Comparing multiple groups in SEM R I am to compare several groups (depressed, bipolar, and controls) on many variables and I was advised to use SEM in R. I am teaching myself R at the moment but I am a bit confused. I am not sure how to proceed. According to my book, invariance is to be used when one wants to evaluate if the structure of the measurement differs across groups or if he/she has genetic data. 
Is invariance to be used even if all I want is to see differences between the different groups (the means etc.)? Do I create three models (for each group) and compare them?
Thanks a lot.
 A: Assuming you are analyzing latent variables (you won't get anywhere with invariance testing for observed variables), the semTools package (which requires lavaan) has a neat function that makes evaluating invariance testing a breeze. 
In a nutshell, you specify a lavaan measurement model to apply to all your groups (w/ group membership indicated in a vector in your data frame), and then use the measurementInvariance function. 
Example taken from the semTools reference manual:  
HW.model <-  'visual =~ x1 + x2 + x3
             textual =~ x4 + x5 + x6
             speed =~ x7 + x8 + x9' 
measurementInvariance(HW.model, data=HolzingerSwineford1939, group="school")

measurementInvariance will fit configural, weak, and strong invariance models, as well as a model constraining latent means to equivalency, for all the groups in your specified vector (e.g., those in "school"). Nested-model comparisons will automatically be calculated and outputted, so you can evaluate whether a given level of invariance is supported. In order to make valid comparisons of latent means, you need to have a model that first supports strong invariance (Little, 2013). If you save the output to an object, you can then get detailed reports and parameter estimates for any/all of the models.
Note, that if you try to use a fixed-factor method of model identification, the measurementInvariance function will incorrectly carry this constraint across all invariance models (it should be relaxed, from weak invariance, onwards), resulting in (inaccurately) worse model fit. Just use the default marker-variable method for invariance testing; it will accurately estimate model fit, and model fit is the same across methods of identification (when they are properly). 
Lastly, though you didn't ask, I highly recommend Beaujean (2014) if you are new to SEM, and specifically SEM in R with lavaan. 
References
Beaujean, A. A. (2014). Latent variable modeling using R: A step-by-step guide. New York, NY: Routledge.
Little, T. D. (2013). Longitudinal structural equation modeling. New York, NY: Guilford Press.
