comparing latent means in lavaan

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GAT

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May 20, 2020, 7:07:19 AM5/20/20
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Hi all: 

I'd like to ask some clarifications concerning how lavaan handles differences among latent means in a multigroup structural equation model comprising three groups.
(I have established full metric and partial scalar invariance and am now comparing means across groups.)
 
I have opted for the marker item approach, according to which I fix the intercept of the market item to 0.
With 5 latent variables and 3 groups:

x1 + y1 + t1 + w1 + f1 ~ c(0,0,0)*1

Next, I'm estimating the latent intercepts 

lat1  ~ c(a1, a2, a3)*1
lat2  
~ c(b1, b2, b3)*1
lat3  
~ c(c1, c2, c3)*1
...
lat5  
~ c(e1, e2, e3)*1

Now, my question is: what are the p-values that the intercept section of the output is producing? In the reference group approach (the default in lavaan, I believe), those refer to the comparison between referent and comparison groups. Do they test the difference between the mean and 0? 

I am now testing differences in latent means using:

lat1difab:= a1 - b1

Does this seem valid?

Thank you for your help.

car...@web.de

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May 20, 2020, 7:17:23 AM5/20/20
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Why a1 - b1? Shouldn't that be a1 - a2?
Am 20.05.20, 13:07 schrieb GAT <garetm...@gmail.com>:
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GAT

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May 20, 2020, 8:07:24 AM5/20/20
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That's right, I am sorry. 
I meant a1 - a2. 
I can't see an obvious way to edit the message now. 

Terrence Jorgensen

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May 21, 2020, 7:09:03 PM5/21/20
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In the reference group approach (the default in lavaan, I believe), those refer to the comparison between referent and comparison groups. Do they test the difference between the mean and 0? 

When group-1's mean is zero, then any other group's mean is by definition the difference from the first group's mean, because x - 0 = x.  So there is no need to use the marker-variable approach.  Differences between groups 2 and 3 are just as easily calculated as (e.g.) a2 - a3, because the reference group's mean cancel's out:

a2 - a1 = a2
a3 - a1 = a3
thus: 
(a2 - a1) - (a3 - a1) = a2 - a3 + a1 - a1 = a2 - a3 

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
 
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