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I am trying to run a single group path analysis with all continuous observed variables with estimator = MLR to handle non-normal and incomplete data.
In the manual pg 668 it states "MLR – maximum likelihood parameter estimates with standard errors and a chi-square test statistic (when applicable) that are robust to non-normality and non-independence of observations when used with TYPE=COMPLEX."
Which I interpreted to mean I need to specify TYPE = COMPLEX for my analysis.
However, when I specify
ESTIMATOR = MLR;
TYPE = COMPLEX;
I get the following error:
*** ERROR in VARIABLE command
TYPE=COMPLEX requires a cluster variable, a stratification variable
or replicate weights. Use the CLUSTER, STRATIFICATION or REPWEIGHTS
options to specify one of the requirements for TYPE=COMPLEX.
I only have one group, so I do not have a cluster variable, but I do want the chi-square test that is robust to non-normality.
Should I leave out the TYPE = COMPLEX in my situation, or is there something else I need to do to get the MLR estimation method to work in my case? |
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| Answer on last question: Yes. |
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| Great, thank you! |
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| shonnslc posted on Monday, June 11, 2018 - 11:37 pm
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Dear Muthen,
Does type=complex with estimator = MLR work fine for SEM model with nested data structure (but number of clusters = 17)?
If no, what would be my option? Thanks. |
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| 17 is a bit low. The alternative is to either use 16 dummy covariates or use Bayes with weakly informative priors. |
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| shonnslc posted on Tuesday, June 12, 2018 - 7:15 pm
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Thank you, Dr. Muthen. Since I am not quite familiar with the Bayes approach. I am wondering if you could give me some directions on 16 dummy covariates:
1. Which group should be the reference category since there are 17?
2. After creating 17 dummy covariates, how can I bring them into my model since they are not related to any structural relationship in my model.
Thanks a lot. |
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1. Your choice - but the largest is common.
2. You regress your DVs (observed or latent) on them, thereby letting them influence their means. |
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| shonnslc posted on Wednesday, June 13, 2018 - 5:37 pm
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Thank you, Dr. Muthen.
It's clear to me now. I am wondering if you, by any chance, know of any reference for justifying creating covariates to adjust for nested data structure for SEM when MLR is not an option? |
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| I think there is a chapter related to this in the classic Complex Survey data book edited by Skinner, Holt and Smith (a Wiley book). |
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| shonnslc posted on Thursday, June 14, 2018 - 11:58 am
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Dear Dr. Muthen,
Thank you so much! I am wondering if this covariate approach can also be implemented in CFA (i.e., bring 16 dummy covariates into CFA model and regress latent factors on these dummy covariates). Is this the right way to account for nesting data structure for CFA when MLR/Type = Complex is not an option?
Also, does this covariate approach allow us to do model comparison as usual in CFA (e.g., one-factor model vs two-factor model with covarites staying the same).
Thank you again. Much appreciated!!! |
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Let me clarify first. You are misinterpreting what Bengt said above. It is not true that "MLR/Type = Complex is not an option." On the contrary, it is your best option, given your description and in particular if you are not interested in modeling the differences across the 17 groups, but just want to account for the nested sampling structure.
Here is how you want to read Bengt's warning: due to small number of clusters you may experience issues with convergence (less likely) or large standard errors (more likely). We can't predict if this will happen or not however. The answer is entirely in the data. More specifically - if there are large differences between the groups the standard errors will become large and will inhibit your ability to make good inference. If the differences across the groups are not that large (are not dominating) you will experience no such problems.
It is a good idea to compare the ML estimates of the standard errors and the MLR complex standard errors to see how much they change. If the ratio on average is more than 2 or 3 you may be better off modeling the differences across groups - through dummy variables, multiple group analysis, even two-level modeling or Bayes analysis.
This is well studied in the complex survey literature under the term "design effect".
To understand the benefit of modeling the differences across groups compare the loading standard errors of the following two Mplus runs (the first is equivalent to type=complex the second is type=twolevel)
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MONTECARLO: NAMES ARE y1-y3;
NOBS = 1700;
NREP = 100;
NCSIZES = 1;
CSIZES = 17(100);
ANALYSIS: TYPE IS TWOLEVEL;
MODEL MONTECARLO:
%WITHIN%
E BY Y1-Y3*0.8;
Y1-Y3*0.36;
E@1;
%BETWEEN%
y1-y3*1;
MODEL:
%WITHIN%
E BY Y1-Y3*0.8;
Y1-Y3*0.36;
E@1;
%BETWEEN%
y1-y3@0;
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MONTECARLO: NAMES ARE y1-y3;
NOBS = 1700;
NREP = 100;
NCSIZES = 1;
CSIZES = 17(100);
ANALYSIS: TYPE IS TWOLEVEL;
MODEL MONTECARLO:
%WITHIN%
E BY Y1-Y3*0.8;
Y1-Y3*0.36;
E@1;
%BETWEEN%
y1-y3*1;
MODEL:
%WITHIN%
E BY Y1-Y3*0.8;
Y1-Y3*0.36;
E@1;
%BETWEEN%
y1-y3*1; |
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