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:
Does this seem valid?
Thank you for your help.