Hi! I'm building a SEM with PISA data, which uses a two-step sampling procedure, where 30 students from each school are selected.
I wish to use the replicate weights in the dataset, combined with using the school ID as clusters, but I get different kind of error messages. When I use BRR, I get an error message which states that the Replicate Weights already contain information about clustering, and when I use Fay's modification (used by PISA), it automatically assumes two strata, and I'm not allowed to set School ID as clusters/strata.
It is possible to solve it. The error message is correct. When you use replicate weights the standard errors are entirely based on the replicate weights and no additional information is needed. The replicate weights are designed to yield correct result. They are very specific to the survey design and should only be used as instructed by the survey admin, i.e., if Fay is the method that they want you to use it would be incorrect to use another method because the replicate weights are constructed to work only with that method. So, indeed remove the instructions for cluster/strata from the input file and specify the replicate weights as Fay.
if we are not able to use TYPE=COMPLEX TWOLEVEL, we will not get a random intercept model with BRR replications.
Using BRR, I think, limits our ability to fit various two level models and using many other special features in Mplus. What are the drawbacks not to use replicated weights (BRR, FAY, etc.)? are sampling weights (both at level 1 and level 2) not enough?
To use type=complex twolevel you need a three level setup - two clustering variables nested above each other. The higher level clustering should be the PSU, the lower level clustering should be the level where you model the random intercept.
If you have just one clustering variable, i.e., the PSU you should either use type=complex or type=twolevel depending on what your goal is.
The reason replicate weights are generally created is to summarize the complex sampling, if you have full information about the complex sampling you don't need the replicate weights.
I am using data with two stage complex sampling. There are exactly 2 PSUs (higher level is school, and lower cluster is teacher, same as you wrote). The data set provides BRR, final teacher and school weights. My goal is to fit a two-level random intercept and a two-level random slope models (with Level 1 and Level 2 predictors). I would like (need) to use BRR and conditional teacher weights for the analysis. However, Mplus does not allow me to use BRR with random intercept and slope models in TYPE=COMPLEX TWOLEVEL.
by 'full information about sampling' if you mean sampling weights, yes I have them. Recently, papers on LSA (e.g., Rutkowski et al., 2010) suggest using both conditional weights and BRR at the same time when fitting two-level models. But I am not sure if I can use TYPE=COMPLEX RANDOM to conduct the analysis I need.
Mplus doesn't support BRR for twolevel yet. You have three options. One you can use TYPE=COMPLEX TWOLEVEL with the teacher between weight and cluster=school teacher. This should give you correct SE. The second option is to convert the model "long to wide" then use BRR. The third option is to use batch model run of Mplus to get the estimate for each BRR weight and compute the SE in excel using the BRR formula.