15
If you're trying to generate data from logistic regression's assumed data generating mechanism, your code does not do that.
Logistic regression's data generating mechanism looks like
$$ \eta = X\beta$$
$$ p = \dfrac{1}{1+e^{-\eta}}$$
$$ y \sim \operatorname{Binomial}(p, n) $$
What it looks like you're trying to do is create a linear regression in the log ...
4
Yes.
$$\begin{align}y_i & =\alpha+(\beta_1+\beta_2)x_1+\beta_2x_2+\epsilon_i\\
\\
& = \alpha+\beta_1x_1+\beta_2x_1+\beta_2x_2+\epsilon_i\\
\\
& =\alpha+\beta_1x_1+\beta_2(x_1+x_2)+\epsilon_i\end{align}$$
2
For the coefficients and standard errors (and $p$-values) to be identical you would need to have interactions between geneder and all the other variables, and also have separate values of the overdispersion parameter by gender
Your interaction model has a separate group coefficient for male and female but has the same coefficients across gender for age, ...
Only top voted, non community-wiki answers of a minimum length are eligible
