I'm currently estimating several Hierarchical Bayes (HB) Models as an evaluation of my CBC.
On the one hand I have covariates which improve the model result strongly if only these covariates are used as in input. For example, at the beginning of the survey I let the respondents allocate 100 points to the different attributes. On the other hand, I have covariates that only marginally improve the model result, such as sociodemographic data. However, these effects, although small in magnitude, are significant.
However, if I now integrate all covariates into the model, both the RLH and the log likelihood decrease. All this is not surprising, but is in line with scientific literature. The Sawtooth paper "Application of Covariates within Sawtooth Software’s CBC/HB Program: Theory and Practical Example (2009)" also draws this conclusion.
But now I ask myself how I can still check the sociodemographic variables and their influence?
I suggest to estimate the model without sociodemographic covariates and use the HB model output again for a structural equation model. Is that methodologically okay? Or how would you proceed?
I look forward to your answers.