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 Shane posted on Thursday, May 29, 2014 - 12:11 am

New to Mplus and enjoying it. A few (hopefully) straightforward questions:

I am running a ‘classic’ random intercepts multilevel model with individuals nested within geographic areas. The dependent variable is at the level of the individual and I am primarily interested in whether geographic area independent variables continue to explain the individual dependent variable outcome after individual independent variables are introduced to the model.

1. I have come across to Mplus from MLwin and am a bit confused by the within/between nomenclature. Does the first part of Example 9.1 in the manual approximate a ‘standard’ random intercepts multilevel model i.e the individual level independent variables should be specified as WITHIN in the VARIABLE menu and included only in the %WITHIN% in the MODEL section and the geographic level independent variables should be specified in as BETWEEN in the VARIABLE menu and included only in the %BETWEEN% in the MODEL section?

2. In reference to the estimation process: Am I correct in understanding the WITHIN and BETWEEN parts are estimated together and not separately? I.e. The introduction of a new individual level independent variable may reduce the coefficient of a geographic level independent variable already in the model.

Many thanks in advance.

 Shane posted on Thursday, May 29, 2014 - 12:13 am
Further question:

I have categorical independent variables. I have been unable to find in the manual the syntax for using the DEFINE function for creating dummy variables. I have a categorical variable for education with 4 categories. How do I specify this?

Alternatively, if I create dummy variables in SPSS, how do I specify them in an Mplus model?
e.g. Educ1 Educ2 Educ3 Educ4.

Many thanks in advance.

 Bengt O. Muthen posted on Thursday, May 29, 2014 - 2:13 pm
We ask that postings be limited to one window so we have time to answer.

1. You are understanding the specifications correctly in your question here. Within and Between correspond to Level-1 and Level-2 in the multilevel literature connected with MLwin. You can take a look at the handout and video of Topics 7 and 8 on our website, where we connect the different modeling traditions.

2. Yes, the two levels form a single model and are therefore analyzed together. And yes, the between-level coefficients can be affected by adding within-level predictors as has been discussed in the multilevel literature.

Mplus does not have an option to automatically turn a nominal variable into binary dummies. This has to be done using Define statements or outside Mplus. With a 4-category Educ variable predicting Y, say, you write

Y ON educ1 educ2 educ3;

where educ4 is the reference category.
 Shane posted on Wednesday, June 04, 2014 - 6:24 am
Hi Bengt,

Your time answering questions much appreciated.

1. Does the reduction in a BETWEEN coefficient with the introduction of a WITHIN variable have interpretable theoretical implications in a logistic multilevel model? For example, in one model (individuals nested within states) with a BETWEEN variable (eg. state level income inequality) the coefficient is 0.1. If I run a second model that introduces a WITHIN variable (eg. individual income) and the coefficient for state level income inequality reduces to 0.05. can I interpret this to mean anything?

I understand that the introduction of new variables in a logistic multilevel model leads to changes in the coefficient values through not only changes in the model, but also rescaling (Hox 2010,134)

2. If I run a multilevel logistic model Mplus will only give odds ratios at the WITHIN level. Why are level 2 coefficients interpretable as odds ratios in MLwiN, but not Mplus?

I am confused about what the BETWEEN coefficient value in Mplus then means in terms of risk i.e if outcome is dead/alive what does the BETWEEN coefficient mean in terms of increased/decreased risk for an individual? How do I convert it in to something meaningful? I have looked at the median odds ratio (as per your slides and talk), but this seems to be a method for quantifying the extent of BETWEEN group residual variance.


 Bengt O. Muthen posted on Wednesday, June 04, 2014 - 6:27 pm
1. You may want to post such a question on a general multilevel discussion list. I also recommend reading the literature on this, for instance the Snijders-Bosker or the Raudenbush-Bryk books.

2. An odds ratio refers to a relationship between two categorical variables. In a two-level model the DVs are continuous variables (random effects) so I don't see where odds ratios come into play.

On Between, there is a random intercept for the binary DV of Within. It describes the cluster environment that contributes to the individual's response. Look at how the multilevel literature interprets two-level modeling with a binary DV on Within.
 Shane posted on Tuesday, June 24, 2014 - 5:01 am
Hi Bengt,
Perhaps I am missing something in your explanation due to my lack of knowledge. But, what I simply want to know is how to interpret a between independent variable coefficient value in Mplus in a logistic multilevel model? As far as I can tell from the literature, a between independent variable coefficient is often interpreted as the log odds for a one unit increase in the variable. It is in MLwiN. What is it interpretable as in Mplus if my outcome is whether an individual is dead/alive?

Many thanks

 Linda K. Muthen posted on Tuesday, June 24, 2014 - 8:06 am
The interpretation depends on the scale of your dependent variable and the interpretation will be the same in any multilevel program. If the dependent variable is a continuous random intercept, the regression is a linear regression. If the dependent variable is a binary variable measured at the between level, it is a logistic regression.
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