How are PCA component scores and factor scores calculated?

How are PCA component scores and factor scores calculated?

It is about computing component scores in PCA and factor scores in factor analysis. Factor/component scores are given by ˆF = XB, where X are the analyzed variables ( centered if the PCA/factor analysis was based on covariances or z-standardized if it was based on correlations).

How is allowing skewed variables related to PCA?

In the context of PCA allowing very skewed variables is pretty similar to doing PCA without centering the data (i.e., doing PCA on the basis of cosine matrix rather than correlation matrix). It is you who decides whether to permit the long tail to influence results so greatly (and let the data be) or not (and transform the data).

How to calculate factor scores in factor analysis?

It is about computing component scores in PCA and factor scores in factor analysis. Factor/component scores are given by F ^ = X B, where X are the analyzed variables ( centered if the PCA/factor analysis was based on covariances or z-standardized if it was based on correlations). B is the factor/component score coefficient (or weight) matrix.

What should the skewness of a variable be?

However, some of my variables are very skewed (skewness calculated from SPSS ranges from 2–80!). Should I keep the skewed variables like that or could I transform the variables on principal component analysis? If yes, how would I interpret factor scores? What type of transformation should I do? log10 or ln?

When to use a principal component analysis ( PCA )?

Assess how many principal components are needed; Interpret principal component scores and describe a subject with a high or low score; Determine when a principal component analysis should be based on the variance-covariance matrix or the correlation matrix; Use principal component scores in further analyses.

What are the coefficients of a PCA loading?

PCA loadings are the coefficients of the linear combination of the original variables from which the principal components (PCs) are constructed.

How is the variance-covariance matrix written in PCA?

This is determined by the Spectral Decomposition Theorem. This will become useful later when we investigate topics under factor analysis. The variance-covariance matrix can be written as the sum over the p eigenvalues, multiplied by the product of the corresponding eigenvector times its transpose as shown in the first expression below:

How are factor / component scores calculated in SPSS?

Factor/component scores are given by F ^ = X B, where X are the analyzed variables ( centered if the PCA/factor analysis was based on covariances or z-standardized if it was based on correlations). B is the factor/component score coefficient (or weight) matrix. How can these weights be estimated?

How to perform a factor analysis with polychoric correlation matrix?

Once we have a polychoric correlation matrix, we can use the factormat command to perform an exploratory factor analysis using the matrix as input, rather than raw variables. The dataset for this example includes data on 1428 college students and their instructors.