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 Sylvana Robbers posted on Tuesday, April 15, 2008 - 8:01 am
Dear Dr. Muthen,

I work with a large sample of twins, and I am using the clustered data option (TYPE=complex) to adjust for nonindependence. I am wondering if I should use TYPE=TWOLEVEL instead. What would be the difference? Is one approach better than the other?

My general question is: In which cases do you use TYPE=COMPLEX and in which cases do you use TYPE=TWOLEVEL?

Thanks in advance.
 Linda K. Muthen posted on Tuesday, April 15, 2008 - 9:05 am
This is described in the introduction to Chapter 9 of the Mplus User's Guide.
 Sylvana Robbers posted on Wednesday, April 16, 2008 - 1:12 am
Thank you for your reaction. I had already read that chapter, but unfortunately I am still not able to decide when I should use one approach versus the other. What would you recommend in the case of twins and what would you recommend in the case of siblings and parents (so 3 family members). Or does the choice depend on your specific research question, interests and analyses (I perform GMM), and not so much on the design of the study? I read that the multilevel approach allows random intercepts and random slopes that vary across clusters. Does the cluster-approach not do that?

Thank you in advance for your time.
 Linda K. Muthen posted on Wednesday, April 16, 2008 - 6:09 am
TYPE=COMPLEX computes standard errors and a chi-square test of model fit taking into account stratification, non-independence of observations due to cluster sampling, and/or unequal probability of selection. TYPE=TWOLEVEL specifies a model for each level of the multilevel data thereby modeling the non-independence of observations due to cluster sampling. So it depends on what you want. Do you want to only correct standard errors and chi-square or do you want a model for the between level. Your research questions should guide you.
 Student 09 posted on Monday, March 02, 2009 - 7:34 am
A colleague of mine claims that type= complex is not appropriate if the aim is to examine the effect of a between-level variable on a dependent variable measured at the individual level.

According to his view, the type = complex framework does not take into account that in a twolevel data structure, there a always less observations on the higher- as compared to the lower-level of analysis. His example: If there are n1 = 1000 pupils nested in n2 = 50 schools and one would examine the effect of "school denomination" as level-2 variable on "math achievement" (measured on level 1), type = complex would not be aible to take into account that "school denomination" refers to 50 (level 2)cases, and not to 1000 pupils.

Is this right or wrong? Are there any references available explaining the logic of the Mplus robust s.e. in the type= complex framework?

Thanks a lot!
 Linda K. Muthen posted on Monday, March 02, 2009 - 10:47 am
I believe that the standard errors are correct with TYPE=COMPLEX when some variables are measured on the cluster level and some on the individual level. To be certain, however, you would need to do a Monte Carlo simulation and see if you obtain the correct standard errors.
 Student 09 posted on Monday, March 02, 2009 - 11:29 am
Dear Dr. Muthen

I like the idea of a MC simulation, but maybe it would even be sufficient if the formula for the type = complex (using MLR)
robust se's would be available, just to see whether the s.e.'s take into account the different N's of level-2 vs. level-1 variables ?

Best wishes
Jan
 Linda K. Muthen posted on Monday, March 02, 2009 - 12:24 pm
See:

Asparouhov, T. (2005). Sampling weights in latent variable modeling.
Structural Equation Modeling, 12, 411-434.

Equation (5) sums over c in the middle of the sandwich, that is, over the number of clusters. This means that independence is assumed only for the C clusters, not all N observations.
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