Beta values change with different reference groups - Glm regression - log link & gamma distribution

[am12scorp]

I was conducting GLM regression with log link and gamma distribution for modeling costs.  I see that beta value for intercept changes with change in the reference groups for the covariates.  Why does this happen?  Can someone explain this?

[Reeza]

Because the estimates are in reference to a standard, your reference group, and the estimate for the reference level itself is incorporated into the intercept.

If you change that reference point (the reference group) then the parameters will change to reflect the actual difference and the intercept will as well. This is correct and the expected behaviour. Your predicted values should not change.