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

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.
 Martijn Van Heel posted on Tuesday, December 20, 2016 - 1:30 am
Dear Dr. Muthen

I am currently looking into the random-intercept cross-lagged panel model (RICLPM) (Hamaker, Kuiper, & Grasman, 2015), which allows to separate within - and between variance.
As I read above, the difference between type= complex and type = twolevel, is that in the latter you can specify a between-person model.

Now my question is whether the cluster approach would also be appropriate in the context of RI-CLPM, since it allows to disentangle within and between person variance.

Many thanks in advance
 Bengt O. Muthen posted on Tuesday, December 20, 2016 - 6:08 pm
Yes, I think so.
 Martijn Van Heel posted on Thursday, December 22, 2016 - 3:23 am
Dear Dr. Muthen

Sorry for the follow-up question, but to be certain, it is sufficient to cluster the data without specifying a between model to capture the essence of RI-CLPM?
Especially if you're interested in the within-person level, this makes the model easier to handle.

Many thanks in advance.
 Bengt O. Muthen posted on Thursday, December 22, 2016 - 5:25 pm
Will get back to you about this before too long. Also, have you seen the new Child Development article by Berry and Willoughby on cross-lagged modeling.
 Bengt O. Muthen posted on Saturday, December 24, 2016 - 1:23 pm
Let me change my answer to say that you don't use type=twolevel or type=complex for the RI-CLPM. It should be done as a single-level, wide-format model as shown in the Hamaker et al Figure 1, right-hand-side. The model already has within- (time) and between (person)-level features, where the random effects kappa and omega for the two outcomes represent the between person variation.
 Martijn Van Heel posted on Tuesday, December 27, 2016 - 2:48 am
So if I understand correctly, the model statement in the Hamaker figure would look something like this with everything on the same level:

x1 by p1
x2 by p2
x3 by p3
y1 by q1
y2 by q2
y3 by q3

Kappa by x1@1 x2@1 x3@1
omega by y1@1 y2@1 y3@1

p2 on p1 q1
p3 on p2 q2

q3 on q2 p2
q2 on q1 p1

q1 with p1
q2 with p2
q3 with p3
 Bengt O. Muthen posted on Tuesday, December 27, 2016 - 4:57 pm
You should say

p1 by x1;
etc for the others.

and also

 Martijn Van Heel posted on Thursday, January 12, 2017 - 1:15 am
Dear Dr. Muthen

Would it be ok to construct the random intercept factor as a second-order latent variable instead of constructing it directly from the manifest variables?

Many thanks in advance.
 Bengt O. Muthen posted on Thursday, January 12, 2017 - 1:40 pm
Yes, if you set it up so that you get the same model (same number of parameters and same model fit).
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