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Link function in Bayes estimation |
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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 ; |
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Bayes estimator uses probit link. 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 http://statmodel.com/download/causalmediation.pdf It is not hard and you can get that via model constraints. |
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