Centering and Intercepts in Mplus PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
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 Paraskevas Petrou posted on Wednesday, February 02, 2011 - 2:27 pm
Dear Mplus users,

In the multilevel SEM model that I am testing I am encountering the following issues:

1. Is there any default centering method for the twolevel analysis in v6 of Mplus or do I still need to define the centering myself?

2. In my model, I have decided not to define within-level variables (but only between-level) because this is the only way I can repeat all my within-level paths at both levels. I need the within-level part of the model to be tested at both levels. This means I cannot use groupmean centering for my within-level predictors as Mplus only permits that for within-level variables, which I have not specified. Is this a problem? Should I use grandmean centering for all predictors?

3. To plot one interaction that is part of my model, I need the intercept of my dependent variable. The answering scale of this variable is 1-5, but the unstandardized intercept in the output is 25.86 and the standardized one is 50.15. How is that possible? I look at the "Intercepts" column in the between part of the output.

Thank you in advance.

Kind regards,
Paris Petrou
 Bengt O. Muthen posted on Wednesday, February 02, 2011 - 11:04 pm
1. No centering is the default.

2. See top of page 243 of the Version 6 User's Guide, showing that when an x variable has both a latent within and a latent between-level part, there is an implicit latent group-mean centering of the latent within-level covariate.

3. The intercept is not the mean of the variable.
 Paraskevas Petrou posted on Thursday, February 03, 2011 - 6:14 am
Thank you very much Bengt.

2. Does that mean that I can leave all my within-level variables (which repeat at both levels) uncentered and only apply centering to my between-level variables (which appear only at the between-level)? Or leave all my variables uncentered?

3. I need to report my interaction plot and the y axis will have a range between 25 and 35. That happens because of the high interecept. I wonder if that will look strange for the reader, because the y variable ranges through a scale of 1-5.

Kind regards,
Paris Petrou
 Bengt O. Muthen posted on Thursday, February 03, 2011 - 5:56 pm
2) You can leave all your covariates uncentered, but you can also center the between-level covariates.

3) The estimated mean for your DV should not be 25-35 if your DV has a sample mean of 1-5. Either the model is set up wrong or is misinterpreted.
 Paraskevas Petrou posted on Friday, February 04, 2011 - 6:59 am
3. By "estimated mean" do you mean intercept? Can I trust an unstandardized estimate of 19.09 for the intercept of a DV which ranges through a scale of 1-5? When I ask for sampstat this DV has a mean of 0.00 at the within level and 2.02 at the between level.

Thank you
Paris Petrou
 Bengt O. Muthen posted on Friday, February 04, 2011 - 9:16 pm
No, the intercept is not the estimated mean. Take for example a regression of y on x:

y= a + b*x + e

so that the mean of y, E(y), is

E(y) = a + b E(x),

where a is the intercept and b is the slope. Mplus estimates a and b, not E(y), but you can express and compute E(y) using a, b, and the sample mean of x.

If this doesn't clear it up, please send input, output, data, and license number to support@statmodel.com.
 Paraskevas Petrou posted on Monday, February 07, 2011 - 8:40 am
I managed to change my model in a way that I don't get these big intercepts any more. But now I get this warning:

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE
CONDITION NUMBER IS 0.422D-34. PROBLEM INVOLVING PARAMETER 1.

Parameter 1 is the alpha for one of my within-level predictors. One way to stop getting this warning is not centering my predictors, which I do not find a good idea since this is multilevel analysis.

I will send my data to the support email, thank you.

Paris
 Linda K. Muthen posted on Tuesday, February 08, 2011 - 5:37 pm
Please send your output and license number to support@statmodel.com.
 Paraskevas Petrou posted on Friday, March 18, 2011 - 12:23 pm
Dear Linda,

Returning to point 3 of my first post (see above) I need to find some parameters in my multilevel SEM model (TECH1)and then get some values of the covariance matrix (TECH3) and use them so as to plot a significant interaction effect.

In particular, I need the parameters that correspond to the intercept of one dependent variable of my model. Is this the ALPHA? In the Mplus guide you say that ALPHA stands for means and/or intercept of the latent variables. But I want the parameter for intercept (and not mean). I am puzzled because in my output I get ALPHAs also for variables which are only treated as predictors and not outcomes (but are correlated with other variables at the between level).

Kind regards,
Paris Petrou
 Linda K. Muthen posted on Friday, March 18, 2011 - 12:50 pm
All mean and intercept parameters are in either alpha or nu. It does not matter which matrix they are in.
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