Browsing by Subject "Negative binomial model"
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Item Count models : with applications to price plans in mobile telecommunication industry(2010-05) Kim, Yeolib; Greenberg, Betsy S.; Peterson, Robert A.This research assesses the performance of over-dispersed Poisson regression model and negative binomial model with count data. It examines the association between price plan features of mobile phone services and the number of people who adopt the plan. Mobile service data is used to estimate the model with a sample of one million customers running from February 2006 to September 2009. Under three main categories, customer type, age, and handset price, we run the model based on price plan features. Estimates are derived from the maximum likelihood estimation (MLE) method. Root mean squared error (RMSE) is used to observe the statistical fits of all the regression models. Then, we construct four estimation and holdout samples, leaving out one, three, six, and twelve months. The estimation constitutes the in-sample (IS) and the holdout represents the out-sample (OS). By estimating the IS, we predict the OS. Root mean squared error of prediction (RMSEP) is checked to see how accurate the prediction is. Results generally suggest that academic year start (AYS), seasonality, duration of months since launch of price plan (DMLP), basic fees, rate with no discount (RND), free call minutes (FCM), free data (FD), free text messaging (FTM), free perk rating (FPR), and handset support all show significant effect. The significance occurs depending on the segment. The RMSE and RMSEP show that the over-dispersed Poisson model outperforms the negative binomial model. Further implications and limitations of the results are discussed.Item Examining the Generalized Waring Model for the Analysis of Traffic Crashes(2013-05-03) Peng, YichuanAs one of the major data analysis methods, statistical models play an important role in traffic safety analysis. A common situation associated with crash data is the phenomenon known as overdispersion which has been discussed and investigated frequently in recent years. As such, researchers have proposed several models, such as the Poisson Gamma (PG) or Negative Binomial (NB), the Poisson-lognormal, or the Poisson-Weibull, to handle the overdispersion. Unfortunately, very few models have been proposed for specifically analyzing the sources of dispersions in the data. Better understanding of sources of variation and overdispersion could help in managing safety, such as establishing relationships and applying appropriate treatments or countermeasures, more efficiently. Given the limitations of existing models for exploring the source of overdispersion of crash data, this research examined a new model function that could be applied to explore sources of extra variability through the use of the Generalized Waring (GW) models. This model, which was recently introduced by statisticians, divides the observed variability into three components: randomness, internal differences between road segments or intersections, and the variances caused by other external factors that have not been included as covariates in the model. To evaluate these models, GW models were examined using both simulated and empirical crash datasets, and the results were compared to the most commonly used NB model and the recently developed NB-Lindley models. For model parameter estimation, both the maximum likelihood method and a Bayesian approach were adopted for better comparison. A simulation study was used to show the better performance of this model compared to NB model for overdispersed data, and then an application in the empirical crash data illustrates its capability of modeling data sets with great accuracy and exploring the source of overdispersion. The performances of hotspot identification for these two kinds of models (i.e., GW models and NB models) were also examined and compared based on the estimated models from the empirical dataset. Finally, bias properties related to the choice of prior distributions for parameters in GW model were examined by using a simulation study. In addition, the suggestions on the choice of minimum sample size and priors were presented for different kinds of datasets.