I have a problem in fitting a regression model:
Y_i = a + b X_i(1) + e_i, ( i = individual)
where X_i(1) is a measurement measured at time 1.
However, what we observe is (Y_i, X_i(t_i), t_i).
In other words, X_i(1) may not always observe, depending on
whether t_i=1 or not. It is possible to build a model to relate
X_i(t_i) and t_i and then predict X_i(1) and plug into the above
regression model. But this is quite ad hoc method.
Any reference? Which topic is the above problem