Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

Also, are the standardized regression weights equivalent to the correlation between a factor and a manifest variable?

I write this question with reference to an example on p138-142 of the following document: ftp://ftp.software.ibm.com/software/analytics/spss/documentation/amos/20.0/en/Manuals/IBM_SPSS_Amos_User_Guide.pdf.

Here are illustrative figures and a table: CFA example

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

Yes, if the factors are uncorrelated. This is also true in exploratory factor analysis - if you do an orthogonal rotation (or if you don't rotate) then you have one loading matrix. If you do an oblique rotation, the factors are correlated, and then you have a pattern matrix (which is correlations) and a structure matrix, which is regressions.

If you think about CFA in terms of regression, it becomes clear why.

When you do regression, the regression weights are given by:

$$ \beta = X^{-1}Y $$ Where X is the correlation matrix of the predictors (if we're doing everything standardized). If the predictors are uncorrelated, then $X^{-1}$ is an identity matrix, and so $\beta = Y$. Same with CFA, if your factors are uncorrelated, then regressions are correlations. If not, then they're not.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.