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I'm trying to fit a discrete-time model in R, but I'm not sure how to do it.

I've read that you can organize the dependent variable in different rows, one for each time-observation, and the use the glm function with a logit or cloglog link. In this sense, I have three columns: ID, Event (1 or 0, in each time-obs) and Time Elapsed (since the beginning of the observation), plus the other covariates.

How do I write the code to fit the model? Which is the dependent variable? I guess I could use Event as the dependent variable, and include the Time Elapsed in the covariates. But what happens with the ID? Do I need it?

Thanks.

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  • $\begingroup$ When you say "I'm trying to fit a discrete time model" ... what model do you want to fit? (If this is for some subject, please add the self-study tag.) $\endgroup$
    – Glen_b
    Commented Apr 25, 2013 at 10:03
  • $\begingroup$ I want to fit a logit discrete-time survival model. $\endgroup$
    – Fran Villamil
    Commented Apr 25, 2013 at 10:10
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    $\begingroup$ It seems unlikely that ID is relevant, but it depends on what, exactly it represents and whether that's something you want to model. $\endgroup$
    – Glen_b
    Commented Apr 25, 2013 at 13:18

3 Answers 3

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Singer and Willett have been published a lot on this subject. I highly recommend that you read some of their papers. You also might want to get their book "Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence". Clearly one of the best textbooks in this field.

For most book chapters there is R sample code (see chapters 11ff) available that demonstrates how your data has to be structured ("person-period format") and how to analyze that kind of data. For a standard discrete-time model you do not need the ID variable and you also do not need to estimate a mixed-effects model as suggested by @ndoogan. A simple glm(event ~ time + ..., family = "binomial") works just fine. Singer and Willett also discuss many issues how to model the time variable (linear, quadratic, ...)

To cite two more references that I highly recommend:

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You can break time time into intervals and perform a multiperiode logit model as in Shumway (2001). E.g., you time intervals are $(0, 1], (1, 2], \dots$. I have implemented this in dynamichazard::static_glm in R which is directly applicable if you have initial data in a typical stop-event setup used in survival analysis. Do notice that the t-stats from the resulting model does not have the correction mentioned in Shumway (2001).

This method differs from the one @ndoogan with time dummies as you only get one common intercept in all time periods with dynamichazard::static_glm. You can, however, get a dummy for each period by calling dynamichazard::get_survival_case_weights_and_data with argument use_weights = FALSE, add the time dummy indicator yourself to the returned data.frame and then call e.g. glm.

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This is called "counting process" data. Survival package has a very nice tmerge() function. It's very useful to insert time dependent or cumulative covariates and partition follow-up time accordingly. The process is very well explained in this vignette

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