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 Anne Chan  posted on Tuesday, April 17, 2012 - 12:13 pm
May I ask if the following two models are nested or not?

Model A:
i s| Y1@0 Y2@1 Y3@2 Y4@4 Y5@7;

Model B:
i s1| Y1@0 Y2@1 Y3@2 Y4@2 Y5@2;
i s2| Y1@0 Y2@0 Y3@0 Y4@2 Y5@5;

Thanks!
 Bengt O. Muthen posted on Tuesday, April 17, 2012 - 11:47 pm
The general rule is as follows. A model A is nested within a model B if model A is a special case of model B obtained by constraining model B parameters (e.g. fixing them to zero, or holding them equal). For chi-square difference testing of model A versus model B to be correct, the constraining of parameters must not be such that a parameter ends up on the border of its admissible space, such as a variance fixed at zero.

Because of this, model A is nested within model B, but you can't do chi-square difference testing because the constraints on the model B parameters are that not only the mean but also the variance of s2 is fixed at zero.

If you had considered a model C with

s2@0;

then model A could be chi-square tested against model C.
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