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? Thank you for any advice Katrin
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.
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?
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.
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.
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?
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?