CFA markers and latent variable's variance 
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*In Confirmatory Factor Analysis (CFA) we set a marker (regression weight = 1) to a randomly or not randomly chosen observed variable. I was wondering under which conditions or in which situation you would not do that? (not apply any marker)

*And similarly, in which situation would you set variance of latent variable to 1 in CFA? 
 A: In CFA, you must impose some constraint upon each separate factor in order to make the factor model statistically identified. Fixing a loading to 1 is one way. Another is to fix the factor variance to 1. A third, called "effects coding," constrains the average loading per factor to 1 without fixing any loading to a given value.
These constraints are often arbitrary and cosmetic, but they can become substantive when a model has across-factor constraints, as when loadings for different factors are constrained to equality.
Fixing a loading to 1, or fixing the factor variance to 1, can create problems in multiple group analysis. Fixing a loading can create a problem when trying to determine if measurement invariance holds, because the observed variable with the constrained loading may not itself demonstrate invariance. Fixing factor variance to 1 creates a potential problem simply because this standardization is done within-group rather than across groups. Within-group standardization (dividing by the within-group estimated standard deviation) can conceal differences (or create differences) across groups, because it obscures the uncertainty associated with those estimates.
On the other hand, if you are treating your observed variables as ordinal rather than continuous, then the changed nature of the factor model may reduce your options and force you to adopt one method or another.
A: 
  
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*In CFA we put a marker (regression weight = 1) to a randomly or not randomly chosen observed variable. I was wondering under which conditions or in which situation you would not do that? 
  



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*Usually, the loading of the first item(indicator) is set to 1 to set the metric of the CFA model. I have seen situations, in which you may want to rerun the model but to set the loading of a different indicator to unity to examine how comparable the remaining loadings are with the initial solution. Note, your model fit will be identical regardless of which indicator you set to unity. 




  
*And similarly, in which situation would you set variance of latent variable to 1 in CFA?
  



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*Variance of a latent variable is commonly set to 1 whenever you want to standardize your latent factor. This works because $\sqrt{Var} = Standard\space Deviation$ (i.e.$\sqrt{1} = 1$) 

