Infectious disease often occurs in small, independent outbreaks in populations with varying characteristics. Each outbreak by itself may provide too little information for accurate estimation of epidemic model parameters. Here we show that using standard stochastic epidemic models for each outbreak and allowing parameters to vary between outbreaks according to a linear predictor leads to a generalized linear model that accurately estimates parameters from many small and diverse outbreaks. By estimating initial growth rates in addition to transmission rates, we are able to characterize variation in numbers of initially susceptible individuals or contact patterns between outbreaks. With simulation, we find that the estimates are fairly robust to the data being collected at discrete intervals and imputation of about half of all infectious periods. We apply the method by fitting data from 75 norovirus outbreaks in health-care settings. Our baseline regression estimates are 0.0037 transmissions per infective-susceptible day, an initial growth rate of 0.27 transmissions per infective day, and a symptomatic period of 3.35 days. Outbreaks in long-term-care facilities had significantly higher transmission and initial growth rates than outbreaks in hospitals.