I want to fit a discrete hazard model and incorporate time-interactions of multiple terms. Since in the basic model, onle the intercept is time dependent, how do the interpretation and the fitting rpocedure change?
So assume, that the deta-manipulation as outligned in Discrete-Time Event History (Survival) Model in R have been accomplished.
The baseline model is then:
$P(T=t|T \geqslant t,X)=\frac{1}{1+exp(-\alpha_t-\beta X_i)}$
The illustrate this in R, i would type:
reg_surv=glm(Y~ -1 +time+X1+ X2,data=data_long,family=binomial(link='logit'))
Now incorporate time interactions, such that the model is given by:
$P(T=t|T \geqslant t,X)=\frac{1}{1+exp(-\alpha_t-[\sum_{k=1}^{T} 1(k=t) \beta_k X_i])}$
In R this would be accompliced by:
reg_surv=glm(Y~ -1 +time+time:X1+ time:X2,data=data_long,family=binomial(link='logit'))
So the question is very open but what changes in the interpretation of the model?
Especially, can I use estimation as outligned above?
And how does the interaction influence the "baseline" hazard? - Is it allready only $\frac{1}{1+exp(-\alpha_t)}$ for timte $t$ ?
