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I want to fit a structural equation model (SEM) on using the lavaan package in R.

Some of the most important variables in my model are count data, e.g. abundance of different species, and thus do not follow a normal distribution.

I tried to transform some of my variables to obtain normal distributed data but this results in an output that is uninterpretable: positive relationships become negative, effect sizes are meaning less.

I have added a figure which basically displays my problem: all the species variables are the count data and these species affect the other species through predation. habitat and climate are my latent variables. I am not really interested in these latent variables, so a solution without these would also be a solution.

enter image description here

Question(s):

Is there a way to model this network assuming a negative binomial or Poisson distribution for my species variables?

Stata has something called Generalized SEM, but this does not return standardized estimates and it doesn't return any measure to validate the model. I really need standardized estimates, because I am most interested in the indirect effect of Species C on Species A via Species B.

Are there other techniques to model these kind of networks?

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    $\begingroup$ Mplus allows count variables (including Poisson, zero-inflated Poisson and negative binomial) to be modeled. $\endgroup$
    – Maxim.K
    Nov 15, 2014 at 17:50
  • $\begingroup$ @Maxim.K Thanks for the suggestion. Do you know if Mplus gives standardized estimates when using these alternative distributions? $\endgroup$
    – Robbie
    Nov 16, 2014 at 23:52
  • $\begingroup$ I can't imagine why not. $\endgroup$
    – Maxim.K
    Nov 17, 2014 at 9:38
  • $\begingroup$ @Maxim.K I had a look at Mplus. It seems that it is not possible to get standardized estimates (st.est.) when having count variables that also function as independent variables. I am able to get st.est. when I only treat species A as count data but not if I do this for any of the other species. I guess it has to do with the fact that standardizing data to a mean of 0 and st.dev of 1 makes no sense when variables are not following a more or less Gaussian distribution. $\endgroup$
    – Robbie
    Nov 22, 2014 at 7:30

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