Scale of W and B decomposed binary pr... PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
 Tay Jeong posted on Monday, August 24, 2020 - 11:56 am
Dear Mplus team,

I have a categorical predictor in a simple two-level regression, in which the predictor variable is not declared as within or between and is therefore decomposed into W and B parts. I am using Bayes with v.8.4. The binary predictor is declared as CATEGORICAL.

I've read how a binary predictor is decomposed through a 2lv probit regression in Asparouhov and Muthen (2018). In my understanding, this effectively amounts to a W and B decomposition of the underlying continuous latent variable, of which variance (and sd) is fixed to 1.

So the coefficients for the binary variable in the output indicate the expected change in the outcome following a 1 sd increase in the underlying continuous variable.

If this right, I have 2 extra questions:

Q1: 1 is the standard deviation of the (latent) Xij, but it is most likely not the sd of Xj (group mean) or Xi (within-group deviation score). So are the coefficients for the between- and within- variation of Xij represented in terms of the sd of Xij?

Q2: I tried having a binary outcome together with a binary predictor, declaring both as CATEGORICAL. The model ran fine. Just to check: Is decomposition of binary predictors supported with categorical outcomes, and is the interpretation of the coefficients analogous to the case with a cont. outcome, except that the outcome is now probit(p(Y=1))?

Thank you
 Tihomir Asparouhov posted on Monday, August 24, 2020 - 4:05 pm
I think you have the correct understanding and interpretation. The model you are describing is similar to (66-72)
 Tay Jeong posted on Monday, August 24, 2020 - 4:47 pm
Thank you Dr.Asparouhov for the reply!
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