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st: lrtest again for clarification
Oops. I thought the opposite way. The smaller, the better, hence A is better.
The model is shown is just an example - the results are different from the example.
However, the concept is the same. Why G turned into H I is because G was incoporated into
a composite variable H and a new variable I was added. In some sense it may or may not be
nested, but I'd use the AIC / BIC as you recommended.