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.
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.
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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
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.
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.
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?
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.