Timeline for In a Poisson model, what is the difference between using time as a covariate or an offset?
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| Feb 19, 2019 at 12:18 | comment | added | gung - Reinstate Monica | @tatami, if you are going to use time as a covariate (rather than an offset), you don't have to take the log of time. However, if you want to compare your result to an offset, you would need to use the log to make them comparable. | |
| Feb 19, 2019 at 7:21 | comment | added | tatami | I know that @Bakaburg had asked about the use of log when time is covariate rather than offset, but I feel that it wasn't really answered. So why do we still need to log? | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Apr 20, 2016 at 0:40 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
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| Oct 9, 2015 at 10:06 | vote | accept | Bakaburg | ||
| Oct 9, 2015 at 7:43 | comment | added | gung - Reinstate Monica | @Bakaburg, time is probably correlated with them. That isn't any different from any other regression modeling situation. I don't see the problem here. You are either interested in modeling average rates or you aren't. | |
| Oct 9, 2015 at 7:33 | comment | added | Bakaburg | The problem is that changing the way Time is treated (offset or coviariate) influences also the estimates of the other coviariates. | |
| Oct 8, 2015 at 1:07 | comment | added | gung - Reinstate Monica | @Bakaburg, I'm not sure about using Poisson regression for continuous data. R at least will complain if you do that. Why not use a Gamma GLM w/ a log link? If the only point is you want the log link & the zero bound, that seems like it should do it for you. As for when to use an offset, again, it depends on the question you are asking. If you want to model the average rate (whether or not the rate at any point in the covariate space is always equal to the marginal mean), then use an offset. If you want to test if the rates are changing over the relevant variable, include it as a covariate. | |
| Oct 7, 2015 at 15:27 | comment | added | Bakaburg | Ok about why time need to be log. Still I haven't understood in which case one should use an offset instead of modelling the time variable. About not integer values with poisson, I'm often in the situation in which I have to model a zero bound continuous dependent variable. Initially I used to model them using log linear regressions, but this would give me problems with in the presence of zeros. Then I found that left alone standard errors, poisson model are ok to get estimates even without counts. I usually then use bootstrap for the intervals. ref: stats.stackexchange.com/a/38588/6479 | |
| Oct 4, 2015 at 14:09 | comment | added | gung - Reinstate Monica | The Poisson dist is for integers only; you should not enter a fraction on the LHS. Not using the log transform means modeling rates of events per exponentially unit time, which will probably never be sensible in the real world. | |
| Oct 4, 2015 at 11:40 | comment | added | Bakaburg | Therefore why one should assume that the relationship between time and events is linear and growing? Wouldn't be better to estimate the shape of such relationship in every case? I have two more questions: 1. what would it mean to use not log transformed time as covariate instead? 2. (maybe I should edit the question or ask a new one for this) I read that poisson models can actually be used with not integer y too. Thus I could write in R: glm(I(y/time) ~ cov.1 + ... + cov.n, poisson) and have the same results that I have using offset(log(time)). I tried this but I get different coefficients. | |
| Oct 4, 2015 at 11:30 | comment | added | Bakaburg | Thank you very much Gung for your comprehensive answer! Please tell me if I understood well. If we use time as an offset we assume a linear positive relationship between time and events whose angular coefficient is given by the other predictors exponentiated $y = {\rm time}*\exp(\sum_{1}^{p}\beta_pX_p + {\rm const})$. Instead if we use log time as covariate we estimate the exponential effect of time on events, which can be either positive o negative $y = {\rm time}^{\beta_{{\rm time}}}*\exp(\sum_{1}^{p}\beta_pX_p + {\rm const})$. (cont...) | |
| Oct 3, 2015 at 21:03 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
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| Oct 3, 2015 at 20:50 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
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| Oct 3, 2015 at 20:43 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
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| Oct 3, 2015 at 20:36 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
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| Oct 3, 2015 at 20:20 | history | answered | gung - Reinstate Monica | CC BY-SA 3.0 |