Message/Author
 Lindsey M. King posted on Monday, March 09, 2015 - 1:39 pm
I am trying to fit a multilevel random-intercept mediation model with Bayes estimates (due to small between-level sample size), non-informative priors, and an ordered dependent variable. I cannot find information about whether the model uses a probit or logit link function by default.

After reading the Asparouhov and Muthen (2010, version 3) paper on the technical implementation of Bayesian analysis, I get the impression it estimates an ordered probit model (I concluded this because the Gibbs sampling algorithm is based on a probability distribution). Have I interpreted this correctly?

Also, I would like to calculate predicted probabilities based on values of the between-level predictor. I think it can be done using MODEL CONSTRAINT, but I'm not quite sure how to do it. Is it possible using the following model?

USEVARIABLES = dv mediator lvl2iv iv country;
CATEGORICAL = dv ;
WITHIN = iv ;
BETWEEN = lvl2iv ;
CLUSTER = country ;

ANALYSIS:
TYPE = TWOLEVEL ;
ESTIMATOR = BAYES ;

MODEL:
%WITHIN%
dv ON mediator iv ;
mediator ON iv ;
%BETWEEN%
mediator ON lvl2iv (x) ;
dv ON mediator (m) ;
dv ON lvl2iv ;

MODEL CONSTRAINT:
NEW(indb) ;
indb=x*m ;
 Tihomir Asparouhov posted on Tuesday, March 10, 2015 - 1:45 pm

Indb - is the indirect effect.

What this model gives you is

P(DV | mediator_within, IV, dv_between)

If you want to be able to marginalize this down to

P(DV | lvl2iv )

you will need to include a model for IV (or condition on that as well)

Such marginalizations are automated for single level model. For two level models you will need to follow the logic of Section 6 of