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I am trying to model time-elapsed data (time from event A to event B) and am stuck on deciding between standard multiple linear regression vs. Poisson regression. A number of papers published on a similar topic seem to use Poisson regression, but in my head I've always associated the Poisson distribution with "count" data. What are your thoughts?

Thanks!

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Unfortunately, linear regression is focused on cross-sectional data -- and Poisson regression usually collapses follow-up data over time and calendar period into cells of a multiway table -- thus each record in Poisson regression may represent age or calendar period, but the ensuing results (coefficients) are commonly interpreted as absolute or relative risk as a function of age group or calendar period (group).

Back to your question: if you have the difference in time between event A to event B for each object, i.e., $y =time_B-time_A$, then you could likely use $y$ as a dependent variable in linear regression, providing the residual values $e_i=y_i-\hat{y}_i$ derived from results are normally-distributed, where $\hat{y}_i$ are the predicted values of $y$.

There happens to be a niche in survival data analysis where a series of regression models allows one to regress a dependent time variable (not delta-time) directly on input predictor variables. The simplest example is called accelerated failure time (AFT) regression models, for which a host of time-based functions can be assumed (exponential, Weibull, Gompertz, logistic, etc).

If you have failed/survived (0,1) data for each object, and the time at which each object failed, you could also employ Cox proportional hazards regression -- which is a survival data analytic approach.

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  • $\begingroup$ Thank you for your help! I do, indeed, have the time difference between A and B (the value you labeled y). It sounds like the best approach for the specific problem I have is going to be using linear regression (as long as the residuals are normally-distributed. Thanks again! $\endgroup$ – Ben May 29 '16 at 1:01
  • $\begingroup$ That will work, it's simply called using "delta time" as the dependent variable. Generate a histogram of the delta-time variable to see if it's normally-distributed -- if there are large left or right tails you'll violate regression assumptions. In this case, run a Shapiro-Wilk test or Lilliefors normality test on the delta-time variable. If any of these tests have a p-value<0.05, then the delta time variable is not normally distributed -- meaning you'd have to convert the delta time variable to ranks or van der Waerden scores before using in regression. $\endgroup$ – JoleT May 29 '16 at 1:05
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If you are modelling the time between events, this can be thought of as being exponentially distributed, i.e a Poisson distribution can be thought of as being the number of events, while the exponential as the time between these events, https://en.wikipedia.org/wiki/Exponential_distribution. Based on this, $ y=time_B−time_A $ probably follows an Exponential distribution.

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