Is there a way to obtain factor correlations with significance levels in lavaan for CFA?

CFA
1

I’m working on a Confirmatory Factor Analysis (CFA) for my survey using the lavaan package in R. I can get the correlation matrix of factors, but I’m struggling to find a way to include the p-values for these correlations. I’ve tried using cov2cor(inspect(fit, what = "est")$psi), but it only gives me the matrix without significance levels.

Here’s a basic example of my CFA model:

model <- '
  factor1 =~ q1 + q2 + q3
  factor2 =~ q4 + q5 + q6
  factor3 =~ q7 + q8 + q9
'

results <- cfa(model, data = my_data, 
               auto.var = TRUE, auto.fix.first = TRUE,
               auto.cov.lv.x = TRUE)

Does anyone know how to get both the correlation matrix and the associated p-values for the factors in this setup? I’d really appreciate any help or suggestions!

2

yo, have u tried the parameterEstimates() function? it might give u what ur looking for. just run it on ur fit object like parameterEstimates(results) and look for the rows where op is ‘~~’. that should show correlations between factors with p-values. hope this helps!

3

While lavaan doesn’t directly provide p-values for factor correlations, there’s a workaround you can try. After running your CFA, extract the standardized estimates and their standard errors:

std_est <- standardizedSolution(results)
factor_corr <- std_est[std_est$op == '~~' & std_est$lhs != std_est$rhs, ]

Then calculate z-scores and p-values:

factor_corr$z <- factor_corr$est.std / factor_corr$se
factor_corr$p <- 2 * (1 - pnorm(abs(factor_corr$z)))

This should give you the factor correlations with their corresponding p-values. Keep in mind that this method assumes normality, so interpret results cautiously if your data violates this assumption. Also, consider adjusting for multiple comparisons if you’re testing many correlations simultaneously.

4

Hey there DancingButterfly! :butterfly:

I’ve been messing around with lavaan for my own research, and I totally get your frustration with those pesky p-values. Have you considered using the semTools package? It’s got some neat functions that play nice with lavaan and might solve your problem.

Try this out:

library(semTools)
factor_corr <- standardizedSolution(results)
factor_corr_table <- subset(factor_corr, op == '~~' & lhs != rhs)

This should give you a nice table with standardized correlations and p-values. It’s been a lifesaver for me!

Also, just curious - what kind of survey are you working on? Sounds interesting if you’ve got multiple factors. Mind sharing a bit about your research? I’m always eager to learn about what others are up to in the CFA world!