Multiple groups, exploratory factor analyses, Tucker's Phi

[Evelyn Mare]

Hello,

I am trying to assess if the loadings on a latent construct are similar for different ethnic groups. I know that this can be done with SEM and invariance tests.

However, I read in a paper (citation 1 below) that estimating an exploratory factor analysis and subsequently estimating Tuckers Phi might be an alternative way to go about this.

This paper seems to suggest the same: Lorenzo-Seva, U., & Ten Berge, J. M. (2006). Tucker's congruence coefficient as a meaningful index of factor similarity. Methodology, 2(2), 57-64.

Does anybody know or have any good resources for me on how to implement this in stata?

grateful for any tipps!

Cheers,

Evelyn

Refrence one:Froehlich, L., Martiny, S. E., Deaux, K., Goetz, T., & Mok, S. Y. (2016). Being smart or getting smarter: Implicit theory of intelligence moderates stereotype threat and stereotype lift effects. British Journal of Social Psychology, 55(3), 564-587. (mentioned on page 569)

[Phil Bromiley]

You didn't get a quick answer, I suggest to try to program it yourself and then ask if you have problems. We're better with tangible problems. We would have to get the paper and puzzle through it to help you which reduces the likelihood of a response. While the cite is good, a brief explanation is also helpful. Remember to follow the FAQ on asking questions.

[daniel klein]

The core-formula for comparing two sets of factor loadings is straightforward. Here is a Mata function that returns the (modified) Tucker coefficient of congruence (Lovik et al. 2020)

version 11.2

mata :

real scalar mtcc(real colvector x, real colvector y, | real scalar m)
{
    if ( m ) return( colsum(abs(x:*y))/sqrt(colsum(x:^2)*colsum(y:^2)) )
    else     return( colsum(x:*y)/sqrt(colsum(x:^2)*colsum(y:^2)) )
}

end

The so-called TCC (Lovik et al. 2020) appears to be calculated for every possible combination of factors and, sometimes, for loadings that have been rotated in a specific way. I did not dive into this. If you were to write this up as a general-purpose program, you would obviously want to implement such things. Much more basic, you would also want to implement some checks to make sure that the input factor loading matrices are, in fact, factor loadings and that they are all based on the same set of variables and, possibly, observations.


Lovik, A., Nassiri, V., Verbeke, G., & Molenberghs, G. 2020. A Modified Tucker’s Congruence Coefficient for Factor Matching. Methodology, 16(1), 59--74.