I am trying to run a fixed parameter model, a random parameter model and a latent class model with the same dataset. My dependent variable is whether or not an individual in wearing a seat belt. And my independent variables include driver's age, gender, etc. Most of the results seem fine. However, when I compare the marginal effects between the three different models, the fixed and random parameter models' marginal effect estimates are at about 10 times higher than that in the latent class model. Expectedly, the scale is also 10 times smaller in the latent class model than the random parameter model. Why is this happening? Can you please explain the interpretation of the 'scale factor'? What does this exactly mean? And what is its relationship with the marginal effects? As I understand, the marginal effects estimates how a dependent variable changes when an independent variable increases or decreases. In that case, I would expect the marginal effects for each independent variable to be somewhat close among different models. Unfortunately, this is not happening and the marginal effect estimates and scale factor are smaller by almost a factor of 10 in the latent class models compared to the fixed and random parameter models. Please let me know any ideas. Thank you!
Are you sure that you compare the marginal effects in all three models ? Are you not currently comparing the coefficients ?
In linear models, the coefficients give you the marginal effect. This is no longer in the non-linear model (as your latent class model). In this latter case, some additional computations have to be performed to get the marginal effects.