Poisson or Linear Regression for Time Data 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!
 A: 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.      
A: 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.
