I have a basic multilevel path analysis with a binary predictor of a continuous outcome. I would like to use the latent decomposition of the predictor (i.e., not declare them as within) into the within and between portions of the variance.
However, when opting for this approach, it is not entirely clear to me what the scale of the predictor now is, and by extension how to interpret the coefficients.
Is it still binary? So, regression coefficients would be interpreted as the difference between those coded 0 and those coded as 1. Or has the scale changed?
Is this the same at the within and between levels of analysis?
Finally, which is the appropriate standardized solution to request in this instance?
Each variable is decomposed as [cluster effect] and [individual variation] and those are used for the regressions on the between and within level. There is no binary predictor. The predictors are based on the underlying continuous latent variable that is dicotomized.
The standardized solutions that Mplus computes are described in http://statmodel.com/download/techappen.pdf and are computed on each level separately. If you are unsure how to use and interpret the standardization, consider standardizing your variables prior to the Mplus analysis.