Comparing factor-loadings

[Mathis]

Dear all,

For my research I would like to test for measurement equivalence, this is to test whether my measure of a latent variable actually measures the same construct when answered by different categories of people. This is not the case when they interpret the questions differently.

I was told I could do this with exploratory factor analyses and comparing factor loadings between groups.

As an example I would like to give the factor loadings of the items of a 'peer delinquency'-scale for girls and boys:

girls|boys

item 1: 0.56 0.70
item 2: 0.69 0.82
item 3: 0.67 0.70
item 4: 0.50 0.61
item 5: 0.65 0.69

On first sight I see some items do load differently where this should be more or less the same when measuring the same construct. But how to determine this in a more mathematical way?

Any ideas?

[Mathis]

Maybe I should arrange them from highest to lowest factor loadings and compare the sequences in both. For my example this would give:

Girls:

item 2
item 3
item 5
item 1
item 4

Boys:

item 2
item 3
item 1
item 5
item 4

Because the items correlate differently with the underlying factor, it might they resemble a different factor? Can anyone back me up on this one?

[trinker]

I think you're more after differential item functioning (DIF) detection.

Mantel–Haenszel and logistic regression are both approaches to detecting DIF. I prefer the latter in that it provides more information.

I don't see what EFA can tell you in this case. Maybe someone more knowledgeable will weigh in here.

[Mathis]

Thanks!!

And how exactly would you perform this logistic regression in SPSS? What variables should I regress? I don't understand how you can regress variables who come from two different groups of respondents.

[trinker]

Well the logistic regression requires a simple yes no (correct incorrect response) if you don't have that there are more complicated models but I am not familiar with them.

As far as running it in SPSS here's a site on logistic regression: http://www.ats.ucla.edu/stat/spss/dae/logit.htm

You need a null model (no group comparison), an additive model, and an interaction model.

If you don't have a yes/no outcome you need something more complicated than this. I don't use SPSS but I know it's pretty easy to do because my psychometrics prof showed this method using SPSS.

[wandatheavenger]

I'm not sure you have the resources to do this, but it seems to be a question better addressed with a multigroup CFA using, assuming good fit, the theoretical model upon which the scale was built.

[trinker]

I don't think CFA is going to tell the poster what they really want (may be wrong) but I think they're more interested in knowing if there's a difference in how people int he two groupd respond regardless of ability. What if one group is of lower ability (say we're comparing infant response with college grads). I think CFA does provide information on how the test items are functioning but does not gice information about differences between groups taking into account ability/trait level.

I may be wrong on this and am curious what others may have to say.

If CFA is a vialable option then:

I'm not sure you have the resources to do this, but it seems to be a question better addressed with a multigroup CFA using, assuming good fit, the theoretical model upon which the scale was built.

can be addressed with the program R which can take care of this for free but requires learning on the part of the user beyond SPSS.

[Mathis]

I'm not sure you have the resources to do this, but it seems to be a question better addressed with a multigroup CFA using, assuming good fit, the theoretical model upon which the scale was built.

Well, indeed in all the literature a similar problem is addressed by CFA. The problem is I have no idea how to perform these tests and my supervisor assured me I could do it with the statistics he taught me, namely EFA with SPSS. (ps: he is on holidays now so I cannot approach him atm)

I was thinking about this:

As factor loadings are actually just the regression coefficients of the items on the common factor, I might use a formula I used in other parts of my work to compare regression coefficients. http://www.talkstats.com/showthread....PSS?highlight=

Even though I realise its not the optimal solution, its probably the only one that goes with my current abilities. Does anyone see any objections with this approach?

[Mathis]

Come to think of it, SPSS does not provide me with the standard error of the factor loadings so using that formula is in fact NOT an option.

[wandatheavenger]

If you want to stay within the EFA framework, look into using a Procrustean/Procrustes rotation where you use the EFA results of one group as the target of the other. This will at least give you some statistical indication of structural similarity. Check out this site for a bit more on it: http://culturemindspace.blogspot.com...-rotation.html. It says you can get SPSS syntax from him if you ask, which would save you the trouble of having to learn a new program.

[Mathis]

If you want to stay within the EFA framework, look into using a Procrustean/Procrustes rotation where you use the EFA results of one group as the target of the other. This will at least give you some statistical indication of structural similarity. Check out this site for a bit more on it: http://culturemindspace.blogspot.com...-rotation.html. It says you can get SPSS syntax from him if you ask, which would save you the trouble of having to learn a new program.

Thank you! This is extremely helpful. I read about this Procrustean rotation before but found it generally to hard to understand, let alone explain it to my reading audience so never considered applying it. This website however makes it much more accessible, not too much information and not too little.

Many thanks for your efforts Trinker and Wandatheavenger!