[LISREL SIMPLIS] help with scalar invariance and calculating latent mean factors

I am conducting measurement equivalence on a two country sample (US and IN). I have established configural (baseline) and metric equivalence. However scalar invariance has not been established (the model change checks out but CFI change is less than .002). I examined the modification indices and for the most part I couldnt do much to improve fit. There were cross loadings or correlated errors and it didnt make theoretical sense to have cross loadings or correlate errors as the factors were different.So I didnt make any changes to the modification indices.
My question is how to i assess partial scalar invariance? Also once and if I etablish partial scalar invariance, I wanted to calculate group differences, however I would need to calculate the latent factors means, and Im not sure what the syntax is for that, or where in the output I could find this, if it is already provided in the scalar invariance output.
Does someone have any example syntax on getting partial scalar invariance or assessing latent factor means for group differences? I looked at Barbara Byrne's book for Lisrel but did not find it useful for these particular issues.

I look forward to any help! Thanks


Phineas Packard
Wait are you saying that the fit change from configural to scalar results in a delta CFI of < .002. I must have read you wrong because this seems like pretty good evidence for invariance to me.

For comparing latent means you use the model in which the loadings and intercepts have been constrained to zero. If you use a usual setup the mean in group 1 will be constrained to zero by default and thus the mean in group two will reflect descrepency from group 1 and will have associated standard errors. So you don't need to calculate factor scores just read straight from the output.
For the purpose of model comparison, a CFI change of .002 or greater is considered a substantial difference in model fit (Meade, Johnson, & Braddy, 2008). People also use different cut offs like CFI change of .01 or more.
Given that for my model, the CFI change from metric to scalar was less than .002, I do not have support for scalar invariance.

I cant seem to find the latent means in the output report.
Right, I did constrain one group to 0 while the other one I gave it a starting value of 1. My issue is figuring out how to do partial scalar invariance and finding and reading the output for the latent means. I would be happy to share portions of my output or an example output if someone could point it out to me.


Phineas Packard
Ok but above you say CFI change of GREATER than .002 is considered a substantial difference. But then in the third sentence you say the cfi in your model change by LESS THAN .002 which would imply than even by the very very strict standards of Meade et al. you are fine. Is the delta chi-square even significant? To be clear you WANT there to be little difference between your metric and scalar model that is to say NO change in CFI would be the thing you want.

In any case, typical practice is to look at the mod indices and identify the item intercept with the biggest MI and free that.
You're right about the CFI change difference. We dont want it to change drastically. I was confused with the wording, but I get it now. Thanks.

So with regard to constraining one group to 0, and leaving the other free, would I need to run this twice, alternating between the two groups, so as to obtain the latent factor means?

Hypothetically speaking if I set my code for the first group as:
Verbal=CONST + 1*Ability
Math=CONST + (1)*Ability

and for the second group as:

Do I swap these around and make the first group be constrained the second time, and the second group be free, to obtain the latent means?

Sorry for my confusion. I am still new to this. Thanks!
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Phineas Packard
Well the latent means don't have any inherent scale so setting one group to zero and the other referent to that is fine. No need to run the model twice. If the mean is arbitrary then arbitrarily assigning zero to one of your groups is fine.

Now some people don't like the arbitrary nature of latent means and want to put them one a meaningful scale. I think this is a reasonable approach so suggest you look into Todd Little's non arbitrary metric.
Thanks Lazar. Could I email you a portion of my scalar invariance output to get a better understanding of the latent factor means and how to interpret them?
It would be most helpful.
It seems that I need to have at least five posts per discussion before being able to send a message to someone on here.


Phineas Packard
Typically it is better to keep the discussion on the forum where possible so others can ) chip in or b) have their own questions answered. I am not really an expert in LISREL with it being 5 or more years since I used it last but I can try to help.
Right, I understand. I just am not sure what part of my output to post here, which is why I was asking if I could message you. I appreciate any help you can offer.