5k views

What is the intuition behind the KMO formula?

In answer to a different question about data assumptions of factor analysis rolando2 writes: There is another condition that is sometimes treated as an "assumption": that the zero-order (vanilla) ...
user1205901 - Слава Україні's user avatar
4 votes
1 answer
713 views

Factor extraction methods: Harris and Image extraction

Is Harris's (1962) extraction method considered a form of principal component analysis (PCA) or factor analysis (FA)? What about image extraction? I am using SAS and the documentation says: HARRIS | ...
ESmyth5988's user avatar
5 votes
1 answer
454 views

Factor Analysis does not give a better covariance estimate than the Empirical Covariance matrix?

I do not see that Factor Analysis gives a better covariance estimate than the empirical covariance estimate, from the toy data simulation with explanation and code below. Am I doing something wrong? ...
Arnout Devos's user avatar
2 votes
0 answers
918 views

Negative Eigenvalues in EFA

Assuming a set of data meet all assumptions for EFA and we are doing a factor analysis (with the SMC used to define the shared variance), how do negative eigenvalues appear and what does that say ...
ESmyth5988's user avatar
0 votes
0 answers
256 views

Can PCA work when the number of observations is smaller than the number of dimensions? [duplicate]

I understand how principal component analysis works. However, in a financial time series sense, I do not understand why the number of observations should be larger than the number of dimensions. I am ...
user48561's user avatar