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I have collected data points from 216 individuals. A1, A2, A3 are three performance measures to be combined into a latent variable lA. I have three observations on this measure for each individual. U is another measure for which I have three observations for each individual, and these observations are paired with A1-3.W is a measure for which I have only one observation for each individual (something like an IQ score).

Now, I would like to fit the following model: enter image description here

As I understand, I have a within-subjects part (A1-3 loading on lA, and U predicting lA) and a between-subjects part (W predicting U and lA), so I should fit a model that takes into account the nested structure of the data. In Mplus, this could be done two ways:

 VARIABLES:
 ...
    cluster = SUBJECT;

 ANALYSIS:
    type = complex;

 MODEL:
    lA by A1 A2 A3;
    lA on U W;
    U  on W;

..or..

 VARIABLES:
  ...
   cluster = SUBJECT;
   between  = W;

 ANALYSIS:
   type = twolevel;

 MODEL:
   %within%
   lA by A1 A2 A3;
   lA on U;

   %between%
   lAb by A1 A2 A3;
   lAb on W;
   U   on W;

When I run these two analyses, I receive quantitatively quite different results. For example, the path from W to lA is 0.154 (standardized) in the first but 0.589 (standardized) in the second analysis. Generally, the results of the second analysis seem odd to me.

Btw, the difference between the two analyses is very small, if I do not model a latent variable lA but, instead, combine the three indicators into a composite variable.

Why do these models differ so much?

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Here are a couple of blog entries by Andrew Gelman about this issue: http://andrewgelman.com/2007/11/28/clustered_stand/ , http://andrewgelman.com/2009/08/21/clustered_stand_1/.

If you add complex (and don't have weights) then all that Mplus will do is correct your standard errors - the estimates should stay the same. If you use multilevel models, you model the random effects and this can change things (and did, in your example).

Also, I would not compare the standardized estimates, as these will change with the variances (which can be a bit weird in multilevel models) but compare the unstandardized estimates.

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