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 ...
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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 ...
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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: ...
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, ...
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 ...
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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 ...
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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?
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) ...
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 | ...
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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? ...
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 ...
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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 ...