Hello all,

I am facing difficulty in deciding how to go about analysis of a situation
explained as follows:

I have two variables Y (response) and X (explanatory)
(There are several other potential candidate explanatory variables, but
right now I am looking at only one variable.)

Y is binary taking values 1 and 0.
X is a continuous variable.

Both variables are observed over a equally spaced time period (say every
day).
moreover, I am suspecting that Y(t) will not only depend on the X(t), but
also X(t-1) ...( or may be till X(t-k))


so I want to construct a model (logistic) :

Y(t) (with logit link)  = alpha + beta1* X(t) + beta2*X(t-1) +.. + e

I was looking at literature and then I found these 'distributed lag' models
which are very much similar what I want to do.
But then, first of all, they are mainly meant for continuous Y ( I haven't
come across the case where they have tried to to that for binary stuff).
And secondly in those cases, intercept is not included in the model
(geometric lag or polynomial lag structure).

Since X(t) is a time series, it is showing lag dependency and hence
contributes to collinearity in the model.
Does the distributed lag structure help removing the collinearity structure?


Else how can I transform the X(t), X(t-1).. so that they will become
independent?
(May I add that deletion of a variable is not the solution for me.)

How do I go about it? Is there any way we can combine logistic regression
with distributed lag structure in explanatory variables?
It will be great if I get directions to do this stuff in R.


thanks in advanced.

-Meghana

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