Testing assumptions
Message/Author
 Katrin Lintorf posted on Thursday, September 10, 2009 - 2:12 am
Hi,
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?
Katrin
 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
Hi,

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

Thanks.
 Linda K. Muthen posted on Monday, September 14, 2009 - 8:24 am
Yes.
 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
Hello!

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?

 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

http://joophox.net/publist/csda04.pdf
 Max Nachbauer posted on Wednesday, August 24, 2016 - 6:24 am

But I'm afraid I did not understand you completely. I'm just starting with Mplus. Some clarifying questions:

Q1: How exactly do I have to specify my model so that the assumptions/definitions don't have to hold?

Q2: How exactly can I save the individual residuals and cluster residuals?

Q3: How exactly can I plot individual residuals and cluster residuals?
 Bengt O. Muthen posted on Wednesday, August 24, 2016 - 5:45 pm
 Sophia Fikuart posted on Thursday, June 15, 2017 - 6:20 am
Is there in the meanwhile an option to display residuals to check for homoscedasticity?
 Bengt O. Muthen posted on Thursday, June 15, 2017 - 5:52 pm
Yes, you can plot residuals vs covariate values.
 Hon Chung Choi posted on Sunday, September 24, 2017 - 12:46 am
Hi all,

I am using Bayesian analysis to run a random slope model. I know that parameter distributions are not required to be normal, but I am wondering if raw data of variable need to be normal.

Is Bayesian robust to against deviations from the normality assumption like MLR estimator?

Tommy
 Bengt O. Muthen posted on Monday, September 25, 2017 - 5:42 pm
I don't think it hasn't been thoroughly examined to which degree Bayes is robust to non-normality and how it compares in that regards to MLR. I would expect it to be similarly robust at least with respect to the point estimates.
 Hon Chung Choi posted on Monday, September 25, 2017 - 5:51 pm
Thanks Bengt for your reply. May I also ask why would you expect Bayes is similarly robust to non-normality as MLR with respect to the point estimates?

I am wondering if I can make the claim that Bayes is robust to non-normality, just like what other people have claimed regarding MLR.
 Bengt O. Muthen posted on Tuesday, September 26, 2017 - 10:22 am
Q1: Because Bayes and ML are asymptotically the same when using non-informative priors.

The issue is if the Bayes SEs are as robust to non-normality as the MLR SEs - I am not sure.
 Max Nachbauer posted on Thursday, June 06, 2019 - 1:34 am
Dear Mplus Team

I want to run an intercept-as-outcome model (students in classes in schools). I am using type = twolevel complex and estimator = mlr. After building the l1 model, I checked model assumptions. An anova of the absolute values of the l1 residuals indicates significant differences between classes, thus variance homogenity is not given (Hox, 2010, p. 24). Further, the correlation between l1 residuals and l2 residuals is r = 0.204***, thus independence of residuals is not given.

How do I have to adapt the model in order to deal with these two violations of model assumptions?

 Bengt O. Muthen posted on Thursday, June 06, 2019 - 5:02 pm
I assume that your study of the residuals is based on a twolevel model. Variances can be allowed to vary across clusters - see new Version 8 UG examples in chapter 9. What level-2 model are you using to get the L2 residuals?
 Max Nachbauer posted on Friday, June 07, 2019 - 1:55 am
Yes, it is a twolevel model (students in classes), using "type = twolevel complex" to adjust for the school level.

In the model I tested, there are no L2 predictors. I want to check the assumptions after building the L1 model. After introducing the L2 predictors I will check again.

The syntax I used for saving the residuals is:

ANALYSIS:
TYPE = twolevel complex;
ESTIMATOR = mlr;

MODEL:
%WITHIN%
math7 ON math5 ses mig sex;
math7@0;
l1res BY math7@1;
%BETWEEN%
math7@0;
l2res BY math7@1;

SAVEDATA:
file = residuals.dat;
save = fscores;
 Tihomir Asparouhov posted on Friday, June 07, 2019 - 5:15 pm
You can use random variance with the Bayes estimator.

For the within / between correlation I would suggest this model

MODEL:
%WITHIN%
math7 ON math5 ses mig sex;
%BETWEEN%
math7 ON math5 ses;

I don't know what mig is - possibly add that as well.