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Mplus Discussion > Multilevel Data/Complex Sample >
 Katrin Lintorf posted on Thursday, September 10, 2009 - 2:12 am
I am running a TYPE = TWOLEVEL COMPLEX RANDOM analysis and I am looking for an output that examines the assumptions (as described in Snijders & Bosker, 2004, p. 121: normal distribution and homoscedasticity of residuals etc.). Is there any possibility in Mplus to ensure that assumptions are met?
Thank you for any advice
 Bengt O. Muthen posted on Thursday, September 10, 2009 - 1:08 pm
The MLR estimator is robust against deviations from the normality assumption. There is currently not an option to display residuals to check for homoscedasticity.
 Moh Yin Chang posted on Monday, September 14, 2009 - 7:24 am

If I use the MODEL TEST: command in mplus for complex survey data, is the wald test adjusted for the complex sampling design?

 Linda K. Muthen posted on Monday, September 14, 2009 - 8:24 am
 Moh Yin Chang posted on Monday, September 14, 2009 - 8:54 am
Can you please provide me the statistical reference for citation?
 Bengt O. Muthen posted on Monday, September 14, 2009 - 10:59 am
The Wald test uses as a "weight matrix" which is whatever covariance matrix is computed for the estimated parameters (see Tech3). With Type=Complex, the complex survey features are taken into account in Tech3. How that is done is shown in Asparouhov (2005) - the SEM article.

We don't have a reference for this aspect of Wald testing, mainly because this is using "first principles" of statistics. Perhaps you can refer to the article above and the UG.
 Max Nachbauer posted on Tuesday, August 23, 2016 - 9:20 am

The most central assumptions of the hierarchical linear model are (Raudenbush/Bryk 2002, Snijders/Bosker 2012):
- A1: Individual residuals have a normal distribution within each cluster
- A2: Individual residuals have the mean 0 within each cluster
- A3: Individual residuals have the same variance in all clusters
- A4: Cluster residuals have a multivariate normal distribution
- A5: Cluster residuals have the mean 0
- A6: Cluster residuals and individual residuals are independent

Q1: Using Mplus 7.11 with TYPE=TWOLEVEL RANDOM, ESTIMATOR=MLR and FIML, which of the assumptions A1-A6 have to be met?

Q2: Which of the assumptions, that have to be met, can be checked with Mplus 7.11 and how?

Thank you in advance!
 Tihomir Asparouhov posted on Tuesday, August 23, 2016 - 2:02 pm
All of these assumptions don't need to hold in Mplus and you can specify models and estimate models where such specifications are modeled in a non-standard way. The standard model uses A1-A6 (Technically speaking A2 and A5 are not assumptions - these are definitions).

You can use LRT, use residual plots or save the residuals and test them separately.
 Tihomir Asparouhov posted on Tuesday, August 23, 2016 - 2:52 pm
You should take a look at this article

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