Finding if the coefficients are significantly different from each other I have a dataset which is segmented into two independent groups. I used multinomial logistic regression to estimate the coefficients corresponding to explanatory variables in both the groups. The independent variables are the same for both groups and are supposed to effect the response variable differently for segmented groups.
I wanted to find if the coefficient for the independent variables are significantly different or not between the groups.
Is it possible to use a Z-test?
$$Z=\dfrac{b_1-b_0}{\sqrt{SE_{b_1}^2-SE_{b_2}^2}}$$
Is this applicable only for linear regressions or also for logistic regressions?
Is there any other way to calculate the statistical difference, when we have coefficient and t-stat for the variables for both segmented groups?
 A: You can use a Z-test, which, as far as I am aware, applies to any kind of regression that gives you standard errors. Make sure you get the right equation, though.
$Var(\beta_1 - \beta_0) = Var(\beta_1) + Var(\beta_0) = SE(\beta_1)^2 + SE(\beta_0)^2$
(as long as β1 and β0 are independent). So
$SE(\beta_1 - \beta_0) = \sqrt{SE(\beta_1)^2 + SE(\beta_0)^2}$
and
$Z = \frac{\beta_1 - \beta_0}{\sqrt{SE(\beta_1)^2 + SE(\beta_0)^2}}$
Technically the coefficients are distributed in a t-distribution rather than a normal distribution, so this is not a perfect estimate. But if you have many more observations than coefficients, the t-distributions will converge to normal distributions, and this will number will be accurate.
You could also put both groups in the same regression and interact a group dummy variable with your independent variable:
$Y = \beta_0 + \beta_1 \times indep\_var + \beta_2 \times group\_dummy \times indep\_var$
Then you can test whether β2 is significant, which will also answer your question.
