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. All this is not surprising, but is in line with scientific literature. The Sawtooth paper "Application of Covariates within Sawtooth Softwareâ€™s CBC/HB Program: Theory and Practical Example (2009)" also draws this conclusion.

However, if I now integrate all covariates into the model, i.e. the results of the 100-point task and the sociodemographic data, I get worse model results compared to the model results with separate covariates. Both, the RLH and the log likelihood, decrease.

My questions now are:

1) Why can the model fit decrease with increasing number of covariates? In my understanding, the influence of covariates should be zero in the worst case, but should not worsen the model fit.

2) If I now only integrate the result of the 100-point task as a covariate, how can I still check whether the socio-demographic variables have an influence on the estimation parameters? Would a structural equation model be a possibility?

I look forward to your answers.

Many greetings

Nico