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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! 


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 chisquare 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 chisquare 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 chisquare tested against model C. 

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