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Hi,
I currently move between MLwiN and Mplus software. I have become confused about the interpretation of level 2 regression co-efficients in MLwiN. My understanding is that with a logistic multilevel model the coefficient values for level 2 variables (contextual independent variables) should be interpreted as log odds of a one unit increase in the variable. In Mplus however the results of multilevel models do not provide odds ratios for level 2 variables on the basis that at level 2 the dependent variable is a continuous latent variable, hence the coefficient is a linear regression coefficient and the odds ratio is inappropriate. Could you please clarify the interpretation of level 2 (or higher) coefficients in MLwiN logistic regression models?

Thanks
Shane

Your interpretation of the L2 coefficients is correct IF your dependent variable is dichotomous. If the dependent variable is continuous, then logistic regression is inappropriate.

Thanks for your response. Yes, the outcome is dichotomous. This leaves the question of why a level 2 coefficient is interpreted differently in two different modeling programs that are ostensibly doing the same thing. I have been unable to get an adequate explanation for this.

Hi Shane,
Saw your question and on the list. I might suggest asking MPlus why they interpret things differently here? Let's suppose one didn't fit level 2 in the model then the model is
a straightforward logistic regression and level 2 variables are just standard fixed effects like level 1 variables. In the case of fitting random effects I guess one can write the model
with the level 2 predictors in the linear predictor along with a zero mean level 2 random effect or move them up into the mean function for the level 2 random effects (a formulation
known as hierarchical centering in the MCMC literature). These two formulations will give the same fixed effect and variance estimates but the level 2 random effects will have different values
as their mean will have changed.
As you'll see in the MlwiN documentation there are issues between cluster specific and population average estimates and so depending on which you use this will give a different odds ratio and
one has to think how to interpret the coefficients and odds ratios. The same is true for level 2 variables which will clearly be also conditional on the level 2 random effects. I personally simply
work with coefficients. Does it suggest constructing such an odds ratio in the MLwiN documentation for a level 2 predictor? If so can you pass me on the page/reference and I'll take a look.
Best wishes,
Bill.