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Mplus Discussion > Multilevel Data/Complex Sample >
 Anonymous posted on Wednesday, September 21, 2005 - 7:02 am
I have a question about using weights in a multilevel SEM model. This model has two latent variables and six oberved at level-2 and the same setup at level-1 with different variables. Because of this and the data are clustered, I wanted to use multilevel SEM analysis. Also, the data come with weights. How would I incorporate the weights into my model? Is there an example in the manual that I am overlooking?

Thank you in advance for your assistance
 Linda K. Muthen posted on Wednesday, September 21, 2005 - 7:34 am
You would use the WEIGHTS option of the VARIABLE command to specify which variable contains the sampling weight information.
 Anonymous posted on Wednesday, September 21, 2005 - 2:33 pm
I'll give it a try.
 Rick Sawatzky posted on Thursday, May 24, 2007 - 9:36 am
Hi, I am using data from a national survey. A bootstrapping procedure was used to create 500 sets of sampling weights which have been provided by the owner of the database for the purpose of estimating standard errors while taking the survey design into account. Is there a way in MPlus to combine model estimates based on these sampling weights or do I have to manually run the models 500 times and then manually calculate the stardand errors based on the distributions of the obtained estimates?
 Linda K. Muthen posted on Thursday, May 24, 2007 - 10:05 am
If you have 500 data sets each with a different weight, you can use external Monte Carlo (Example 11.6, Step 2) to analyze them. You will obtain results that are the average parameter estimates, the average standard error, etc. (see Chapter 11, Monte Carlo Output. I'm not sure this is exactly how these replicate weights should be used.
 Thais Rogatko posted on Tuesday, November 11, 2008 - 10:03 am
Hi, I'm using the European Social Survey data which has two sampling weight variables (a Design weight to control for not all people being given the same chance of selesction, and a population weight to accurately represent country populations). I am testing a two-level model (country level and individual level). I'm wondering how I include both weight variables. Do I say WEIGHT = DWEIGHT PWEIGHT

Thanks for your help
 Tihomir Asparouhov posted on Tuesday, November 11, 2008 - 1:33 pm
For the twolevel model you should use only WEIGHT = DWEIGHT, however if you want to estimate population totals you should use single level models with weight the product of DWEIGHT and PWEIGHT.
 Dennis Koethemann posted on Friday, April 27, 2012 - 9:03 am
Do you know any reference explaining why we should not use pweight in a twolevel sem model?

Many thanks
 Tihomir Asparouhov posted on Friday, April 27, 2012 - 3:59 pm
You should construct your weights so that the level 2 weight is 1 / Prob of including that cluster in the sample and the level 1 weight is 1 / Prob of including the observation in the sample.

 Laura Wray-Lake posted on Monday, November 12, 2012 - 10:20 am
We are trying to estimate a latent class growth analysis using Add Health data, and we are therefore applying complex sampling weights. Importantly, we are using a subsample of the full data (i.e., only 7th graders).

We used Type=Complex TwoLevel and included wtscale=ecluster to try to accommodate for using only a portion of the full data. However, we only wish to specify a within-group model, and the results of the two-level model were uninterpretable. [All individuals were assigned to a single group even though three groups were specified.]

Can we use Type=Complex (without TwoLevel) and incorporate some other method of adjusting the weights to account for use of a subpopulation?
 Linda K. Muthen posted on Monday, November 12, 2012 - 11:02 am
You can use the SUBPOPULATION option with TYPE=COMPLEX.
 Diana Paksarian posted on Thursday, June 05, 2014 - 10:49 am
I am working on a multilevel analysis using survey data and comparing different weight scaling methods following Asparouhov (2006). I am using data in which students were selected from within schools with probabilities proportional to size. Based on my initial reading of the paper I decided that this would be classified as an invariant selection mechanism since it is the same across schools and gives meaning to the ratio of weights from students in different schools. After a few re-readings I have begun to question whether I understood the issue correctly. If someone could confirm or disconfirm that would be very helpful.
Thank you,
 Tihomir Asparouhov posted on Thursday, June 05, 2014 - 8:45 pm
Typically the above language translates to: the schools were selected with probability proportional to the size of the school, then in a second stage sampling a fixed number of students were selected at random from each of the selected schools. Assuming that you are modeling the school as your level 2 cluster unit in Mplus you should use the "bweight=1/prob selection=1/size of school" command and do not specify any weight on the within level.

The 2005 paper and the invariant and non-invariant selection deal with the case where you have within level weight so it would not apply to your situation.
 Diana Paksarian posted on Friday, June 06, 2014 - 7:56 am
Thank you for your reply. I left some information out of my previous post. The schools were selected as the SSUs in a complex survey, so the school-level weight I've been using is 1 / [p(psu selection)*p(ssu selection)]. In my case, using this as the level 2 weight and omitting level 1 weights is equivalent to the scaling methods A and B that you describe in the 2006 paper.

I am somewhat confused by your comment that the invariant v. non-invariant distinction is not relevant, since I got the impression that it affects the calculation of the level 2 weights. I apologize if I am missing something basic.
Thank you,
 Tihomir Asparouhov posted on Friday, June 06, 2014 - 8:36 am
Scaling A v.s. B and invariance of selection are relevant only when there are within level weights. If the within level sampling is random both concepts are irrelevant. The case of no within level weights is the best situation since it simplifies so much. When there are no within level sampling weights that technically doesn't even qualify as a two-level model, because there is a multivariate single level model equivalent to your two-level model - that's explained in the 2005 paper.
 TD posted on Tuesday, March 28, 2017 - 4:08 pm
Dear Mplus team,

I have two survey datasets with three years apart and no subject selected in more than one survey. The sampling methods used in these surveys (with unequal probability) are the same and I have sampling weights calculated (with respect to the population and non-response) for each survey. I want to combine the two surveys for bigger sample sizes.My question is related to the adjustment of the weights
Lets assume that w1i is the weight for subject i in the first sample and w2i is the weight for subject i in the second sample; n1 and n2 are the respective sample sizes and that N1= sum of w1i and N2 is the sum of w2i.
The fist adjustment I used is : w1i= w1i*1/2 and w2i= w2i*1/2.
The second adjustment is: w1i= w1i*N2/(N1+N2) and w2i= w2i*N2/(N1+N2).
Given that none of these adjustments necessary produce the most efficient estimates in term of variance, is it important to choose one adjustment instead of the other?
Is it better to use another adjustment?

Thank you in advance for your help.
 Tihomir Asparouhov posted on Thursday, March 30, 2017 - 10:10 am
Whatever adjustment you use should obey this simple logic. If the first sample was random (equal weights) and the second sample was random (equal weights) the combined sample is also random so the weights should be equal. The first adjustment you propose doesn't satisfy that so I would not use that. In the second adjustment you clearly have a typo and I wouldn't speculate what you meant but the weights standardization that we typically use is to standardize the weights so they add up to the sample size. Then you can combine them.
w1i= w1i*n1/N1
w2i= w2i*n2/N2
This could be equivalent to your second adjustment (depending on what n1,n2,N1,N2 are). You can also run this as a multiple group and Mplus will do that for you.
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