How can we compare SEM models by using delta ChiSq probabilities and the assessment of direct and indirect effects.
I suppose with SEM you are referring to Structural Equation Models.
I further assume you already have formalized your theory in a SEM, let's call it model A. In order to test your theory, you might have derived an alternative model representing your null hypothesis, let's call it model B. If model B can be derived from model A by adding linear restrictions on the parameters in model A, they are said to be nested. Particularly, this entails setting parameters in the model to zero or setting parameters in the model to be the same. If H0 is true, one can show that the difference between their negative two log-likelihoods is chi-square distributed. Thus, you can use classic hypothesis testing logic to reject model B if the associated p value is significant.
In your particular case, you might want to create model B such that it sets a direct effect to zero. If the nested model comparison yields a significant P value, you reject the hypothesis of no direct effect.
Thanks for your answer. I want to clear out one more thing. first I make the model as based on theory then shall i move on towards complex models based on theoritical simple model. Is that appropriate?
Usually, i see the models create from complex to simple, but in my case if it is otherway round, can we say is this nested models?
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